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diff --git a/old/63884-0.txt b/old/63884-0.txt deleted file mode 100644 index 633462e..0000000 --- a/old/63884-0.txt +++ /dev/null @@ -1,22049 +0,0 @@ -The Project Gutenberg EBook of Twentieth Century Standard Puzzle Book, by -Cyril Pearson - -This eBook is for the use of anyone anywhere in the United States and -most other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms -of the Project Gutenberg License included with this eBook or online at -www.gutenberg.org. If you are not located in the United States, you -will have to check the laws of the country where you are located before -using this ebook. - -Title: Twentieth Century Standard Puzzle Book - Three Parts in One Volume - -Author: Cyril Pearson - -Release Date: November 26, 2020 [EBook #63884] - -Language: English - -Character set encoding: UTF-8 - -Produced by: MFR, Branden Aldridge, Harry Lamé and the Online Distributed - Proofreading Team at https://www.pgdp.net - -*** START OF THE PROJECT GUTENBERG EBOOK TWENTIETH CENTURY STANDARD PUZZLE -BOOK *** - - - Transcriber’s Notes - - Text printed in italics has been transcribed _between underscores_, - bold face text =between equal signs=. Blackletter and spaced out text - are represented by ~tildes~ and ^carets^ respectively. Small capitals - have been replaced with ALL CAPITALS. - - Please see the end of the text for more notes regarding this - transcription, corrections made and other remarks. - - - - - GOOD VALUE - GAMAGES - - - Latest Conjuring - By WILL GOLDSTON - _The Latest and Best Book Published_ - -[Illustration] - -=_A Few Principal Items--_= - - CHAPTER I.--Latest tricks with and without apparatus, many published - for the first time. Illustrated. - - CHAPTER II.--Every new and startling illusion accurately explained - with illustrations. - - CHAPTER III.--Latest methods for performing the “Mystic Kettle” that - boils on ice, including the “Magic Kettle,” the most remarkable - utensil to hold liquor. This little kettle can produce almost any - drink from milk to whisky. Illustrated. - - CHAPTER IV.--Correct methods to escape from Handcuffs, Leg-irons, - Rope, Iron Collars, Padlocks, Sacks, Iron Trunks, Wooden Boxes, - Barrels, Iron Cages. Illustrated. - - CHAPTER V.--Hand Shadows and how to work them. Illustrated. - - Without a doubt the greatest and cheapest book ever published on - Magic. - - ORDER IMMEDIATELY TO AVOID DISAPPOINTMENT - - _Handsomely Bound in Cloth_, =2/-= Post Free, =2/3= - - - The Secrets of Magic - BY WILL GOLDSTON - -[Illustration] - - Over 100 pages and as many illustrations. This up-to-date work, - describing only the latest secrets and effects in conjuring, also - contains biographies of leading magicians. - - This book is in its 4th Edition, and is without doubt a very useful - book, as it contains many valuable tricks and illusions never before - divulged. - - Cloth Bound. Price =2/6=. Postage 3d. - - - A. W. GAMAGE, Ltd - HOLBORN - LONDON, E.C. - - - - - THE TWENTIETH CENTURY - =STANDARD PUZZLE - BOOK= - THREE PARTS IN ONE VOLUME - - EDITED BY - A. CYRIL PEARSON, M.A. - AUTHOR OF - ‘_100 Chess Problems_,’ ‘_Anagrams, Ancient and Modern_,’ _etc._ - - _PROFUSELY ILLUSTRATED_ - - SECOND IMPRESSION - - LONDON - GEORGE ROUTLEDGE & SONS, LTD. - NEW YORK: E. P. DUTTON & CO. - - - - -=Also in Three Parts= - - I.--MAGIC SQUARES, PICTURE PUZZLES, ENIGMAS, CHARADES, RIDDLES, - CONUNDRUMS, NUTS TO CRACK, SOLUTIONS. - - II.--OPTICAL ILLUSIONS, FREAKS OF FIGURES, CHESS CAMEOS, SCIENCE AT - PLAY, CURIOUS CALCULATIONS, WORD AND LETTER PUZZLES, SOLUTIONS. - - III.--WORD PUZZLES, MISSING WORDS, LETTER PUZZLES, ANAGRAMS, PICTURE - PUZZLES, PALINDROMES, SOLUTIONS. - -=Also by the same Author= - - PICTURED PUZZLES AND WORD PLAY. Profusely Illustrated. Crown 8vo. - Cloth. - - - - -=PART I.= - - -CONTENTS - - PAGE - - MAGIC SQUARES, PUZZLES, TRICKS, ENIGMAS I-1 - - CHARADES, ETC. I-80 - - RIDDLES AND CONUNDRUMS I-104 - - NUTS TO CRACK I-115 - - SOLUTIONS I-148 - - -MAGIC SQUARES - - -No. I.--FOUR HUNDRED YEARS OLD! - -In Albert Dürer’s day, as in Milton’s, “melancholy” meant -_thoughtfulness_, and on this ground we find on his woodcut, -“Melancholia, or the Genius of the Industrial Science of Mechanics,” a -very early instance of a Magic Square, showing that Puzzles had a -recognised place in mental gymnastics four hundred years ago. - -[Illustration] - - -No. II.--A SIMPLE MAGIC SQUARE - -Much time was devoted in olden days to the construction and elaboration -of Magic Squares. Before we go more deeply into this fascinating -subject, let us study the following pretty and ingenious method of -making a Magic Square of sixteen numbers, which is comparatively simple, -and easily committed to memory:-- - - +--+--+--+--+ - | 1|15|14| 4| - +--+--+--+--+ - |12| 6| 7| 9| - +--+--+--+--+ - | 8|10|11| 5| - +--+--+--+--+ - |13| 3|2 |16| - +--+--+--+--+ - -Start with the small square at the top left-hand corner, placing there -the 1; then count continuously from left to right, square by square, but -only insert those numbers which fall upon the diagonals--namely, 4, 6, -7, 10, 11, 13, and 16. - -Then start afresh at the bottom right-hand corner, calling it 1, and -fill up the remaining squares in order, from right to left, counting -continuously, and so placing in their turn 2, 3, 5, 8, 9, 12, 14, and -15. Each row, column, diagonal, and almost every cluster of four has 34 -as the sum of its numbers. - - -No. III.--ANOTHER MAGIC SQUARE - - +--+--+--+--+--+ - | 1|20|16|23| 5| - +--+--+--+--+--+ - |15| 7|12| 9|22| - +--+--+--+--+--+ - |24|18|13| 8| 2| - +--+--+--+--+--+ - | 4|17|14|19|11| - +--+--+--+--+--+ - |21| 3|10| 6|25| - +--+--+--+--+--+ - -In this Magic Square the rows, columns, and diagonals add up to 65, and -the sum of any two opposite and corresponding squares is 26. - - -ENIGMAS - - -1 - -A MYSTIC ENIGMA - - He stood himself beside himself - And looked into the sea; - Within himself he saw himself, - And at himself gazed he. - Now when himself he saw himself - Within himself go round, - Into himself he threw himself, - And in himself was drowned. - Now if he had not been himself, - But other beast beside, - He would himself have cut himself - Nor in himself have died. - - -No. IV.--A NEST OF CENTURIES - - +--+--+--+--+--+--+--+ - |22|47|16|41|10|35| 4| - +--+--+--+--+--+--+--+ - | 5|23|48|17|42|11|29| - +--+--+--+--+--+--+--+ - |30| 6|24|49|18|36|12| - +--+--+--+--+--+--+--+ - |13|31| 7|25|43|19|37| - +--+--+--+--+--+--+--+ - |38|14|32| 1|26|44|20| - +--+--+--+--+--+--+--+ - |21|39| 8|33| 2|27|45| - +--+--+--+--+--+--+--+ - |46|15|40| 9|34| 3|28| - +--+--+--+--+--+--+--+ - -The numbers in this Magic Square of 49 cells add up in all rows, -columns, and diagonals to 175. The four corner cells of every square or -rectangle that has cell 25 in its centre, and cells 1, 7, 49, 43, add up -to 100. - - -2 - - One morning Chloe, to avoid the heat, - Sat in a corner of a shady seat. - Young Strephon, on the self-same errand bound, - This fairest flower of all the garden found. - Her peerless beauty set his heart aflame, - Three monosyllables expressed his aim. - - At a respectful distance he conversed - About the weather; then became immersed - In other topics, lessening the while - The space between them, heartened by her smile. - The same three simple words, now joined in one, - Expressed their happy state at set of sun. - - -No. V.--THE MAKING OF A MAGIC SQUARE - -An ideal Magic Square can be constructed thus: - -Place 1, 2, 3, 4, 5 in any order in the five top cells, set an asterisk -over the third column, as shown in the diagram; begin the next row with -this figure, and let the rest follow in the original sequence; continue -this method with the other three rows. - -PREPARATORY SQUARE NO. 1. - - * - +--+--+--+--+--+ - | 1| 3| 5| 2| 4| - +--+--+--+--+--+ - | 5| 2| 4| 1| 3| - +--+--+--+--+--+ - | 4| 1| 3| 5| 2| - +--+--+--+--+--+ - | 3| 5| 2| 4| 1| - +--+--+--+--+--+ - | 2| 4| 1| 3| 5| - +--+--+--+--+--+ - -PREPARATORY SQUARE NO. 2. - - * - +--+--+--+--+--+ - | 5|15| 0|10|20| - +--+--+--+--+--+ - |10|20| 5|15| 0| - +--+--+--+--+--+ - |15| 0|10|20| 5| - +--+--+--+--+--+ - |20| 5|15| 0|10| - +--+--+--+--+--+ - | 0|10|20| 5|15| - +--+--+--+--+--+ - -Make a similar square of 25 cells with 0, 5, 10, 15, 20, as is shown in -No. 2, placing the asterisk in this case over the fourth column of -cells, and proceeding as before, in an unchanging sequence. Using these -two preparatory squares, try to form a Magic Square in which the same -number can be counted up in forty-two different ways. - - -No. VI.--ANOTHER WAY TO MAKE A MAGIC SQUARE - -Here is one of many methods by which a Magic Square of the first -twenty-five numbers can readily be made. - - +--+ - | 1| - +--+--+--+ - | 2| | 6| - +==+==+==+==+==+ - ∥ 3|20| 7|24|11∥ - +--+--+--+--+--+--+--+ - | 4∥16| 8|25|12| 4∥16| - +--+--+--+--+--+--+--+--+--+ - | 5| ∥ 9|21|13| 5|17∥ |21| - +--+--+--+--+--+--+--+--+--+ - |10∥22|14| 1|18|10∥22| - +--+--+--+--+--+--+--+ - ∥15| 2|19| 6|23∥ - +==+==+==+==+==+ - |20| |24| - +--+--+--+ - |25| - +--+ - -This is done by first placing the figures from 1 to 25 in diagonal rows, -as is shown above, and then introducing the numbers that are _outside_ -the square _into_ it, by moving each of them five places right, left, -up, or down. A Magic Square is thus formed, the numbers of which add up -to 65 in lines, columns and diagonals, and with the centre and any four -corresponding numbers on the borders. - - -No. VII.--A MONSTER MAGIC SQUARE - -Here is what may indeed be called a Champion Magic Square:-- - - +---+---+---+---+---+---+---+---+---+---+---+ - | 23|464|459|457|109|111|108|110|132|133|130| - +---+---+---+---+---+---+---+---+---+---+---+ - | 25| 41|436|435|433|432|196|195|241|242|200| - +---+---+---+---+---+---+---+---+---+---+---+ - | 27| 45| 13|474|469|467| 82| 81| 72| 90| 91| - +---+---+---+===+===+===+===+===+===+===+===+ - |461| 55| 15∥ 34|450|449|447|446|156|157|180| - +---+---+---+---+---+---+---+---+---+---+---+ - |456| 56| 17∥ 42| 3|484|479|477| 66| 65| 68| - +---+---+---+---+---+===+===+===+===+===+===+ - |137|428|471∥ 41| 5∥127|126|125|361|362|363| - +---+---+---+---+---+---+===+===+===+===+===+ - |153|431|466∥ 31| 7∥347∥148|338|339|145|143| - +---+---+---+---+---+---+---+---+---+---+---+ - |154|439| 98∥453|481∥325∥161|169|168|318|319| - +---+---+---+---+---+---+---+---+---+---+---+ - |384|266|407∥445|476∥292∥293|191|190|299|298| - +---+---+---+---+---+---+---+---+---+---+---+ - |383|268|406∥442|424∥270∥280|272|273|211|210| - +---+---+---+---+---+---+---+---+---+---+---+ - |379|265|392∥172| 60∥248∥227|250|251|230|232| - +---+---+---+---+---+---+---+---+---+---+---+ - |378|267|391∥173| 59∥226∥249|228|229|252|254| - +---+---+---+---+---+---+---+---+---+---+---+ - |351|282|405∥176| 74∥204∥214|206|207|277|276| - +---+---+---+---+---+---+---+---+---+---+---+ - |350|263|390∥177| 73∥182∥192|301|300|189|187| - +---+---+---+---+---+---+---+---+---+---+---+ - |334|199| 77∥330|423∥171∥315|323|322|164|165| - +---+---+---+---+---+---+---+---+---+---+---+ - |333|216| 96∥311|413∥149∥346|147|146|340|341| - +---+---+---+---+---+---+===+===+===+===+===+ - |100|221| 76∥310|414∥369|359|360|124|123|122| - +---+---+---+---+---+===+===+===+===+===+===+ - | 99|223| 75∥291|483| 1| 6| 8|419|420|417| - +---+---+---+---+---+---+---+---+---+---+---+ - |104|202| 97∥452| 35| 36| 38| 39|329|328|305| - +---+---+---+===+===+===+===+===+===+===+===+ - |105|238|473| 11| 16| 18|403|404|393|395|394| - +---+---+---+---+---+---+---+---+---+---+---+ - |136|438| 49| 50| 52| 53|289|290|244|243|285| - +---+---+---+---+---+---+---+---+---+---+---+ - |463| 21| 26| 28|376|374|377|375|353|352|355| - +---+---+---+---+---+---+---+---+---+---+---+ - - +---+---+---+---+---+---+---+---+---+---+---+ - |131|373|371|357|356|372|382|370|335| 30| 22| - +---+---+---+---+---+---+---+---+---+---+---+ - |225|284|287|246|245|288|261| 51| 58| 47|460| - +---+---+---+---+---+---+---+---+---+---+---+ - | 83|401|400|396|398|399|397| 20| 12|440|458| - +===+===+===+===+===+===+===+===+---+---+---+ - |181|326|327|306|307| 44| 37| 33∥470|430| 24| - +---+---+---+---+---+---+---+---+---+---+---+ - | 67|422|421|416|415| 10| 2|443∥468|429| 29| - +===+===+===+===+===+===+---+---+---+---+---+ - |364|365|366|118|117|116∥480|444∥ 14| 57|348| - +===+===+===+===+===+---+---+---+---+---+---+ - |342|142|344|345|139∥138∥478|454∥ 19| 54|332| - +---+---+---+---+---+---+---+---+---+---+---+ - |320|321|163|162|324∥160∥ 4|32 ∥387| 46|331| - +---+---+---+---+---+---+---+---+---+---+---+ - |297|186|185|184|302∥193∥ 9| 40∥ 78|219|101| - +---+---+---+---+---+---+---+---+---+---+---+ - |209|208|278|279|205∥215∥ 61| 43∥ 79|217|102| - +---+---+---+---+---+---+---+---+---+---+---+ - |231|233|256|257|258∥237∥425|313∥ 93|220|106| - +---+---+---+---+---+---+---+---+---+---+---+ - |253|255|234|235|236∥259∥426|312∥ 94|218|107| - +---+---+---+---+---+---+---+---+---+---+---+ - |275|274|212|213|271∥281∥411|309∥ 80|203|134| - +---+---+---+---+---+---+---+---+---+---+---+ - |188|296|295|294|183∥303∥412|308∥ 95|222|135| - +---+---+---+---+---+---+---+---+---+---+---+ - |166|167|317|316|170∥314∥ 62|155∥408|286|151| - +---+---+---+---+---+---+---+---+---+---+---+ - |144|343|141|140|337∥336∥ 72|174∥389|269|152| - +===+===+===+===+===+---+---+---+---+---+---+ - |121|120|119|367|368|358∥ 71|175∥409|264|385| - +===+===+===+===+===+===+---+---+---+---+---+ - |418| 63| 64| 69| 70|475|482|194∥410|262|386| - +---+---+---+---+---+---+---+---+---+---+---+ - |304|159|158|179|178|441|448|451∥388|283|381| - +===+===+===+===+===+===+===+===+---+---+---+ - |402| 84| 85| 89| 87| 86| 88|465|472|247|380| - +---+---+---+---+---+---+---+---+---+---+---+ - |260|201|198|239|240|197|224|434|427|437|349| - +---+---+---+---+---+---+---+---+---+---+---+ - |354|112|114|128|129|113|103|115|150|455|462| - +---+---+---+---+---+---+---+---+---+---+---+ - -Its 484 cells form, as they are numbered, a Magic Square, in which all -rows, columns, and diagonals add up to 5335, and it is no easy matter to -determine in how many other symmetrical ways its key-number can be -found. - -When the cells outside each of the dark border lines are removed, three -other perfect Magic Squares remain. - -Collectors should take particular note of this masterpiece. - - -No. VIII.--A NOVEL MAGIC SQUARE - -A Magic Square of nine cells can be built up by taking any number -divisible by 3, and placing, as a start, its third in the central cell. -Thus:-- - - +--+--+--+ - |28|29|24| - +--+--+--+ - |23|27|31| - +--+--+--+ - |30|25|26| - +--+--+--+ - -Say that 81 is chosen for the key number. Place 27 in the centre; 28, -29, in cells 1, 2; 30 in cell 7; 31 in 6; and then fill up cells 3, 4, -8, and 9 with the numbers necessary to make up 81 in each row, column, -and diagonal. - -Any number above 14 that is divisible by 3 can be dealt with in this -way. - - -3 - - Enriched I am with much that’s fat, - Yet money I possess not; - Enlightening all who come to me, - True wisdom I express not. - I may be wicked, but protest - That sinful none have found me; - Though I destroy myself to be - Of use to those around me. - - -No. IX.--TWIN MAGIC SQUARES - -Among the infinite number of Magic Squares which can be constructed, it -would be difficult to find a more remarkable setting of the numbers 1 to -32 inclusive than this, in which two squares, each of 16 cells, are -perfect twins in characteristics and curious combinations. - - +--+--+--+--++--+--+--+--+ - | 1| 8|29|28||11|14|23|18| - +--+--+--+--++--+--+--+--+ - |30|27| 2| 7||21|20| 9|16| - +--+--+--+--++--+--+--+--+ - | 4| 5|32|25||10|15|22|19| - +--+--+--+--++--+--+--+--+ - |31|26| 3| 6||24|17|12|13| - +--+--+--+--++--+--+--+--+ - -There are at least forty-eight different ways in which 66 is the sum of -four of these numbers. Besides the usual rows, columns, and diagonals, -any square group of four, both corner sets, all opposite pairs on the -outer cells, and each set of corresponding cells next to the corners, -add up exactly to 66. - - -4 - - Of Spanish extraction, my hue - Is as dark as a negro can be; - I am solid, and yet it is true - That in part I am wet as the sea, - My second and first are the same - In all but condition and name; - My second can burst - The abode of my first, - And my whole from the underground came. - - -No. X.--A BORDERED MAGIC SQUARE - -Here is a notable specimen of a Magic Square:-- - - +--+--+--+--+--+--+--+ - | 4| 5| 6|43|39|38|40| - +--+==+==+==+==+==+--+ - |49∥15|16|33|30|31∥ 1| - +--+--+==+==+==+--+--+ - |48∥37∥22|27|26∥13∥ 2| - +--+--+--+==+--+--+--+ - |47∥36∥29∥25∥21∥14∥ 3| - +--+--+--+==+--+--+--+ - | 8∥18∥24|23|28∥32∥42| - +--+--+==+==+==+--+--+ - | 9∥19|34|17|20|35∥41| - +--+==+==+==+==+==+--+ - |10|45|44| 7|11|12|46| - +--+--+--+--+--+--+--+ - -The rows, columns, and diagonals all add up to exactly 175 in the full -square. Strip off the outside cells all around, and a second Magic -Square remains, which adds up in all such ways to 125. - -Strip off another border, as is again indicated by the darker lines, and -a third Magic Square is left, which adds up to 75. - - -5 - -AN OLD ENIGMA - -BY HANNAH MORE - - I’m a strange contradiction: I’m new and I’m old, - I’m sometimes in tatters and sometimes in gold, - Though I never could read, yet letter’d I’m found, - Though blind I enlighten, though free I am bound. - - I’m English, I’m German, I’m French, and I’m Dutch; - Some love me too dearly, some slight me too much. - I often die young, though I sometimes live ages, - And no Queen is attended by so many pages. - - -No. XI.--A LARGER BORDERED MAGIC SQUARE - -Here is another example of what is called a “bordered” Magic Square:-- - - +--+--+--+--+--+--+--+--+--+ - | 5|80|59|73|61| 3|63|12|13| - +--+==+==+==+==+==+==+==+--+ - | 1∥20|55|30|57|28|71|26∥81| - +--+--+==+==+==+==+==+--+--+ - | 4∥14∥31|50|29|60|35∥68∥78| - +--+--+--+==+==+==+--+--+--+ - |76∥58∥46∥38|45|40∥36∥24∥ 6| - +--+--+--+--+--+--+--+--+--+ - | 7∥65∥33∥43|41|39∥49∥17∥75| - +--+--+--+--+--+--+--+--+--+ - |74∥64∥48∥42|37|44∥31∥18∥ 8| - +--+--+--+==+==+==+--+--+--+ - |67∥10∥47|32|53|22|51∥72∥15| - +--+--+==+==+==+==+==+--+--+ - |66∥56|27|52|25|54|11|62∥16| - +--+==+==+==+==+==+==+==+--+ - |69| 2|23| 9|21|79|19|70|77| - +--+--+--+--+--+--+--+--+--+ - -These 81 cells form a complete magic square, in which rows, columns, and -diagonals add up to 369. As each border is removed fresh Magic Squares -are formed, of which the distinctive numbers are 287, 205, and 123. The -central 41 is in every case the greatest common divisor. - - -No. XII.--A CENTURY OF CELLS - -Can you complete this Magic Square, so that the rows, columns, and -diagonals add up in every case to 505? - - +----+----+----+----+----+----+----+----+----+-----+ - |_91_| _2_| _3_|_97_| _6_|_95_|_94_| _8_| _9_|_100_| - +----+----+----+----+----+----+----+----+----+-----+ - |_20_| | | |_16_|_15_| | | | _81_| - +----+----+----+----+----+----+----+----+----+-----+ - |_21_| | | |_25_|_26_| | | | _30_| - +----+----+----+----+----+----+----+----+----+-----+ - |_60_| | | |_66_|_65_| | | | _41_| - +----+----+----+----+----+----+----+----+----+-----+ - |_50_|_49_|_48_|_57_|_55_|_56_|_54_|_43_|_42_| _51_| - +----+----+----+----+----+----+----+----+----+-----+ - |_61_|_59_|_58_|_47_|_45_|_46_|_44_|_53_|_52_| _40_| - +----+----+----+----+----+----+----+----+----+-----+ - |_31_| | | |_35_|_36_| | | | _70_| - +----+----+----+----+----+----+----+----+----+-----+ - |_80_| | | |_75_|_76_| | | | _71_| - +----+----+----+----+----+----+----+----+----+-----+ - |_90_| | | |_86_|_85_| | | | _11_| - +----+----+----+----+----+----+----+----+----+-----+ - | _1_|_99_|_98_| _4_|_96_| _5_| _7_|_93_|_92_| _10_| - +----+----+----+----+----+----+----+----+----+-----+ - -We have given you a substantial start, and, as a further hint, as all -the numbers in the first and last columns end in 0 or 1, so in the two -next columns all end in 2 or 9, in the two next in 3 or 8, in the two -next in 4 or 7, and in the two central columns in 5 or 6. - - -6 - -HALLAM’S UNSOLVED ENIGMA - - I sit on a rock while I’m raising the wind, - But the storm once abated I’m gentle and kind. - I’ve Kings at my feet, who await but my nod - To kneel in the dust on the ground I have trod. - Though seen to the world, I am known to but few, - The Gentile detests me, I’m pork to the Jew. - I never have passed but one night in the dark, - And that was with Noah alone in the ark. - My weight is three pounds, my length is a mile. - And when I’m discovered you’ll say, with a smile, - That my first and my last are the pride of this isle. - - -No. XIII.--A SINGULAR MAGIC SQUARE - -In this Magic Square, not only do the rows, columns, and diagonals add -up to 260, but this same number is produced in three other and quite -unusual ways:-- - - +--+--+--+--+--+--+--+--+ - |18|63| 4|61| 6|59| 8|41| - +--+--+--+--+--+--+--+--+ - |49|32|51|14|53|12|39|10| - +--+--+--+--+--+--+--+--+ - | 2|47|36|45|22|27|24|57| - +--+--+--+--+--+--+--+--+ - |33|16|35|46|21|28|55|26| - +--+--+--+--+--+--+--+--+ - |31|50|29|20|43|38| 9|40| - +--+--+--+--+--+--+--+--+ - |64|17|30|19|44|37|42| 7| - +--+--+--+--+--+--+--+--+ - |15|34|13|52|11|54|25|56| - +--+--+--+--+--+--+--+--+ - |48| 1|62| 3|60| 5|58|23| - +--+--+--+--+--+--+--+--+ - -(1) Each group of 8 numbers, ranged in a circle round the centre; there -are six of these, of which the smallest is 22, 28, 38, 44, 19, 29, 35, -45, and the largest is 8, 10, 56, 58, 1, 15, 49, 63. (2) The sum of the -4 central numbers and 4 corners. (3) The diagonal cross of 4 numbers in -the middle of the board. - - -No. XIV.--SQUARING THE YEAR - -On another page we give an interesting Magic Square of 121 cells based -upon the figures of the year 1892. Here, in much more condensed form, is -one more up to date. - - +---+---+---+ - |637|630|635| - +---+---+---+ - |632|634|636| - +---+---+---+ - |633|638|631| - +---+---+---+ - -The rows, columns, and diagonals of these nine cells add up in all cases -to the figures of the year 1902. - -The central 634 is found by dividing 1902 by its lowest factor greater -than 2, and this is taken as the middle term of nine numbers, which are -thus arranged to form a Magic Square. - - -7 - -RANK TREASON - -BY AN IRISH REBEL, 1798 - - The pomps of Courts and pride of Kings - I prize above all earthly things; - I love my country, but the King - Above all men his praise I sing. - The royal banners are displayed, - And may success the standard aid! - - I fain would banish far from hence - The “Rights of Men” and “Common Sense;” - Confusion to his odious reign, - That Foe to princes, Thomas Payne. - Defeat and ruin seize the cause - Of France, its liberties and laws! - -Where does the treason come in? - - -No. XV.--SQUARING ANOTHER YEAR - -The following square of numbers is interesting in connection with the -year 1906. - - +------+------+------+------+ - |_A_ |_B_ |_C_ |_D_ | - | _476_| _469_| _477_| _484_| - +------+------+------+------+ - |_E_ |_F_ |_G_ |_H_ | - | _483_| _478_| _470_| _475_| - +------+------+------+------+ - |_I_ |_J_ |_K_ |_L_ | - | _471_| _474_| _482_| _479_| - +------+------+------+------+ - |_M_ |_N_ |_O_ |_P_ | - | _480_| _481_| _473_| _472_| - +------+------+------+------+ - - Add the rows --ABCD, EFGH, IJKL, MNOP. - or the squares --ABEF, CDGH, IJMN, KLOP. - or semi-diagonals--AFIN, BEJM, CHKP, DGLO, - AFCH, BEGD, INKP, MJOL. - -and the sum, in every case, is 1906. - - -No. XVI.--MANIFOLD MAGIC SQUARES - -Here is quite a curious nest of clustered Magic Squares, which is worth -preserving:-- - - +--+--+--+--+--+--+--+--+--+--+--+ - | 2|13|24|10|16| 2|13|24|10|16| 2| - +--+--+--+--+--+--+--+--+--+--+--+ - | 9|20| 1|12|23| 9|20| 1|12|23| 9| - +--+--+--+--+--+==+==+==+==+==+--+ - |11|22| 8|19| 5∥11|22| 8|19| 5∥11| - +--+--+--+--+--+--+--+--+--+--+--+ - |18| 4|15|21| 7∥18| 4|15|21| 7∥18| - +--+--+--+--+--+--+--+--+--+--+--+ - |25| 6|17| 3|14∥25| 6|17| 3|14∥25| - +--+--+--+--+--+--+--+--+--+--+--+ - | 2|13|24|10|16∥ 2|13|24|10|16∥ 2| - +--+--+==+==+==+==+==+--+--+--+--+ - | 9|20∥ 1|12|23∥ 9|20∥ 1|12|23∥ 9| - +--+--+--+--+--+==+==+==+==+==+--+ - |11|22∥ 8|19| 5|11|22∥ 8|19| 5|11| - +--+--+--+--+--+--+--+--+--+--+--+ - |18| 4∥15|21| 7|18| 4∥15|21| 7|18| - +--+--+--+--+--+--+--+--+--+--+--+ - |25| 6∥17| 3|14|25| 6∥17| 3|14|25| - +--+--+--+--+--+--+--+--+--+--+--+ - | 2|13∥24|10|16| 2|13∥24|10|16| 2| - +--+--+==+==+==+==+==+--+--+--+--+ - | 9|20| 1|12|23| 9|20| 1|12|23| 9| - +--+--+--+--+--+--+--+--+--+--+--+ - |11|22| 8|19| 5|11|22| 8|19| 5|11| - +--+--+--+--+--+--+--+--+--+--+--+ - -Every square of every possible combination of 25 of these numbers in -their cells, such as the two with darker borders, is a perfect Magic -Square, with rows, columns, and diagonals that add up in all cases to -65. - - -8 - -AN ENIGMA FOR CHRISTMAS HOLIDAYS - - Formed half beneath and half above the earth, - We owe, as twins, to art our second birth. - The smith’s and carpenter’s adopted daughters, - Made upon earth, we travel on the waters. - Swifter we move as tighter we are bound, - Yet never touch the sea, or air, or ground. - We serve the poor for use, the rich for whim, - Sink if it rains, and if it freezes swim. - - -No. XVII.--LARGER AUXILIARY MAGIC SQUARES - -A very interesting method of constructing a Magic Square is shown in -these three diagrams:-- - - +---+---+---+---+---+---+---+---+---+---+---+ - | 1| 2| 3| 4| 5| 6| 7| 8| 9| 10| 11| - +---+---+---+---+---+---+---+---+---+---+---+ - | 3| 4| 5| 6| 7| 8| 9| 10| 11| 1| 2| - +---+---+---+---+---+---+---+---+---+---+---+ - | 5| 6| 7| 8| 9| 10| 11| 1| 2| 3| 4| - +---+---+---+---+---+---+---+---+---+---+---+ - | 7| 8| 9| 10| 11| 1| 2| 3| 4| 5| 6| - +---+---+---+---+---+---+---+---+---+---+---+ - | 9| 10| 11| 1| 2| 3| 4| 5| 6| 7| 8| - +---+---+---+---+---+---+---+---+---+---+---+ - | 11| 1| 2| 3| 4| 5| 6| 7| 8| 9| 10| - +---+---+---+---+---+---+---+---+---+---+---+ - | 2| 3| 4| 5| 6| 7| 8| 9| 10| 11| 1| - +---+---+---+---+---+---+---+---+---+---+---+ - | 4| 5| 6| 7| 8| 9| 10| 11| 1| 2| 3| - +---+---+---+---+---+---+---+---+---+---+---+ - | 6| 7| 8| 9| 10| 11| 1| 2| 3| 4| 5| - +---+---+---+---+---+---+---+---+---+---+---+ - | 8| 9| 10| 11| 1| 2| 3| 4| 5| 6| 7| - +---+---+---+---+---+---+---+---+---+---+---+ - | 10| 11| 1| 2| 3| 4| 5| 6| 7| 8| 9| - +---+---+---+---+---+---+---+---+---+---+---+ - - +---+---+---+---+---+---+---+---+---+---+---+ - | 0| 11| 22| 33| 44| 55| 66| 77| 88| 99|110| - +---+---+---+---+---+---+---+---+---+---+---+ - | 33| 44| 55| 66| 77| 88| 99|110| 0| 11| 22| - +---+---+---+---+---+---+---+---+---+---+---+ - | 66| 77| 88| 99|110| 0| 11| 22| 33| 44| 55| - +---+---+---+---+---+---+---+---+---+---+---+ - | 99|110| 0| 11| 22| 33| 44| 55| 66| 77| 88| - +---+---+---+---+---+---+---+---+---+---+---+ - | 11| 22| 33| 44| 55| 66| 77| 88| 99|110| 0| - +---+---+---+---+---+---+---+---+---+---+---+ - | 44| 55| 66| 77| 88| 99|110| 0| 11| 22| 33| - +---+---+---+---+---+---+---+---+---+---+---+ - | 77| 88| 99|110| 0| 11| 22| 33| 44| 55| 66| - +---+---+---+---+---+---+---+---+---+---+---+ - |110| 0| 11| 22| 33| 44| 55| 66| 77| 88| 99| - +---+---+---+---+---+---+---+---+---+---+---+ - | 22| 33| 44| 55| 66| 77| 88| 99|110| 0| 11| - +---+---+---+---+---+---+---+---+---+---+---+ - | 55| 66| 77| 88| 99|110| 0| 11| 22| 33| 44| - +---+---+---+---+---+---+---+---+---+---+---+ - | 88| 99|110| 0| 11| 22| 33| 44| 55| 66| 77| - +---+---+---+---+---+---+---+---+---+---+---+ - - +---+---+---+---+---+---+---+---+---+---+---+ - | 1| 13| 25| 37| 49| 61| 73| 85| 97|109|121| - +---+---+---+---+---+---+---+---+---+---+---+ - | 36| 48| 60| 72| 84| 96|108|120| 11| 12| 24| - +---+---+---+---+---+---+---+---+---+---+---+ - | 71| 83| 95|107|119| 10| 22| 23| 35| 47| 59| - +---+---+---+---+---+---+---+---+---+---+---+ - |106|118| 9| 21| 33| 34| 46| 58| 70| 82| 94| - +---+---+---+---+---+---+---+---+---+---+---+ - | 20| 32| 44| 45| 57| 69| 81| 93|105|117| 8| - +---+---+---+---+---+---+---+---+---+---+---+ - | 55| 56| 68| 80| 92|104|116| 7| 19| 31| 43| - +---+---+---+---+---+---+---+---+---+---+---+ - | 79| 91|103|115| 6| 18| 30| 42| 54| 66| 67| - +---+---+---+---+---+---+---+---+---+---+---+ - |114| 5| 17| 29| 41| 53| 65| 77| 78| 90|102| - +---+---+---+---+---+---+---+---+---+---+---+ - | 28| 40| 52| 64| 76| 88| 89|101|113| 4| 16| - +---+---+---+---+---+---+---+---+---+---+---+ - | 63| 75| 87| 99|100|112| 3| 15| 27| 39| 51| - +---+---+---+---+---+---+---+---+---+---+---+ - | 98|110|111| 2| 14| 26| 38| 50| 62| 74| 86| - +---+---+---+---+---+---+---+---+---+---+---+ - -It will be noticed that each row after the first, in the two upper -auxiliary squares, begins with a number from the same column in the row -above it, and maintains the same sequence of numbers. When the -corresponding cells of these two squares are added together, and placed -in the third square, a Magic Square is formed, in which 671 is the sum -of all rows, columns, and diagonals. - - -No. XVIII.--SQUARING BY ANNO DOMINI - -Here is a curious form of Magic Square. The year 1892 is taken as its -basis. - - +---+---+---+---+---+---+---+---+---+---+---+ - |112|124|136|148|160|172|184|196|208|220|232| - +---+---+---+---+---+---+---+---+---+---+---+ - |147|159|171|183|195|207|219|231|122|123|135| - +---+---+---+---+---+---+---+---+---+---+---+ - |182|194|206|218|230|121|133|134|146|158|170| - +---+---+---+---+---+---+---+---+---+---+---+ - |217|229|120|132|144|145|157|169|181|193|205| - +---+---+---+---+---+---+---+---+---+---+---+ - |131|143|155|156|168|180|192|204|216|228|119| - +---+---+---+---+---+---+---+---+---+---+---+ - |166|167|179|191|203|215|227|118|130|142|154| - +---+---+---+---+---+---+---+---+---+---+---+ - |190|202|214|226|117|129|141|153|165|177|178| - +---+---+---+---+---+---+---+---+---+---+---+ - |225|116|128|140|152|164|176|188|189|201|213| - +---+---+---+---+---+---+---+---+---+---+---+ - |139|151|163|175|187|199|200|212|224|115|127| - +---+---+---+---+---+---+---+---+---+---+---+ - |174|186|198|210|211|223|114|126|138|150|162| - +---+---+---+---+---+---+---+---+---+---+---+ - |209|221|222|113|125|137|149|161|173|185|197| - +---+---+---+---+---+---+---+---+---+---+---+ - -Within this square 1892 can be counted up in all the usual ways, and -altogether in 44 variations. Thus any two rows that run parallel to a -diagonal, and have between them eleven cells, add up to this number, if -they are on opposite sides of the diagonal. - - -9 - - The sun, the sun is my delight! - I shun a gloomy day, - Though I am often seen at night - To dart across the way. - Sometimes you see me climb a wall - As nimble as a cat, - Then down into a pit I fall - Like any frightened rat. - Catch me who can--woman or man-- - None have succeeded who after me ran. - - -No. XIX.--A MAGIC SQUARE OF SEVEN - - +----+ - | _1_| - +----+----+----+ - | _8_| | _2_| - +----+----+----+----+----+ - |_15_| | _9_| | _3_| - +====+====+====+====+====+====+====+ - ∥_22_|_47_|_16_|_41_|_10_|_35_| _4_∥ - +----+----+----+----+----+----+----+----+----+ - |_29_∥ _5_|_23_|_48_|_17_|_42_|_11_|_29_∥ _5_| - +----+----+----+----+----+----+----+----+----+----+----+ - |_36_| ∥_30_| _6_|_24_|_49_|_18_|_36_|_12_∥ | _6_| - +----+----+----+----+----+----+----+----+----+----+----+----+----+ - |_43_| |_37_∥_13_|_31_| _7_|_25_|_43_|_19_|_37_∥_13_| | _7_| - +----+----+----+----+----+----+----+----+----+----+----|----+----+ - |_44_| ∥_38_|_14_|_32_| _1_|_26_|_44_|_20_∥ |_14_| - +----+----+----+----+----+----+----+----+----+----+----+ - |_45_∥_21_|_39_| _8_|_33_| _2_|_27_|_45_∥_21_| - +----+----+----+----+----+----+----+----+----+ - ∥_46_|_15_|_40_| _9_|_34_| _3_|_28_∥ - +====+====+====+====+====+====+====+ - |_47_| |_41_| |_35_| - +----+----+----+----+----+ - |_48_| |_42_| - +----+----+----+ - |_49_| - +----+ - -This Magic Square of 49 cells is constructed with a diagonal arrangement -of the numbers from 1 to 49 in their proper order. Those that fall -outside the central square are written into it in the seventh cell -inwards from where they stand. It is interesting to find out the many -combinations in which the number 175 is made up. - - -10 - -WHAT MOVED HIM? - - I grasped it, meaning nothing wrong, - And moved to meet my friend, - When lo! the stalwart man and strong - At once began to bend. - The biped by the quadruped - No longer upright stood, - But bowed the knee and bent his head - Before the carved wood. - - -No. XX.--CURIOUS SQUARES - -These are two interesting Magic Squares found on an antique gong, at -Caius College, Cambridge:-- - - +--+--+--+ +--+--+--+ - | 6|13| 8| | 7|14| 9| - +--+--+--+ +--+--+--+ - |11| 9| 7| |12|20| 8| - +--+--+--+ +--+--+--+ - |10| 5|12| |11| 6|13| - +--+--+--+ +--+--+--+ - -In the one nine numbers are so arranged that they count up to 27 in -every direction; and in the other the outer rows total 30, while the -central rows and diagonals make 40. - - -11 - -RINGING THE CHANGES - - My figure, singular and slight, - Measures but half enough at sight. - I rode the waters day and night. - I tell the new in Time’s quick flight, - Or how old ages rolled in might. - Cut off my tail, it still is on! - Put on my head, and there is none! - - -No. XXI.--A MOORISH MAGIC SQUARE - -Among Moorish Mussulmans 78 is a mystic number. - - +--+--+--+--+ - |40|10|20| 8| - +--+--+--+--+ - | 7|21| 9|41| - +--+--+--+--+ - |12|42| 6|18| - +--+--+--+--+ - |19| 5|43|11| - +--+--+--+--+ - -Here is a cleverly-constructed Magic Square, to which this number is the -key. - -The number 78 can be arrived at in twenty-three different -combinations--namely, ten rows, columns, or diagonals; four corner -squares of four cells; one central square of four cells; the four corner -cells; two sets of corresponding diagonal cells next to the corners; and -two sets of central cells on the top and bottom rows, and on the outside -columns. - - -No. XXII.--A CHOICE MAGIC SQUARE - -Here is a Magic Square of singular charm:-- - - +==+==+==+==+==+==+==+==+==+ - |31|36|29∥76|81|74∥13|18|11| - +--+--+--+--+--+--+--+--+--+ - |30|32|34∥75|77|79∥12|14|16| - +--+--+--+--+--+--+--+--+--+ - |35|28|33∥80|73|78∥17|10|15| - +==+==+==+==+==+==+==+==+==+ - |22|27|20∥40|45|38∥58|63|56| - +--+--+--+--+--+--+--+--+--+ - |21|23|25∥39|41|43∥57|59|61| - +--+--+--+--+--+--+--+--+--+ - |26|19|24∥44|37|42∥62|55|60| - +==+==+==+==+==+==+==+==+==+ - |67|72|65∥ 4| 9| 2∥49|54|47| - +--+--+--+--+--+--+--+--+--+ - |66|68|70∥ 3| 5| 7∥48|50|52| - +--+--+--+--+--+--+--+--+--+ - |71|64|69∥ 8| 1| 6∥53|46|51| - +==+==+==+==+==+==+==+==+==+ - -The 81 cells of this remarkable square are divided by parallel lines -into 9 equal parts, each made up of 9 consecutive numbers, and each a -Magic Square in itself within the parent square. Readers can work out -for themselves the combinations in the larger square and in the little -ones. - - -12 - -CANNING’S ENIGMA - - There is a noun of plural number, - Foe to peace and tranquil slumber. - Now almost any noun you take - By adding “s” you plural make. - But if you add an “s” to this - Strange is the metamorphosis. - Plural is plural now no more, - And sweet what bitter was before. - - -XXIII.--THE TWIN PUZZLE SQUARES - - +-+-+-+ +-+-+-+ - |1|2|3| | |2|3| - +-+-+-+ +-+-+-+ - | |5|6+====+4|5| | - +-+-+-+ +-+-+-+ - |7|8| | |7|8|9| - +-+-+-+ +-+-+-+ - -Fill each square by repeating two of its figures in the vacant cells. -Then rearrange them all, so that the sums of the corresponding rows in -each square are equal, and the sums of the squares of the corresponding -cells of these rows are also equal; and so that the sums of the four -diagonals are equal, and the sum of the squares of the cells in -corresponding diagonals are equal. - - -13 - -There is an old-world charm about this Enigma:-- - - In the ears of young and old - I repeat what I am told; - And they hear me, old and young, - Though I have no busy tongue. - When a thunder-clap awakes me - Not a touch of terror takes me; - Yet so tender is my ear - That the softest sound I fear. - Call me not with bated breath, - For a whisper is my death. - - -No: XXIV.--MAGIC FRACTIONS - -Here is an arrangement of fractions which form a perfect Magic Square:-- - - +-------+-------+-------+ - | _³⁄₈_ | _⁵⁄₁₂_| _⁵⁄₂₄_| - +-------+-------+-------+ - | _¹⁄₆_ | _¹⁄₃_ | _¹⁄₂_ | - +-------+-------+-------+ - |_¹¹⁄₂₄_| _¹⁄₄_ | _⁷⁄₂₄_| - +-------+-------+-------+ - -If these fractions are added together in any one of the eight -directions, the result in every case is unity. Thus ³⁄₈ + ¹⁄₃ + ⁷⁄₂₄ = -1, ¹⁄₆ + ¹⁄₃ + ¹⁄₂ = 1, and so on throughout the rows, columns, and -diagonals. - - -14 - -“DOUBLE, DOUBLE, TOIL AND TROUBLE!” - - “By hammer and hand - All arts do stand”-- - So says an ancient saw; - But hammer and hand - Will work or stand - By my unwritten law. - Behold me, as sparks from the anvils fly, - But fires lie down at my bitter cry. - - -No. XXV.--MORE MAGIC FRACTIONS - -We are indebted to a friend for the following elaborate Magic Square of -fractions, on the lines of that on the preceding page. - - +-------+-------+-------+-------+-------+ - |_¹⁹⁄₈₀_| _⁷⁄₂₀_| _¹⁄₄₀_|_¹¹⁄₈₀_| _¹⁄₄_ | - +-------+-------+-------+-------+-------+ - |_¹³⁄₄₀_| _¹⁄₈_ | _⁹⁄₈₀_| _⁹⁄₄₀_|_¹⁷⁄₈₀_| - +-------+-------+-------+-------+-------+ - | _¹⁄₁₀_| _⁷⁄₈₀_| _¹⁄₅_ | _⁵⁄₁₆_| _³⁄₁₀_| - +-------+-------+-------+-------+-------+ - | _³⁄₁₆_| _⁷⁄₄₀_|_²³⁄₈₀_|_¹¹⁄₄₀_| _³⁄₄₀_| - +-------+-------+-------+-------+-------+ - | _³⁄₂₀_|_²¹⁄₈₀_| _³⁄₈_ | _¹⁄₂₀_|_¹³⁄₈₀_| - +-------+-------+-------+-------+-------+ - -The composer claims that there are at least 160 combinations of 5 cells -in which these fractions add up to unity, including, of course, the -usual rows, columns, and diagonals. - - -15 - - Two brothers wisely kept apart, - Together ne’er employed; - Though to one purpose we are bent - Each takes a different side. - - We travel much, yet prisoners are, - And close confined to boot, - Can with the fleetest horse keep pace, - Yet always go on foot. - - -No. XXVI.--A MAGIC OBLONG - -On similar lines to Magic Squares, but as a distinct variety, we give -below a specimen of a Magic Oblong. - - +--+--+--+--+--+--+--+--+ - | 1|10|11|29|28|19|18|16| - +--+--+--+--+--+--+--+--+ - | 9| 2|30|12|20|27| 7|25| - |--+--+--+--+--+--+--+--| - |24|31| 3|21|13| 6|26| 8| - |--+--+--+--+--+--+--+--| - |32|23|22| 4| 5|14|15|17| - +--+--+--+--+--+--+--+--+ - -The four rows of this Oblong add up in each case to 132, and its eight -columns to 66. Two of its diagonals, from 10 to 5 and from 28 to 23, -also total 66, as do the four squares at the right-hand ends of the top -and bottom double rows. - - -16 - - My name declares my date to be - The morning of a Christian year; - And motherless, as all agree, - And yet a mother, too, ’tis clear. - A father, too, which none dispute, - And when my son comes I’m a fruit. - And, not to puzzle overmuch, - ’Twas I took Holland for the Dutch. - - -17 - - My head is ten times ten, - My body is but one. - Add just five hundred more, and then - My history is done. - Although I own no royal throne, - Throughout the sunny South in fame I stand alone. - - -No. XXVII.--A MAGIC CUBE - -Much more complicated than the Magic Square is the Magic Cube. - -First Layer from Top. - - +---+---+---+---+---+ - |121| 27| 83| 14| 70| - +---+---+---+---+---+ - | 10| 61|117| 48| 79| - +---+---+---+---+---+ - | 44|100| 1| 57|113| - +---+---+---+---+---+ - | 53|109| 40| 91| 22| - +---+---+---+---+---+ - | 87| 18| 74|105| 31| - +---+---+---+---+---+ - -Second Layer from Top. - - +---+---+---+---+---+ - | 2 | 58|114| 45| 96| - +---+---+---+---+---+ - | 36| 92| 23| 54|110| - +---+---+---+---+---+ - | 75|101| 32| 88| 19| - +---+---+---+---+---+ - | 84| 15| 66|122| 28| - +---+---+---+---+---+ - |118| 49| 80| 6| 62| - +---+---+---+---+---+ - -Third Layer from Top. - - +---+---+---+---+---+ - | 33| 89| 20| 71|102| - +---+---+---+---+---+ - | 67|123| 29| 85| 11| - +---+---+---+---+---+ - | 76| 7| 63|119| 50| - +---+---+---+---+---+ - |115| 41| 97| 3| 59| - +---+---+---+---+---+ - | 24| 55|106| 37| 93| - +---+---+---+---+---+ - -Fourth Layer from Top. - - +---+---+---+---+---+ - | 64|120| 46| 77| 8| - +---+---+---+---+---+ - | 98| 4| 60|111| 42| - +---+---+---+---+---+ - |107| 38| 94| 25| 51| - +---+---+---+---+---+ - | 16| 72|103| 34| 90| - +---+---+---+---+---+ - | 30| 81| 12| 68|124| - +---+---+---+---+---+ - -Lowest Layer. - - +---+---+---+---+---+ - | 95| 21| 52|108| 39| - +---+---+---+---+---+ - |104| 35| 86| 17| 73| - +---+---+---+---+---+ - | 13| 69|125| 26| 82| - +---+---+---+---+---+ - | 47| 78| 9| 65|116| - +---+---+---+---+---+ - | 56|112| 43| 99| 5| - +---+---+---+---+---+ - -Those who enjoy such feats with figures will find it interesting to work -out the many ways in which, when the layers are placed one upon another, -and form a cube, the number 315 is obtained by adding together the -cell-numbers that lie in lines in the length, breadth, and thickness of -the cube. - - -18 - - Sad offspring of a blighted race, - Pale Sorrow was my mother; - I’ve never seen the smiling face - Of sister or of brother. - - Of all the saddest things on earth, - There’s none more sad than I, - No heart rejoices at my birth. - And with a breath I die! - - -No. XXVIII.--A MAGIC CIRCLE - -The Magic Circle below has this particular property:-- - - 32 - 61 94 - 52 38 - 191 4 - + - 28 193 - 26 44 - 98 67 - 16 - -The 14 numbers ranged in smaller circles within its circumference are -such that the sum of the squares of any adjacent two of them is equal to -the sum of the squares of the pair diametrically opposite. - - -19 - - Add a hundred and nothing to ten, - And the same to a hundred times more, - Catch a bee, send it after them, then - Make an end of a fop and a bore. - - -No. XXIX.--MAGIC CIRCLE OF CIRCLES - -We have had some good specimens of Magic Squares. Here is a very curious -and most interesting Magic Circle, in which particular numbers, from 12 -to 75 inclusive, are arranged in 8 concentric circular spaces and in 8 -radiating lines, with the central 12 common to them all. - - 57 24 15 14 - 31 71 64 72 - 48 17 22 23 - 38 69 66 65 - 50 19 20 21 - 36 60 75 67 - 59 26 13 12 - 29 12 12 74 - 12 12 - + - 12 12 - 42 12 12 61 - 44 45 58 27 - 35 43 28 68 - 53 52 51 18 - 33 34 37 70 - 55 54 49 16 - 40 32 39 63 - 46 47 56 25 - 41 30 - -The sum of all the numbers in any of the concentric circular spaces, -with the 12, is 360, which is the number of degrees in a circle. - -The sum of the numbers in each radiating line with the 12, is also 360. - -The sum of the numbers in the upper or lower half of any of the circular -spaces, with half of 12, is 180, the degrees of a semi-circle. - -The sum of any outer or inner four of the numbers on the radiating -lines, with the half of 12, is also 180. - - -No. XXX.--THE UNIQUE TRIANGLE - -In the following triangle, if two couples of the figures on opposite -sides are transposed, the sums of the sides become equal, and also the -sums of the squares of the numbers that lie along the sides. Which are -the figures that must be transposed? - - /\ - / \ - / 5 \ - / \ - / 4 6 \ - / \ - / 3 7 \ - / \ - / 2 1 9 0 \ - ------------------ - - -20 - - They did not climb in hope of gain, - But at stern duty’s call; - They were united in their aim, - Divided in their fall. - - -21 - - Forsaken in some desert vast, - Where never human being dwelt, - Or on some lonely island cast, - Unseen, unheard, I still am felt. - - Brimful of talent, sense, and wit, - I cannot speak or understand; - I’m out of sight in Church, and yet - Grace many temples in the land. - - -No. XXXI.--MAGIC TRIANGLES - -Here is a nest of concentric triangles. Can you arrange the first 18 -numbers at their angles, and at the centres of their sides, so that they -count 19, 38, or 57 in many ways, down, across, or along some angles? - -[Illustration] - -This curiosity is found in an old document of the Mathematical Society -of Spitalfields, dated 1717. - - -22 - - Allow me, pray, to go as first, - And then as number two; - Then after these, why, there you are, - To follow as is due. - - But lest you never guess this queer - And hyperbolic fable, - Pray let there follow after that - Whatever may be able. - - -No. XXXII.--TWIN TRIANGLES - -The numbers outside these twin triangles give the sum of the squares of -the four figures of the adjacent sides:-- - - /\ - / \ - / 7 \ - / \ - 135 / 2 3 \ 99 - / . . \ - / 9 . . 5 \ - / . . \ - / 1 8 6 4 \ - ------------------ - . 117 . - . . - . . - . . - .. - . . - . . - . . - . 137 . - ------------------ - \ 6 4 2 9 / - \ . . / - \ 5 . . 1 / - \ . . / - 119 \ 7 8 / 155 - \ / - \ 3 / - \ / - \/ - -The twins are also closely allied on these points:-- - -18 is the common difference of 99, 117, 135, and of 119, 137, 155. - -19 is the sum of each side of the upper triangle. - -20 is the common difference of any two sums of squares symmetrically -placed, both being on a line through the central spot. - -21 is the sum of each side of the lower triangle. - -10 is the sum of any two figures in the two triangles that correspond. - -254 is the sum of 135, 119, of 117, 137, and of 90, 155. - -By transposing in each triangle the figures joined by dotted lines, the -nine digits run in natural sequence. - - -No. XXXIII.--A MAGIC HEXAGON - -We have dealt with Magic Squares, Circles, and Triangles. Here is a -Magic Hexagon, or a nest of Hexagons, in which the numbers from 1 to 73 -are arranged about the common centre 37. - - 1 5 6 70 60 59 58 - - 63 8 - - 62 19 53 46 22 45 9 - - 61 20 24 64 - - 2 48 31 42 38 49 57 - - 3 47 39 40 44 56 - - 67 51 41 37 33 23 7 - - 66 50 34 35 54 11 - - 65 25 36 32 43 26 12 - - 10 30 27 13 - - 17 29 21 28 52 55 72 - - 18 71 - - 16 69 68 4 14 15 73 - -Each of these Hexagons always gives the same sum, when counted along the -six sides, or along the six diameters which join its corners, or along -the six which are at right angles to its sides. These sums are 259, 185, -and 111. - - -23 - - When I am in, its four legs have no motion; - When I am out, as fish it swims the ocean. - Then, if transposed, it strides across a stream, - Or adds its quality to eyes that gleam. - - -No. XXXIV.--MAGIC HEXAGON IN A CIRCLE - -Inscribe six equilateral triangles in a circle, as shown in this -diagram, so as to form a regular hexagon. - -[Illustration] - -Now place the nine digits round the sides of each of the triangles, so -that their sum on each side may be 20, and so that, while there are no -two triangles exactly alike in arrangement, the squares of the sums on -the other sides may be alternately equal. - - -24 - -A PERSONAL ENIGMA - - We can but see his sad reverse, - And while we say alas! - We hail his work so keen and terse, - With just a touch of gas. - - -No. XXXV.--A MAGIC CROSS - -There are 33 different combinations of four of the numbers in the cells -of this magic cross which total up in each case to 26. - - +----+----+ - | _1_|_12_| - +----+----+----+----+ - | _9_| _8_| _5_| _4_| - +----+----+----+----+ - | _2_| _7_| _6_|_11_| - +----+----+----+----+ - |_10_| _3_| - +----+----+ - -Those who care to work them out on separate crosses will find that there -is a very regular correspondence in the positions which the numbers -occupy. - - -25 - - What boy can live on with a prospect of age, - If you cut off his head at an early stage? - - -26 - -BY LORD MACAULAY - - Here’s plenty of water, you’ll all of you say; - And minus the _h_ a thing used every day; - And here is nice beverage; put them together-- - What is it with claws, but with never a feather? - - -No. XXXVI.--A CHARMING PUZZLE - -Here is quite a charming little puzzle, which is by no means easy of -accomplishment:-- - - ✦ ✦ ✦ - - ✦ ✦ ✦ - - ✦ ✦ ✦ - -Start from one of these nine dots, and without taking the pen from the -paper draw four straight lines which pass through them all. Each line, -after the first, must start where the preceding one ends. - - -27 - -A BROKEN TALE - - The deil jumped - the clouds so high - That he bounded almost - right - the sky. - the trees - gates and fields and - He dodged with his tail - dragging - all these, - But, alas! made a terrible - bl, - For a twist in his tail - a rail, - hooked - And broke that appendage - as. - - -No. XXXVII.--LEAP-FROG - -Place on a chess or draught-board three white men on the squares marked -_a_, and three black men on the squares marked _b_. - - +---+---+---+---+---+---+---+ - |_a_|_a_|_a_| |_b_|_b_|_b_| - +---+---+---+---+---+---+---+ - -The pieces marked _a_ can only move one square at a time, from left to -right, and those marked _b_ one square at a time, from right to left, on -to unoccupied squares; and any piece can leap over one of the other -colour, on to an unoccupied square. What is the least number of moves in -which the positions of the white and the black men can be reversed, so -that each square now occupied by a white is occupied by a black, and -each now occupied by a black holds a white piece? - - -28 - - To a word of assent join the first half of fright, - Then add what will never be seen in the night. - By such a conjunction we quickly attain - What most men have seen, but can’t see again. - - -29 - - My first is stately, proud, and grave, - My next will guard your treasure; - My whole, a slow but sturdy slave, - Will wait upon your pleasure. - - -No. XXXVIII.--SORTING THE COUNTERS - -In the upper row of this diagram four white and four black counters are -placed alternately. - - 1 2 3 4 5 6 7 8 9 10 - +---+---+---+---+---+---+---+---+---+---+ - | ○ | ● | ○ | ● | ○ | ● | ○ | ● | | | - +---+---+---+---+---+---+---+---+---+---+ - - 1 2 3 4 5 6 7 8 9 10 - +---+---+---+---+---+---+---+---+---+---+ - | | | ● | ● | ● | ● | ○ | ○ | ○ | ○ | - +---+---+---+---+---+---+---+---+---+---+ - -It is possible, by moving these counters two at a time, to arrange them -in four moves as they stand on the lower row. Can you do this? -Draughtsmen are handy for solving this puzzle, on a paper ruled as -above. - - -30 - - I am a word of letters six, - First link me with your mind; - Then shuffle me, and lo! I mix - With grief of noisy kind. - Shake me again, and you may fix - A cloak that hangs behind. - - -31 - - We are of use to every man - In walking, riding, rambling; - We join the gambols of the knave, - And play the knave in gambling! - - -No. XXXIX.--A TRANSFORMATION - -Take five wooden matches, and bend each of them into a V. Place them -together, as is shown in the diagram, so that they take the form of an -asterisk, or a ten-pointed star. - -[Illustration] - -Lay them on some smooth surface, and without touching them transform -them into a star with five points. - - -32 - - Strange that a straggling tiresome weed - Will change its meaning quite, - And turn into a sign of grief - If we transpose it right; - And, stranger still, transposed again - Will tell of ease from grief or pain. - - -33 - - Find me two English verbs that ever - In a united state will blend, - Let one say “join,” the other “sever,” - While I divide them to the end. - - -No. XL.--DOMINO BUILDING - -It is possible, with plenty of patience, to build up a whole set of -dominoes, so that they are safely supported on only two stones set up on -end. - -[Illustration] - -This, which might well seem impossible, is done by placing, as a -foundation, dominoes in the positions indicated by dotted lines. The -arch is then carefully constructed, as shown in the diagram, and for the -finish the four stones between the two foundation arches are drawn out, -and placed in pairs on end above, and finally, with the utmost care, the -other four are drawn away, and built in on the top. Thus the stones -indicated by the dotted lines at the base take their place within the -dotted lines above. - - -No. XLI.--FAST AND LOOSE - -This diagram represents a shallow box, on the bottom of which twelve -counters or draughtsmen are lying loose. - -[Illustration] - -How can they be readjusted so that they will wedge themselves together, -and against the side of the box, and it can be turned upside down -without displacing them? - - -34 - - Taken entire - I’m full of fire. - With head away - A tax I pay. - If tail you bar - I turn from tar. - Headless again, - With tail restored. - Goddess of pain, - I sow discord. - - -No. XLII.--MAZY PROGRESS. - -The diagram below is an exact reproduction of an old-fashioned maze, cut -in the ground near Nottingham. It is eighteen yards square, and the -black line represents the pathway, which is 535 feet in length. - -[Illustration] - -The point of this convoluted path is not so much to puzzle people, as to -show how much ground may be covered without diverging far from a centre, -or going over the same ground twice. As we advance along the line there -are no obstructions, and we find ourselves, after passing over the whole -of it, on the spot whence we set out. - - -35 - - Thrice three pins in shining line - Mary meant to fix; - Why did Mary turn the nine - Into thirty-six? - - -No. XLIII.--FOR CLEVER PENCILS - -Start at _A_, and trace these figures with one continuous line, -finishing at _B_. - -[Illustration] - -You must not take your pencil from the paper, or go over any line twice. - - -36 - - A ring and a wing and three-fourths of a fog, - Will bring to your view a most obstinate dog. - - -37 - - Add fifty-seven to two-thirds of one, - Then take a fiddle, - And it will help to show you what is done, - To make this riddle. - - -38 - - I am a fish so neat and clever, - In pools and crystal streams I play, - To find me out my name you sever - As near the middle as you may. - - -No. XLIV.--TEST AND TRY - -Those who have not seen it will find some real fun in the following -little experiment. Fix three matches as shown in the diagram, light the -cross match in the middle, and watch to see which of the ends will first -catch fire, or what will happen. - -[Illustration] - - -39 - - I stand stock still, let who will hurry, - You cannot put me in a flurry, - Nor stir my stumps, for all your worry. - - I am in haste, let none delay me - As fleetest couriers convey me. - You must transpose me ere you stay me. - - -40 - - Two to one, in case we hide, - You will find us in our site; - We are harmless side by side, - Parted we prepare to bite. - When united we divide, - When divided we unite. - - -No. XLV.--A CURIOUS PHENOMENON - -Equal volumes of alcohol and water, when mixed, occupy less space than -when separate, to the extent indicated in this picture: - -[Illustration] - -If the sum of the volume of the two separate liquids is 100, the volume -of the mixture will be only 94. It is thought that the molecules of the -two liquids accommodate themselves to each other, so as to reduce the -pores and diminish the volume of the mixture. - - -41 - - Cut off my head, I’m every inch a king, - A warrior formed to deal a heavy blow; - Halve what remains, my second is a thing - Which nothing but my third can e’er make go. - My whole will vary as you take your line, - This less than human, that way all divine. - - -42 - - One half of me in solid earth you find, - The other half in ocean’s ample bed: - When in my whole we see these parts combined, - The earth remains, but all the sea is fled. - - -No. XLVI.--A HOME-MADE MICROSCOPE - -The simplest and cheapest of all microscopes can easily be made at home. -The only materials needed are a thin slip of glass, on to which one or -two short paper tubes, coated with black sealing wax, are cemented with -the wax, a small stick, and a tumbler half full of water. - -[Illustration] - -Water is dropped gradually by aid of the stick into the cells, until -lenses are formed of the desired convexity, and objects held below the -glass will be more or less magnified. - - -43 - - Not ever changed unless unchanged, - Nor hanged unless beheaded; - Quick eyes may find in me arranged - Almost an angel bedded. - - -No. XLVII.--A PRETTY EXPERIMENT - -For this curious experiment a glass bottle or decanter about half full -of water and a sound stalk of straw are needed. - -[Illustration] - -Bend the straw without breaking it, and put it, as is shown, into the -bottle, which can then be lifted steadily and safely by the straw, if it -is a sound one. - - -44 - - “WHAT THE DICKENS IS HIS NAME?” - _Merry Wives of Windsor._ - -A Russian nobleman had three sons. Rab, the eldest, became a lawyer, his -brother Mary was a soldier, and the youngest was sent to sea. What was -his name? - - -No. XLVIII.--A BOTTLED BUTTON - -The button in a clear glass bottle, as is shown below, hangs attached by -a thread to the cork, which is securely sealed at the top. - -[Illustration] - -How can you sever the thread so that the button falls to the bottom -without uncorking or breaking the bottle? - - -45 - -A NEW “LIGHT BRIGADE” - - Six before six before - Five times a hundred; - This must be brilliant, or - Solvers have blundered. - - -No. XLIX.--CLEARING THE WAY - -Here is a pretty trick which requires an empty bottle, a lucifer match, -and a small coin. - -[Illustration] - -Break the wooden match almost in half, and place it and the coin in the -position shown above. Now consider how you can cause the coin to drop -into the bottle, if no one touches it, or the match, or the bottle. - - -46 - - Scorned by the meek and humble mind, - And often by the vain possessed, - Heard by the deaf, seen by the blind, - I give the troubled spirit rest. - - -47 - - To fifty for my half append - Two-thirds of one; - The other third my whole will end - When you have done. - - -No. L.--IS WATER POROUS? - -Our belief that two portions of matter cannot occupy the same space at -the same time is almost shaken by the following experiment: - -[Illustration] - -If we introduce slowly some fine powdered sugar into a tumblerful of -warm water a considerable quantity may be dissolved in the water without -increasing its bulk. - -It is thought that the atoms of the water are so disposed as to receive -the sugar between them, as a scuttle filled with coal might accommodate -a quantity of sand. - - -48 - -A DOUBLE SHUFFLE - - See, the letters that I bring - Change their meaning quite; - Spell a hard and heavy thing, - Spell a soft and light. - - -No. LI.--A TEST OF GRAVITY - -Set a stool, as is shown in the diagram below, about nine or ten inches -from the wall. - -[Illustration] - -Clasp it firmly by its two side edges, plant your feet well away from -it, and rest your head against the wall. Now lift the stool, and then -try, without moving your feet, to recover an upright position. - -It will be as impossible as it is to stand on one leg while the foot of -that leg rests sideways against a wall or door. - - -No. LII.--BILLIARD MAGIC - -Place a set of billiard balls as is shown in the diagram, the spot ball -overhanging a corner pocket, and the red and the plain white in a -straight line with it, leaving an eighth of an inch between the balls. - -[Illustration] - -How can you pot the spot white with the plain white, using a cue, and -without touching, or in any way disturbing, the red ball? There is not -room to pass on either side between the red ball and the cushion. - - -No. LIII.--THE NIMBLE COIN - -Prepare a circular band of stiff paper, as is shown in the diagram, and -balance it, with a coin on the top, on the lip of a bottle. - -[Illustration] - -How can you most effectively transfer the coin into the bottle? - - -49 - -AN ENIGMA BY MUTATION - - Search high or low, you’d find me where you list; - For not a place without me can exist. - I lose my head, and, seen with shoulders fair, - Become the very fairest of the fair. - Again I lose it, and, like some staunch hound, - The first and best amongst a pack am found. - And if at first both head and tail I lose - I am a portion such as all would choose. - - -No. LIV.--HIT IT HARD! - -Place a strip of thin board, or a long wide flat ruler, on the edge of a -table, so that it just balances itself, and spread over it an ordinary -newspaper, as is shown in the illustration. - -[Illustration] - -You may now hit it quite hard with your doubled fist, or with a stick, -and the newspaper will hold it down, and remain as firmly in its place -as if it were glued to the table over it. You are more likely to break -the stick with which you strike than to displace the strip of wood or -the paper. Try the experiment. - - -50 - -AN ENIGMA BY SWIFT - - We are little airy creatures - All of different voice and features. - One of us in glass is set, - One of us is found in jet. - Another you may see in tin, - And the fourth a box within. - If the others you pursue - They can never fly from you. - - -No. LV.--THE BRIDGE OF KNIVES - -Here is an after-dinner balancing trick, which it is well to practise -with something less brittle than the best glass:-- - -[Illustration] - -It will be seen that the blades of the knives are so cunningly -interlaced as to form quite a firm support. - - -51 - -A MEDLEY - - Twice six is six, and so - Six is but three; - Three is just five you know, - What can we be? - Would you count more of us, - Nine are but four of us, - Ten are but three. - - -No. LVI.--DIFFERENT DENSITIES - -Here is a pretty little experiment, which shows the effect of liquids of -different densities. - -[Illustration] - -Drop an egg into a glass vessel half full of water, it sinks to the -bottom. Drop it into strong brine, it floats. Introduce the brine -through a long funnel at the bottom of the pure water, and the water and -the egg will be lifted, so that the egg floats between the water and the -brine in equilibrium. The egg is denser than the water, and the brine is -denser than the egg. - - -52 - -THE MISSING LINK - - A friend to all the human race - From emperor to peasant, - None is more missed when out of place, - More opportune when present. - - Obedient to the general will - I yield to due control; - And yet the public twist me, till - They put me in a hole! - - -No. LVII.--COLUMBUS OUTDONE - -Here is a very simple and effective little trick. Offer to balance an -egg on its end on the lip of a glass bottle. - -[Illustration] - -The picture shows how it is done, with the aid of a cork and a couple of -silver forks. - - (From “La Science Amusante”). - - -53 - - Two words of equal length we here indite, - Which hold a famous father and his mate. - Embracing five, with fifty left and right, - The mother, looking both ways, keeps things straight. - - Her husband, following a thousand quite, - With them has changed his sex, a funny fate, - And if this lady lose her head, she might, - Being a man, oppose the water-rate. - - -No. LVIII.--WHAT WILL HAPPEN? - -The boy in this picture is blowing hard against the bottle, which is -between his mouth and the candle flame. - -[Illustration] - -What will happen? - - -54 - - In marble walls as white as milk, - Lined with a skin as soft as silk, - Within a fountain crystal clear - A golden apple doth appear. - No doors are there to this stronghold, - Yet thieves break in, and steal the gold. - - -No. LIX.--THE FLOATING NEEDLE - -Here is a simple way to make a needle float on water:-- - -[Illustration] - -Fill a wineglass or tumbler with water, and on this lay quite flat a -cigarette paper; place a needle gently on this, and presently the paper -will sink, and the needle will float on the water. - - -55 - - A one-syllable adjective I, - Indeterminate, misty, obscure: - Reduce me by five, and then try - How you like my attacks to endure. - - I’m now a two-syllable noun, - My victims are hot and are cold; - In country more rife than in town, - I’m not such a pest as of old. - - -No. LX.--VIS INERTIÆ - -Here is a pile of ten draughtsmen--one black among nine white. - -[Illustration] - -If I take another draughtsman, and with a strong pull of my finger send -it spinning against the column, what will happen? - - -56 - -DR. WHEWELL’S ENIGMA - - A headless man had a letter to write, - He who read it had lost his sight. - The dumb repeated it word for word, - And deaf was the man who listened and heard. - - -57 - -AN ENIGMA FOR MOTORISTS - - I am rough, I am smooth, - I am wet, I am dry; - My station is low, - My title is high. - The King my lawful master is, - I’m used by all, though only his. - - -No. LXI.--CUT AND COME AGAIN - -How long would it take to divide completely a 2 ft. block of ice by -means of a piece of wire on which a weight of 5 lb. hangs? - -[Illustration] - - -58 - - Without a dome, we are within a dome; - Homeless and roofless, we have roof and home. - Though frequent streams may flood our base and roof, - We rest unharmed, and always waterproof. - - -59 - - I’m the most fearful of fates upon earth, - Cut off my head and bright moments have birth, - Lop off my shoulders, and riddle my riddle; - Anything seems to be found in my middle. - - -No. LXII.--WHERE WILL IT BREAK? - -When weak cords of equal strength are attached to opposite parts of a -wooden or metal ball which is suspended by one of them, a sharp, sudden -pull will snap the lower cord before the movement has time to affect the -ball; but a gentle, steady pull will cause the upper cord to snap, as it -supports the weight below it. - -[Illustration] - - -60 - - I may be safe when honest ways prevail, - With no unworthy tricks or jobbery. - Cut off my head and fix it to my tail, - And I become at once rank robbery. - - -No. LXIII.--CATCHING THE DICE - -Hold a pair of dice, and a cup for casting them, in one hand as is shown -in the diagram. - -[Illustration] - -Now, holding the cup fast, throw up one of the dice and catch it in the -cup. How can you best be sure of catching the other also in the cup? - - -61 - -Here is a metrical Enigma, which appeals with particular force to all -married folk, and to our cousins in America: - - This is of fellowship the token, - Reverse it, and the bond is broken. - - -No. LXIV.--WILL THEY FALL? - -Build up seven dominoes into a double arch, as is shown in the diagram -below, and place a single domino in the position indicated. - -[Illustration] - -Now put the fore-finger carefully through the lower archway, and give -this domino quite a smart tip up by pressing on its corner. What will -happen if this is done cleverly? Try it. - - -62 - - A monk in a moment, by violence heated, - Endangered the peace of his soul. - To atone for my second, my first he repeated - Just ten times a day on my whole. - - -No. LXV.--A TRANSPOSITION - -Place three pennies in contact in a line as is shown below, so that a -“head” is between two “tails.” - -[Illustration] - -Can you introduce the coin with a shaded surface between the other two -in a straight line, without touching one of these two, and without -moving the other? - - -63 - - Two syllables this word contains: - Reverse them and then what remains? - - * * * * * - - With cap and pipe and goggles too - The comics hold him up to view, - Reverse his parts you would declare - A dog should not be quartered there. - - -64 - - Though I myself shut up may be, - My work is to set prisoners free. - No slave his lord’s commands obeys - With more insinuating ways. - All find me handy, sharp, and bright, - Where men in wit and wine delight; - While many keep me for their ease, - And turn and twist me as they please. - - -No. LXVI.--COIN COUNTING - -Place ten coins in a circle, as is shown in this diagram, so that on all -of them the king’s head is uppermost. - - ==== - = = - = 1 = - ==== = = ==== - = = ==== = = - = 10 = = 2 = - = = = = - ==== ==== ==== ==== - = = = = - = 9 = = 3 = - = = = = - ==== ==== - - ==== ==== - = = = = - = 8 = = 4 = - = = = = - ==== ==== ==== ==== - = = = = - = 7 = = 5 = - = = ==== = = - ==== = = ==== - = 6 = - = = - ==== - -Now start from any coin you choose, calling it 1, the next 2, and so on, -and turn the _fourth_, so that the tail is uppermost. Start again on any -king’s head, and again turn the fourth, and continue to do this until -all but one are turned. - -Coins already turned are reckoned in the counting, but the count of -“four” must fall on an unturned coin. - -Can you find a plan for turning all the coins but one in this way -without ever failing to count four upon a fresh spot, and to start on an -unturned coin? - - -No. LXVII.--THE BALANCED CORK - -The diagram below shows how, using one hand only, and grasping a bottle -of wine by its body, the contents can be poured out without cutting or -boring the cork, or altogether removing it from the bottle. - -[Illustration] - - -65 - - Transformed by art, and fond of port, - I blister in the sun; - But when I turn, and face the sport, - Away full tilt I run; - For if I double I am caught, - And that can be no fun. - - -66 - - A man without eyes saw plums on a tree, - He neither took plums nor plums left he. - - -No. LXVIII.--NUTS TO CRACK - -A sharply-pointed knife with a heavy handle is stuck very lightly into -the lintel of a door, and the nut that is to be cracked is placed under -it, so that when the knife is released by a touch the nut is cracked. - -[Illustration] - -What simple and certain plan can you suggest for making sure that the -knife shall hit the nut exactly in the middle without fail? - - -67 - -A SINGULAR ENIGMA - - Strange paradox! though my two halves are gone, - I still remain an undivided whole. - But were I double what I am, though one, - I then should be but half, upon my soul! - - -No. LXIX.--THE FLOATING CORKS - -If we throw an ordinary wine cork into a tub of water it will naturally -float on its side. It is, however, possible to arrange a group of seven -such corks, without fastening them in any way, so that they will float -in upright positions. - -[Illustration] - -Place them together, as is shown in the illustration, and, holding them -firmly, dip them under the water till they are well wetted. Then, -keeping them exactly upright, leave go quietly, and they will float in a -compact bunch if they are brought slowly to the surface. - - -68 - -A PARADOX - - I start with five thousand, and take nothing off, - Yet really in doing so nine-tenths I doff; - And it proves with no strain upon numbers or reason, - That the smaller are larger in size and in season. - - -No. LXX.--A LIGHT, STEADY HAND - -As an exercise of patience and dexterity, try to balance a set of -dominoes upon one that stands upon its narrow end:-- - -[Illustration] - -This is no easy matter, but a little patience will enable us to arrange -the stones in layers, which can with care be lifted into place and -balanced there. - - -69 - - With letters three indite my name, - Add one to show what I became, - Or try to tell what brought me fame. - - -No. LXXI.--WHAT IS THIS? - -We expect to puzzle our readers completely by this diagram:-- - -[Illustration] - -It is simply the enlargement by photography of part of a familiar -picture. - - -70 - - Eight letters respond to the quest - Of all for enjoyment athirst; - Two articles lead to the rest, - And the last of the rest is the first. - - -71 - - When letters five compose my name - I’m seldom seen but in a flame. - Take off one letter, then you see - That winter is the time for me. - Another take, and I appear - What many must be year by year. - - -No. LXXII.--TAKING THE GROUND FROM UNDER IT - -Place a strip of smooth paper on a table so that it overhangs the side, -as is shown in the diagram. Stand a new penny steadily on edge upon the -paper. - -[Illustration] - -Take hold of the paper firmly, and give it a smart, steady pull. If this -is properly done it will leave the penny standing unmoved in its place. - - -72 - - A shining wit pronounced of late - That water in a freezing state - Is like an acting magistrate. - What was the quibble in his pate? - - -73 - - By something formed I nothing am, - Yet anything that you can name. - In all things false, yet ever true, - And still the same but never new; - Like thought I’m in a moment gone, - Nor can I ever be alone. - - -No. LXXIII.--A READY RECKONER - -Two men, standing on the bank of a broad stream, across which they could -not cast their fishing lines, could not agree as to its width. A bet on -the point was offered and accepted, and the question was presently -decided for them by an ingenious friend who came along, without any -particular appliances for measurement. - -He stood on the edge of the bank, steadied his chin with one hand, and -with the other tilted his cap till its peak just cut the top of the -opposite bank. - -[Illustration] - -Then, turning round, he stood exactly where the peak cut the level -ground behind him, and, by stepping to that spot, was able to measure a -distance equal to the width of the stream. - - -74 - - When you and I together meet, - Then there are six to see and greet. - If I and you should meet once more, - Our company would be but four. - And when you leave me all alone - I am a solitary one. - - -No. LXXIV.--THE CLIMBING HOOP - -Paste or pin together the ends of a long strip of stiff paper so as to -form a hoop, and place on the table a board resting at one end upon a -book. Challenge those in your company to make the hoop run up the board -without any impulse. - -[Illustration] - -They must of course fail, but you can succeed by secretly fastening with -beeswax a small stone or piece of metal inside the hoop, as is indicated -in the diagram. - - -75 - - Invisible yet never out of sight, - I am indeed a centre of delight. - In quiet times I help to make things right, - Yet act as second in the fiercest fight. - - -No. LXXV.--THE SEAL OF MAHOMET - -[Illustration] - -This double crescent, called the Seal of Mahomet, from a legend that the -prophet was wont to describe it on the ground with one stroke of his -scimitar, is to be made by one continuous stroke of pen or pencil, -without going twice over any part of it. - - -76 - - Though I mingle with thieves, - And with all that deceives, - And never keep clear of depravity - Though possessed by a devil, - Or seen in a revel, - I do keep my centre of gravity. - - -77 - - There’s not a bird that cleaves the sky - With crest or plume more gay than I, - Yet guess me by this token: - That I am never seen to fly - Unless my wings are broken. - - -No. LXXVI.--MOVE THE MATCHES - -Arrange 15 matches thus-- - - --------| --------| -------| - | | | | | |\ | - | | | |-------| | \ | - | | | | | | \ | - |-------- |-------- |------- - -Remove 6 and what number will be left? - - -78 - - Split into three and mixed, - With Dives I am found. - Split into two and fixed - On four legs, flat or round. - In my most kindly sense unbroken, - Warm hearts and helpers I betoken. - - -79 - - I am high, I am low, - I am thick, I am thin, - I can keep out the snow, - But may let the rain in. - - -80 - -HIDDEN FRUIT - - Go range through every clime, where’er - The patriot muse appears - He deeds of valour antedates, - His ban an army fears. - - By midnight lamp each poet soul - Is plumed for flight sublime; - Pale monarch moon and shining stars - Witness his glowing rhyme! - - Incited by the muse man goes - To grapple with his wrongs; - The poet cares not who makes laws, - If he may make the songs. - -Can you discover ten fruits in these lines? - - -No. LXXVII.--LINES ON AN OLD SAMPLER - - | | - --+-----------------------------------------+-- - |~When I can plant with seventeen trees | - | Twice fourteen rows, in each row three;| - |A friend of mine I then shall please, | - | Who says he’ll give them all to me.~ | - --+-----------------------------------------+-- - | | - - -81 - - The last of you before the end - Close to an inn we first must find, - If nothing follows all will tend - To hints that rankle in the mind. - - -No. LXXVIII.--DOMINO DUPLICITY - -By the following ingenious arrangement of the stones a set of dominoes -appears to be unduly rich in doublets:-- - - +-------+ +-------+ - | 1 1 | | 3 3 | - +---+---+---+-------+---+---+---+ - | 1 | 1 5 | 5 0 | 0 3 | 3 | - | +---+---+---+---+-------+ | - | 6 | 6 | 5 5 | 0 | 0 6 | 6 | - +---+ +-------+ +-------+---+ - | 6 | 6 | 4 4 | 4 | 4 6 | 6 | - | +---+---+---+---+-------+ | - | 2 | 2 4 | 4 | 4 | 4 5 | 5 | - +---+-------+ | +-------+---+ - | 2 | 2 1 | 1 | 3 | 3 5 | 5 | - | +-------+---+---+-------+ | - | 0 | 0 1 | 1 3 | 3 2 | 2 | - +---+---+---+-------+---+---+---+ - | 0 0 | | 2 2 | - +-------+ +-------+ - -It will be noticed that the charm of this arrangement is that the whole -figure contains a double set of quartettes, on which the pips are -similar. - - -82 - - Many men of many minds, - Many birds of many kinds, - Some are dun, and some are gray-- - Which is this one? tell me, pray! - See him where the water shines, - But not perching on the pines. - - -No. LXXIX.--MORE DOMINO DUPLICITY - - +-------+ +-------+ +-------+ +-------+ - | 2 2 | | 0 0 | | 1 1 | | 3 3 | - +---+---+---+---+---+---+ +---+---+---+---+---+---+ - | 2 | 2 3 | 3 0 | 0 | | 1 | 1 6 | 6 3 | 3 | - | +---+---+-------+ | | +-------+---+---+ | - | 6 | 6 | 3 | 3 1 | 1 | | 4 | 4 6 | 6 | 4 | 4 | - +---+ | +-------+---+ +---+-------+ | +---+ - | 6 | 6 | 5 | 5 1 | 1 | | 4 | 4 0 | 0 | 4 | 4 | - | +---+---+-------+ | | +-------+---+---+ | - | 5 | 5 | 5 | 5 2 | 2 | | 2 | 2 0 | 0 | 5 | 5 | - +---+ | +-------+---+ +---+-------+ | +---+ - | 5 | 5 | 0 | 0 2 | 2 | | 2 | 2 5 | 5 | 5 | 5 | - | +---+---+---+---+ | | +-------+---+---+ | - | 4 | 4 0 | 0 | 4 | 4 | | 1 | 1 5 | 5 | 6 | 6 | - +---+-------+ | +---+ +---+---+---+ | +---+ - | 4 | 4 6 | 6 | 4 | 4 | | 1 | 1 3 | 3 | 6 | 6 | - | +-------+---+---+ | | +-------+---+---+ | - | 3 | 3 6 | 6 1 | 1 | | 0 | 0 3 | 3 2 | 2 | - +---+---+---+---+---+---+ +---+---+---+---+---+---+ - | 3 3 | | 1 1 | | 0 0 | | 2 2 | - +-------+ +-------+ +-------+ +-------+ - -This again shows how the stones can be placed so that an ordinary set of -dominoes seems to be unduly rich in doublets. - - -83 - -We know how, by the addition of a single letter, our _cares_ can be -softened into a _caress_; but in the following Enigma a still more -contradictory result follows, without the addition or alteration of a -letter, by a mere separation of syllables:-- - - None can locate the subject of my riddle. - For all the world would seek its place in vain; - Cut it asunder almost in the middle, - And in our very midst its place is plain. - - An aching void, an absolute negation, - Into the opposite extreme it breaks; - With just a gap to mark their new relation - Each letter still the same position takes. - - -No. LXXX.--TWO MORE PATTERNS - -Here are two more perfect arrangements of a set of dominoes in -quartettes, so that the pips and blanks are similarly grouped and -repeated:-- - - +---+-------+-------+-------+---+ +---+-------+-------+-------+---+ - | 3 | 3 0 | 0 5 | 5 2 | 2 | | 0 | 0 2 | 2 3 | 3 1 | 1 | - | +---+---+---+---+---+---+ | | +---+---+---+---+---+---+ | - | 3 | 3 | 0 | 0 | 5 | 5 | 2 | 2 | | 0 | 0 | 2 | 2 | 3 | 3 | 1 | 1 | - +---+ | | | | | +---+ +---+ | | | | | +---+ - | 2 | 2 | 1 | 1 | 6 | 6 | | 4 | 4 | 5 | 5 | 0 | 0 | - +---+---+---+---+---+---+ +---+---+---+---+---+---+ - | 2 | 2 | 1 | 1 | 6 | 6 | | 4 4 | 5 | 5 0 | 0 | - +---+ | | | | | +---+ +-------+ +-------+ | - | 1 | 1 | 4 | 4 | 3 | 3 | 0 | 0 | | 6 6 | 5 | 5 6 | 6 | - | +---+---+---+---+---+---+ | +---+---+---+---+---+---+ - | 1 | 1 | 4 | 4 | 3 | 3 | 0 | 0 | | 6 | 6 | 5 | 5 | 6 | 6 | - +---+ | | | | | +---+ +---+ | | | | | +---+ - | 6 | 6 | 5 | 5 | 4 | 4 | | 2 | 2 | 1 | 1 | 4 | 4 | 3 | 3 | - +---+---+---+---+---+---+ | +---+---+---+---+---+---+ | - | 6 6 | 5 5 | 4 4 | | 2 | 2 1 | 1 4 | 4 3 | 3 | - +-------+-------+-------+ +---+-------+-------+-------+---+ - - -CHARADES - - -1 - -SIR WALTER SCOTT’S CHARADE - - Sir Hilary fought at Agincourt, - Sooth! ’twas an awful day - And though in olden days of sport - The rufflers of the camp and court - Had little time to pray, - ’Tis said Sir Hilary muttered there - Two syllables by way of prayer. - - “My first to all the brave and proud - Who see to-morrow’s sun; - My next with her cold and quiet cloud - To those who find a dewy shroud - Before the day is won. - And both together to all bright eyes - That weep when a warrior nobly dies!” - - -No. LXXXI.--COUNTING THEM OUT - -Arrange twelve dominoes as is shown in this diagram, and start counting -_in French_ from the double five, thus u, n, _un_; remove the stone you -thus reach, which has _one_ pip upon it, and start afresh with the next -stone, d, e, u, x, _deux_; this brings you to the stone with two pips; -then t, r, o, i, s, _trois_, brings you to that with _three_, and so on -until _douze_ brings you to twelve. - - +---+---+---+---+---+---+---+---+---+---+---+---+ - | 2 | 3 | 4 | 3 | 2 | 5 | 2 | 6 | 6 | 0 | 1 | 5 | - | | | | | | | | | | | | | - | 4 | 1 | 5 | 4 | 0 | 3 | 3 | 6 | 5 | 1 | 2 | 5 | - +---+---+---+---+---+---+---+---+---+---+---+---+ - -Always remove the stone as you hit upon each consecutive number. - -Now who can re-arrange these same stones so that a similar result works -out in _English_, thus--o, n, e, _one_ (remove the stone), t, w, o, -_two_, and so on throughout? - - -2 - -A FAMILY CHARADE - - A man with fourscore winters white - Sat dozing in his chair; - His frosted brow was quite my first, - Crowned with its silver hair. - - My whole, when playing at his feet, - Sly glances upward stole; - My second, standing at his side, - Was father of my whole. - - -No. LXXXII.--TRICKS WITH DOMINOES - -In this diagram the word EACH is formed by the use of a complete set of -stones, placing every letter in proper domino sequence. - - +-------+-------+ +---+-------+ +---+-------+---+ +---+ +---+ - | 6 5 | 5 3 | | 1 | 1 5 | | 1 | 1 1 | 1 | | 5 | | 0 | - +---+---+-------+ | +---+---+ | +-------+ | | | | | - | 6 | | 0 | | 5 | | 6 | | 2 | | 4 | | 3 | - | | +---+ | | +---+ +---+ +---+ +---+ - | 0 +-------+ | 0 | | 2 | | 6 | | 4 +-------+ 3 | - +---+ 0 2 | | +---+---+ | | | | 4 3 | | - | 0 +-------+ | 4 | 4 2 | | 6 | | 4 +-------+ 3 | - | | +---+---+---+ +---+ +---+ +---+ +---+ - | 0 | | 4 | | 2 | | 6 | | 2 | | 4 | | 3 | - +---+---+-------+ | | | | | +-------+ | | | | | - | 0 5 | 5 5 | | 6 | | 6 | | 3 | 3 2 | 2 | | 1 | | 1 | - +-------+-------+ +---+ +---+ +---+-------+---+ +---+ +---+ - -There are also the same number of pips in each letter. Can you construct -another English word under the same conditions? As a hint, the word that -we have in mind is plural. - - -3 - - Upon my face is not a single hair, - Although my beard uncut is growing there. - Men call me Shelley, though I can’t converse, - To me all tongues alike would be a curse. - I in my house must night and day abide, - And though quite well must keep my bed, outside. - For me no bell shall toll a funeral knell, - I’m doomed, like Shelley, dead to have no shell. - - -4 - -This amusing Charade is from the pen of a wise and witty Irish Bishop:-- - - True to the trumpet call of fame and duty - The soldier arms, and hastens to depart; - Nor casts one look behind, though love and beauty - Whisper _my first_ in tones that thrill his heart. - - The war is o’er, with wealth and honour laden - The hero seeks the well-remembered Hall: - He woos and wins the unreluctant maiden, - And bids _my second_ o’er her blushes fall. - - He takes her hand--a mist of rapture thickens - Before her eyes. Such bliss succeeding pain - O’ertasks her strength, and fainting nature sickens, - Until _my whole_ is rudely snapt in twain. - - -No. LXXXIII.--THE HOUR GLASS - -This very beautiful specimen of a knight’s tour on the chess-board takes -its name from the figure formed by the tracery at its centre. - -[Illustration] - -An endless number of symmetrical patterns of varied design can be -formed, by a knight’s consecutive moves, with patience and ingenuity. - - -No. LXXXIV.--A STAR’S TOUR - -Here is a pretty and very regular specimen of a knight’s tour on the -chess board. - -[Illustration] - -It is one of many variations which produce in the tracery a central -star. - - -5 - -MAKE IT KNOWN - - My first she was a serving maid, - Who went to buy some tea; - How much she bought my second tells, - As all may plainly see. - - Now when the answer you have found - Tell it to others too; - My whole will then to maids and men - Explain what ’tis you do. - - -No. LXXXV.--THE MARBLE ARCH - -Here is a remarkably symmetrical specimen of a knight’s tour on the -chess board. - -[Illustration] - -It takes its name from the central archway, which this arrangement -forms. - - -6 - - My fourth is just ten times my first - When that takes on my second; - My third and second when reversed - Double my first are reckoned. - All this is empty, though my pen - So full may seem to show it; - Reverse my first and second, then - My whole becomes a poet. - - -7 - - O’er distant hills the rising moon - The evening mist dispersed: - And beaming radiant in the sky - She plainly showed _my first_. - - A horseman guided by her light, - Approached with headlong speed - And as he rode _my second_ said - To urge his flagging steed. - - His lady waited at the gate, - Though trysting hour was past. - She was _my whole_, because her lord - Was then _my third_ and last. - - -No. LXXXVI.--ANOTHER TOUR AMONG STARS - -In No. LXXXIV we gave a pretty illustration of a knight’s tour, with a -central star. - -[Illustration] - -Here is a good course which shows in its symmetrical tracery a pair of -stars. - - -No. LXXXVII.--THE WINDMILL - -Among the countless fanciful variations of the knight’s tour that are -possible, some have been so designed that more than a merely symmetrical -pattern is involved. - -[Illustration] - -Here is, for example, an excellent suggestion of the sails of a windmill -with their central fittings. - - -8 - -A TROPICAL CHARADE - - My first’s a liquid or a solid snare, - My all is hot, or in a maiden’s hair; - My second just a track. - Transpose my first, and they will both declare - My all is now a black. - - -No. LXXXVIII.--LAZY TONGS - -Here is a very distinctive specimen of the knight’s tour, in which the -design reminds us of the old-fashioned lazy-tongs, which stretched out -and then back, by opening or shutting their handles on finger and thumb. - -[Illustration] - - -9 - -A FLORAL CHARADE - - My first must be below the ground, - To do its proper duty; - Within my second may be found - Chaps that can boast no beauty; - Some simple garden holds the two combined, - Old-fashioned emblem of a candid mind. - - -No. LXXXIX.--CHESS ARITHMETIC - -This beautiful symmetrical knight’s tour involves in its accomplishment -a pretty problem in arithmetic:-- - -[Illustration] - -If we follow the course of the knight step by step, and number -consecutively the squares on which it rests at each move, we find that -there is a constant difference of 32 between the numbers on any two of -these squares that correspond in position on opposite sides of the -central line. - - -10 - - My first can be no joke to crack, - My second I adore; - Reverse her name, and you will see - Just what that maiden is to me. - My whole is grown where boys are black - Upon a sultry shore. - - -No. XC.--A SHORT KNIGHT’S TOUR - -This short symmetrical knight’s tour can be tested on a corner of the -chessboard:-- - -[Illustration] - -The knight can start from any square, and, taking the course indicated, -return on the twentieth move to the starting point. - - -11 - -BY GEORGE CANNING - - Though weak my first is reckoned, - And game made of my second; - Yet both bade hosts defiance - When joined in close alliance. - - -12 - - As Lubin did my first, and, scythe in hand, - Espied his Phyllis by the hedgerow stand, - He called out to my next, in cheery tones and clear, - “Tell me, sweet all, you’ll fetch a pot of beer.” - - -No. XCI.--THE STOLEN PEARLS - -A dishonest jeweller, who had a cross of pearls to repair for a lady of -title, on which nine pearls could be counted from the top, or from -either of the side ends to the bottom, kept back two of the pearls, and -yet contrived to return the cross re-set so that nine pearls could still -be counted in each direction, as at first. How was this done? - -[Illustration] - - -13 - -A WORD OF WARNING - - Says William to his thriftless wife, - “To _first_ unless you try, - Your wasteful ways will spoil our life.” - Her’s is a curt reply. - - _Second_ and _third_ her answer give; - Full soon their fortunes fall, - Each of the hapless pair must live - And wander as my _all_. - - -14 - -A FINE CHARADE BY PRAED - - Come from my first, ay, come; - The battle dawn is nigh, - And the screaming trump and the thundering drum - Are calling thee to die. - Fight, as thy father fought, - Fall, as thy father fell: - Thy task is taught, thy shroud is wrought, - So forward and farewell! - - Toll ye my second, toll; - Fling high the flambeau’s light, - And sing the hymn for a parted soul - Beneath the silent night. - The helm upon his head, - The cross upon his breast, - Let the prayer be said, and the tear be shed - Now take him to his rest! - - Call ye my whole, go call - The lord of lute and lay, - And let him greet the sable pall - With a noble song to-day. - Ay, call him by his name, - No fitter hand may crave - To light the flame of a soldier’s fame - On the turf of a soldier’s grave! - - -15 - - My first has cause in dread to hold - The foggy month November. - My next, when given to knights of old - Was held to mean “remember!” - - -16 - - With one line many do my first, - With two it can but meet; - My second, as its breakers burst, - Around my whole may beat. - - -17 - - She was my first; one happy day - She was my second, - And shewed my all. Now can you say - How this is reckoned? - - -18 - - My first it may a seaman save, - Or cause a fighter’s fall; - My next reminds us of the wave, - Or of unseemly brawl. - My whole is rather pert than brave, - And like a rubber ball. - - -19 - - Seen with a stolen spoon, my first was reckoned - Bad as my whole in moral tone. - Whether a number or alone my second - Touched by my third is turned to stone. - - -20 - -NOT A CATECHISM - - My first a friend, companion, guide, - Is loving, staunch, and cheery; - My second has a cleansing side, - My third denotes a theory. - My whole, good luck! is held by few - To bore and make us weary. - - -21 - - My first is an insect, - My second a border; - My whole puts the face - Into tuneful disorder. - - -22 - - My first seldom crosses your path, - Though wheels and a body it hath; - My next from a clown - Much applause will bring down, - My whole was Goliath of Gath. - - -23 - - My first he sat upon my whole - And used it as my second. - His halves akin in Latin and - In English may be reckoned. - - -24 - -A PHONETIC FLORAL CHARADE - - My first comes often to our mind - When for a saint we look. - My second sees the greetings kind - Of Bobby and the cook. - My whole in hothouse you may find, - Or pictured in a book. - - -25 - - Man cannot live without my first, - By day and night ’tis used; - My second is by all accursed, - By day and night abused. - My whole is never seen by day, - And never used by night, - ’Tis dear to friends when far away, - But hated when in sight. - - -26 - -BY AN OXFORD OAR - - I am my first, my second thou mayest be - In classic shades, where gently roll - The crystal waters of my whole - To seek the sea. - - -27 - - My first is worn by night and day, - And very useful reckoned; - London, or Bath, or Bristol may - With truth be styled my second. - Now if you cannot find me out - You lack my whole without a doubt. - - -28 - - My first now marks the soldier’s face, - Who was my next’s defender; - But when my whole attacked the place - It drove him to surrender. - - -29 - - My first is away from Paris, and may - Come round with a rap at your portal; - My second is Spanish, but quickly will vanish - If it turns to a nod from a mortal. - - -30 - - Often my first a B begins, - One always starts my second. - My all, though free from grosser sins, - Of little worth is reckoned. - - -31 - - My first is a kind of butter, - My second is a sort of cutter; - My whole, whether smaller or larger, - Was always a kind of charger. - - -32 - - My first is but lately promoted - To a place in our language, and quoted. - My second it lives in the sea. - On the hill-tops it flourishes free. - My whole I should certainly call - A delectable dainty for all. - - -33 - -AN ENIGMA-CHARADE - - Take in my first, and you will find - It helps you to make up your mind. - Write to my second, and behold - You see into the secret told. - - -34 - -A QUAINT CHARADE - -BY CHARLES JAMES FOX - - My first is expressive of no disrespect, - But I never call you by it when you are by; - If my second you still are resolved to reject, - As dead as my whole I shall presently lie. - - -35 - - My first reversed will plainly show - An apple in its embryo. - Reverse my second, and we see - That which in sight can never be. - Replace them both, and write me down - Six letters that will spell a town. - - -36 - - My first is equal to the rest, - My second not so much; - My whole is better than the best, - Beyond compare nonsuch. - - -37 - -AN ITALIAN POET’S LOVE SONG - - Hear me, my all: oh, be my first! - My second is a single; - If you say yes, then in my third - Our happy lives shall mingle. - - -38 - -A PARADOX - - My first a simple verb, or half a verb, may be; - Almost the same my next, or half the same, we see. - My whole may weigh a ton or more, and yet be light, - Dull, and bereft of motion; swift, exceeding bright. - - -39 - - My first is found in fruit, - You take it for my second; - My whole in church to suit - Attentive ears is reckoned. - - -40 - - My _first_ is frugal, lean, and thin, - My _second_ leads to eve, - My _whole_ is hidden by a skin, - But not of sheep or beeve. - - -41 - -VERY PERSONAL - - My first to us may point ’tis clear, - And what I say is true, sir! - My next to her your thoughts will steer, - My whole it is in view, sir! - - -42 - - My second in my first can speed - Across United States; - My third from Q’s pen we can read, - My whole has water-rates; - My first and second drive my first along, - My third and second drive a mind all wrong. - - -43 - - To puzzle solvers can I shine, - And so my first is writ. - With this my second did combine - To make a happy hit. - My whole, with both fixed in a line - Firm as I can, did fit. - - -44 - -A RUSTIC CHARADE - - My first and second are my third, - My third my first and second may be; - My whole, if right you read the word, - May never have a wife or baby. - - -45 - - Let my second cut my first - Into slices thin; - Seek in Shakespeare for my whole, - Injured by his kin. - - -46 - -A FIRM GRIP - - I may give you my first with my second, - Or my second may give with my first; - The one act as friendly is reckoned, - The other will rank with the worst. - If my whole through my second creeps over my first, - It will cling as a bond that no effort can burst. - - -47 - - My first is called a sin in name, - My third its simple cure; - My second puts an end to fame, - My whole in ease is sure. - - -48 - - In my first ’tis sweet to tarry - ’Mid my second’s realms of bliss. - In the two, though none can marry, - All are subject to a kiss. - - -49 - - My first, which washes half a nation’s gums, - From foreign climes within my second comes: - And though, my whole, thine is no teacher’s part, - Thou art not science, but thou teachest art! - - -50 - - My first on country hedges grows, - My next is found in garden rows, - My third to make it more transpose, - My whole is one of London’s shows. - - -51 - - My first the best solver can never find out, - My second is looked for in vain; - My third may hide all from our view round about, - My whole must be weak, or in pain. - - -52 - -SORROW’S ANTIDOTE - - My first does affliction denote, - Which my second is destined to bear; - My whole is the sweet antidote - That affliction to soothe and to share. - - -53 - - I see a sign of music not reversed, and then - My second and my third both pass beyond my ken. - - -54 - - My first has my second my third his mouth; - My whole was a tribe in the sunny south. - - -55 - -“QUOD” ERAT DEMONSTRANDUM - - My second makes my ending, - My first is its reverse; - My whole bad men is sending - From court to quarters worse. - - -56 - - My first, though won and never lost, - Reversed is now before ye: - My second turns as red as blood - Upon a field of glory. - My whole is plain, yet you’ll confess - It is a wonder if you guess. - - -57 - - I get my second when I take my first, - And then my upright character is lost; - My whole gives quarters to a rat reversed, - Or is a refuge for the tempest tost. - - -58 - - My first is almost a cropper; - My second is often a propper; - My whole was entirely a whopper. - - -59 - -A FLORAL CHARADE - - My first by poet’s eye was seen - Sad watching at the gates of heaven. - My next in tints of tender green - By Dickens with quaint art was given. - - -60 - - My first is nothing but a name - My second is more small; - My whole is of such slender fame - It has no name at all. - - -61 - - When second is of whole a fourth, - And first a fifth of second, - Then first by second multiplied - To make my whole is reckoned. - - -62 - -A CHARADE WITH A MORAL - - My first is black, my second red, - My whole no man should take to bed. - - -63 - - My first upon their prey can dart, - My next can ne’er be down; - My whole performs a saucy part - In country or in town. - - -64 - - My first makes hills unpleasant - To every cyclist’s wheel. - My next is where they take you to - If in the streets you steal. - My whole is what I most dislike - When in the dumps I feel. - - -65 - - My first is the voice of heart-sorrows or joys, - My second, bar one, have been all of them boys, - My whole is made ill by the harsh raven’s noise. - - -66 - -QUITE SELF-CONTAINED - - My first is in my second, - My third contains an ass; - And when my whole is reckoned - You see it is in glass. - - -67 - - Safe on Lucinda’s arm my first may rest, - And raise no tumult in Alonzo’s breast. - My second can the want of legs supply - To those that neither creep, nor walk, nor fly; - My whole is rival to the fairest toast, - And when most warmly welcomed suffers most. - - -68 - - My second, my first can control, - If his understanding is reckoned. - My second may not be my whole, - But my whole must be always my second. - - -69 - -AN OLD COCKNEY CHARADE - - My first’s a little thing that hops, - My second comes with summer crops, - My whole is good with mutton chops. - - -70 - -A STRIKING CHARADE - - My first I gently strike, and lo! - It soon becomes my second. - Indeed if this should not be so - My whole it is not reckoned. - - -71 - -PLANTING PEAS - - “I think,” said Ted, “it will be wise - To set the peas this way; - For here they will face friendly skies, - And sun shines all the day.” - - “Your first is good,” the gardener said, - “Peas thrive in sun and shower; - So now, good second, dig the bed - Where all can see them flower.” - -Can you fit a word of two syllables to this Charade? - - -72 - - My first is found where wit and wine - Combine to grace the festal board; - My second where sad captives pine, - In dungeon of some tyrant lord. - My whole is ready for the doomed, - Twice tried by fire ere once consumed. - - -73 - -A BRAIN TWISTER - - My first is half my second - And my third is half my first - My second and my third are good - To quench a mighty thirst. - - -RIDDLES AND CONUNDRUMS - - -1. Woman is my end, was my beginning, and you will find her in my midst. - - -2 - - I am an uncle, but it is not nice - To be saluted as an uncle twice. - -Why not? - - -3. If a tailor and a goose are on the top of the Monument, which is the -quickest way for the tailor to get down? - - -4. My first is almost all, so is my second, and also my whole? - - -5 - - Those who have me do not desire me, - And yet they never wish to lose me, - Those who gain me have me no longer. - - -6. Why may a barrister’s fees be said to be cheap? - - -7 - - Two brothers are we, great burdens we bear, - By which we are heavily prest: - We are full all the day to endure wear and tear, - But empty when able to rest. - - -8. Peter Portman was so proud of his small feet that a wag started the -following riddle: “Why are Portman’s feet larger than any others in his -club?” - - -9 - - There is a word of letters four, - Take two away, and four remain; - Take three away, and five before - Your eyes you see as plain as plain. - - -10 - - To one syllable adjusted, - Running on the ground, - I have two, no longer trusted, - If you turn me round. - - -11. Why is a raven like a writing desk? - - -12. What do they do with peaches in California? - - -13. What is the utmost effort ever made by a piebald horse at a high -jump? - - -14 - - “In my first my second sat, - Then my third and fourth I ate.” - - Under my first my second stood, - That’s your riddle: mine’s as good! - - -15. What are the differences between a gardener, a billiard-marker, a -precise man, and a verger? - - -16. Which can see most, a man with two eyes, or a man with one? - - -17. When you do not know the time, and “ask a policeman” what o’clock it -is, why are you like the Viceroy of India? - - -18. What is the question to which “yes” is the only possible reply? - - -19. What is that which will go up a pipe down, but will not go down a -pipe up; or will go down a pipe down, but not up a pipe up, and yet when -it has gone up a pipe or down a pipe, will go up or down? - - -20. Why was London for many years a wonderful place for carrying sound? - - -21. Why is a motor-car like swimming fish? - - -22. Who can decipher this? - - 1/6d. me a bloater. - - -23. Why is a moth flying round a candle like a garden-gate? - - -24 - - To half a dozen add half a score, - And you will plainly see - Just twenty, neither less nor more-- - Now say, how can this be? - - -25. If I caught a newt why would it be a small one? - - -26. How can a lawyer’s fee be paid with only a threepenny piece? - - -27. When does the cannon ball? - - -28. Why should children go to bed soon after tea? - - -29. Which may weigh the most, Scotsmen or Irishmen? - - -30. Why cannot we have our hair cut? - - -31. Divide a hundred and fifty by half of ten, add two-thirds of ten, -and so you will find a town. - - -32. The following riddle is from the pen and fertile brain of Archbishop -Whately, who, it is said, offered in vain £50 for its solution:-- - - When from the Ark’s capacious round - Mankind came forth in pairs, - Who was it that first heard the sound - Of steps upon the stairs? - - -33. If Moses was the son of Pharaoh’s daughter, who was the daughter of -Pharaoh’s son? - - -34. I am a word of three syllables, and in all my fulness I represent -woman. Rob me of five letters and I am a man. Take away but four, I am -woman again. Remove only three, and I resume my manhood. What am I? - - -35. A cyclist on a night journey punctures his tyre, and finds that he -has forgotten his outfit for repairs. After wheeling the disabled -machine uphill for about two miles he registers a vow. What is it? - - -36 - - Some more than the mere whole my whole contains; - Remove that whole, and some of it remains! - - -37. Why were Younghusband’s pack-horses in Thibet like up-to-date motor -cars? - - -38 - - The public credit and the public shame - Differ in everything except in name. - - -39. Why is a telescope like a miser? - - -40. If I were in the sun, and you were out of it, what would it be? - - -41 - - I’m a word of four letters akin to the snow, - Just half of my first my third letter will show. - One fifth of my fourth my first you may call, - Of my second ’tis best to say nothing at all. - - -42. What is the chief and most natural thing for politicians to desire -to do when for the time they are out in the cold, awaiting a change of -Government? - - -43. I am long lasting, beginning at my end, ending with no beginning, -and my end and my beginning between them will bring you to an end. - - -44 - - With both feet crossed sit steady on a stool, - Then uncross one, and try to find a fool. - - -A RABBIT RUN - -45. How far can a rabbit run into a square wood, with sides that each -measure a mile, if it keeps on a straight course and does not break -cover? - - -46 - - Often talked of, never seen, - Ever coming, never been, - Daily looked for, never here, - Still approaching in the rear. - Thousands for my presence wait, - But, by the decree of Fate, - Though expected to appear - They will never see me here. - - -47. I received my first because I was rash enough to say my second to my -third, when seeking re-election at my whole. - - -48 - - How is it, in this charming weather, - You and I can’t lunch together? - - -49 - - With a head, and without a head, - With a tail, and without a tail, - With a head without a tail, - With a tail without a head, - With a head and tail, - Without a head and tail. - - -50. “Ask me another,” she said, when he pressed her to name the happy -day. “I will,” he replied. “Why is the letter ‘d’ like the answer which -I seek from you?” - - -51 - -SWIFT’S RIDDLE - - Two thirds of an ass, and a hole in the ground, - Will dress you a dinner worth many a pound. - - -TOM HOOD’S RIDDLE - -52. Here is a riddle for which Tom Hood was responsible. Can you solve -it? - - Twice to thine, - Once to mine, - With Congou make a gift divine. - - -53. Hold up your hand and you will see what you never have seen, never -can see, and never will see. What is this? - - -54. Can you tell the difference between the Emperor of Russia and an -ill-shod beggar? - - -55. Why did Eden Philpotts? - - -56. We have heard much of man’s imagined connection with the monkey, -through some missing link. What evidence can we gather from early -records of, at any rate, some verbal kinship with the patient ass? - - -57. My first is gold, my second is silver, my third is copper, and my -whole is tin. - - -58. What is highest when its head is off? - - -59. What word is there of six letters which can be so read that it -claims to be spelt with only one? - - -60. If a good oyster is a native, what is a bad one? - - -61. Why is John Bright? - - -62. If I walk into a room full of people, and place a new penny upon the -table in full view of the company, what does the coin do? - - -63. Jones, who had made it, and put it into his waistcoat pocket, lost -it. Brown picked it up, and lighted his cigar with it. Then they both -went to the train in it, and ran all the way. - - -64. Why cannot a deaf and dumb man tickle nine people? - - -65. When did “London” begin with an _l_ and end with an _e_? - - -66. I sent my second to my first, but many a whole passed before he came -back to me. - - -67. Which weighs most, the new moon or the full moon? - - -68. Here is a puzzle which is unique and most remarkable, and which -seems to be impossible, though it is absolutely sound:-- - -There is an English word of more than two letters, of which “la” is the -middle, is the beginning, and is the end, though there is but one “a” -and one “l” in the word. What is it? - - -69. Why is a bee like a rook? - - -70 - -A DARK REBUS - - O - B =e= D - - -71 - -A MONKEY PUZZLER - -If a monkey is placed before a cross, why does it at once get to the -top? - - -72 - -A RIDDLE BY COWPER - - I am just two and two, warm and cold, - And the parent of numbers untold; - Lawful, unlawful, duty, fault, - Often costly, worthless bought. - A priceless boon, a matter of course, - Willingly yielded, taken by force. - -The answer has been defined as “two heads and an application.” - - -HOW’S THAT, UMPIRE? - -73. How can the Latin exhortation “Macte!” which may be roughly rendered -“Go on and prosper!” be applied at cricket to a batsman at a critical -moment? - - -BY TAPE MEASUREMENT - -74. Are you good at topography? If so, can you discover and locate, from -this description of its surroundings, a town within 30 miles of London? - -Half an inch before the trees, and half a foot and half a yard after -them, lead us to an English town. - - -75. We know how, by the addition of a single letter, our cares can be -softened into a caress; but in the following enigma a still more -contradictory result follows, without the addition or alteration of a -letter, by a mere separation of syllables:-- - - None can locate the subject of my riddle, - For all the world would seek its place in vain; - Cut it asunder almost in the middle, - And in our very midst its place is plain. - - An aching void, an absolute negation, - Into the opposite extreme it breaks; - With just a gap to mark their new relation - Each letter still the same position takes. - - -76. MULTUM IN PARVO - -What two letters describe in nine letters the position of one who has -been left alone in his extremity? - - -77. A CHANGE OF SEX - -“Oh! would I were a man,” cried a schoolmistress, “that I might always -teach boys.” - -We boys overheard her, and placed her with us. What did we thus turn her -into? - - -78. A STRIKING MATCH PUZZLE - -How can you make a Maltese cross with less than twelve unbent and -unbroken matches? - - -79 - -Have we any reason to suppose that in very early times there were less -vowels than we have now? - - -80. A FRENCH RIDDLE - -As Susette was sitting in the cool shadow of an olive grove at Mentone, -Henri came up and said to her, with his best bow, “Je sais que vous -n’avez pas mon premier, mais que vous êtes mon second, et je vous -donnerai mon tout!” What did he hold out to her? - - -81 - -On a church close to an old ruined priory, near Lewes, there is a -weathercock in the shape of a fish, probably an emblem of the faith. -What moral lesson does this relic of early days convey to us? - - -82 - - Take five from half of ten, - Set fifty in the middle, - Add twice five hundred then - To finish up the riddle, - And make it with your pen - As fit as any fiddle. - - -83. A PARADOX - -“For the want of water we drank water, and if we had had water we should -have drank wine.” - -Who can have said this, and what did they mean? - - -84. WHAT IS IT? - - The poor have two, the rich have none, - Millions have many, you have one. - - -85 - - A thousand and one, - And a sixth part of twenty; - Some may have none, - But others have plenty! - - -86. GREAT SCOTT! - - “Charge, Chester, charge! on, Stanley, on!” - Were the last words of Marmion. - Now, had I been in Stanley’s place - When Marmion urged him to the chase, - You would have thought, unless you knew, - That Scottish fray was Irish stew! - -Shade of Sir Walter! What does all this mean? - - -87 - - I may be half of ten, - I may be nearly nine; - If eight contains me then - Two-thirds of six are mine. - A third of one, a fourth of four, - I am an eighth of many more. - - -88. QUITE A BEATITUDE - - Let her be, or beat her, - Give her little ease; - Then in safety seat her - All among the bees. - - -89 - - Sharpen your wits till they are keen, - Then see if you can guess - What word it is that I have seen, - And spell it with an s! - - -90. RATHER PERSONAL - - Take part of a foot, - And with judgment transpose. - You will find that you have it - Just under your nose. - - -NUTS TO CRACK - - -CRAZY LOGIC - -1. Can you prove, by what we may call crazy logic, that madman is equal -to madam? - - -A BIT OF BOTANY - -2. A rat with its teeth in the webbed feet of its prey was what the -squirrel saw one summer’s day, when he ran down from the tree-tops for a -cool drink in the pond below his nest. Can you find out from this the -name of the water-plant that was floating in the shade? - - -SIX SUNKEN ISLANDS - - 3. He set down the answer to that sum at random. - By bold policy Prussia became a leading power. - A great taste for mosaic has arisen lately. - The glad news was swiftly borne over England. - At dusk, year after year, the old man rambled home. - The children cried, hearing such dismal tales. - -In each of these lines the name of an island is buried. - - -BURIED GEOGRAPHICAL NAMES - -4. We could hide a light royal boat with a man or two; the skipper, -though, came to a bad end. - -In this short sentence seven geographical names are buried, formed by -consecutive letters, which are parts always of more than one word. Can -you dig them out? - - -A TRANSPOSITION - -5. What can you make of this? The letters are jumbled, but the words are -in due order. - - Eltsheothwoedlaniscimtyyesrmh - Tsihptsnrtoniaisoetcra; - Ndaothetdandartssdensitemeb - Ehcatreeltnisitlpace. - - -6 - -ALL IN A ROW - - Three little articles all in a line - Lead to a thousand, expressing, - If with another all these you combine - What can be never a blessing. - - -7 - -ASK A POLICEMAN - - Ask a policeman, possibly he knows, - In uniformed array. - If not, an added letter plainly shows - How little he can say. - - -8 - -RULING LETTERS - - We rule the world, we letters five, - We rule the world, we do; - And of our number three contrive - To rule the other two. - - -MIND YOUR STOPS - -9. How would you punctuate the following sentence? - -Maud like the pretty girl that she was went for a walk in the meadows. - - -10. ANSWER BY ECHO - - What were they who paid three guineas - To hear a tune of Paganini’s? - - -11. BREAKING A RECORD - -Only eight different letters are used in the construction of this -verse:-- - - Sad as the saddest end is his, - He hath insensate died. - He sinned, and that his Satan is - That standeth at his side. - -Wishing to break this record, we have put together a rhyming verse of -similar length, in which only _five_ letters are used. They are these: - - (18 times) ^eeeeeeeeeeeeeeeeee^. - (20 times) ^nnnnnnnnnnnnnnnnnnnn^. - (18 times) ^tttttttttttttttttt^. - (16 times) ^iiiiiiiiiiiiiiii^. - (15 times) ^sssssssssssssss^. - - -12. A CATCH SENTENCE - -If is is not is and is not is is what is it is not is and what is it is -is not if is not is is? Can you punctuate this so that it has meaning? - - -13. CATCHING A HINT - -Passing one day by train through a station I caught sight of two words -upon a large advertisement, which seemed cut out for puzzle purposes; -and before long I had framed the following riddle: - -Bisect my first, transpose its first half, and between this and its -second half insert what remains if you take my second from my first. The -result is as good to eat as my first and second are to drink. - - -14. IS IT GRAMMAR? - -It is difficult at first sight to grasp the meaning of this apparently -simple sentence:--“Time flies you cannot they pass at such irregular -intervals.” How does it read? - - -15. ROYAL MEMORIES - -In Queen Victoria’s Jubilee year I went to the South Kensington Museum. -As I entered, looking at my watch, I thought of the good Queen. After -some hours of quiet enjoyment I came away, again looking at my watch, -and was reminded that the Prince Consort was not alive to share the -Jubilee joys. At what time, and for how long was I in the Museum? - - -16. A SEASONABLE MOTTO - - CCC - --- - SAW - - -17. AN OLD LATIN LEGEND - - +------------------+ - | AMANS TAM ERAT | - | HI DESINT HERO | - |AD DIGITO UT MANDO| - +------------------+ - -What is the interpretation? - - -18. THINGS ARE NOT WHAT THEY SEEM - -Does the following statement imply that there is a curative virtue in -rose-coloured rays? - - “I know that roseate hues preserve.” - - -19. DOCTOR FELL - - “Keep the patients warm and quiet; - Solids are not well; - Let all sops be now their diet,” - So said Doctor Fell. - -To what objection was this diet open? - - -20. DISLOCATED WORDS - -These thirty-six letters form an English sentence:-- - - SAR BAB SAR BAB SAR BAB - SAR BAB SAR BAB SAR ARA - -What can it be? - - -21. BROAD WILTSHIRE - - “Igineyvartydreevriswutts.” - -Can you interpret this sentence, spoken by a sturdy farmer in the corn -market? - - -22. FIND A RHYME - -Try to find a rhyme to Chrysanthemum. - - -23. ABOUT THE EGGS - -Did you hear that pathetic tale of the three eggs? - - -24. AN ANCIENT LEGEND - - +--------------+ - |Doun tooth ers| - | A sy | - | Ouw ould bed | - | One by. | - +--------------+ - - -25. A FAMILY PARTY - -HERE LIE - - Two grandmothers, and their two granddaughters; - Two husbands, and their two wives; - Two fathers, and their two daughters; - Two mothers, and their two sons; - Two maidens, and their two mothers; - Two sisters, and their two brothers; - Yet but ---- in all lie buried here. - -How many does the ---- represent? - - -26. A SIMPLE CHARM - -A superstitious couple in the country who heard mysterious noises at -night in their house, sought the advice of a “wise woman” in the -neighbourhood. She gave them on paper the following charm, which would, -she assured them, counteract their evil star, and solve the mystery:-- - - ground - turn evil star. - -What was its significance? - - -27. MADE IN FRANCE - - We are five varied vowels of foreign sound, - Supported by one consonant between us. - Three letters now in four, where may be found - Another trio, quite a silly genus. - - -28. A PARADOX - - What in his mind no man can find - Four symbols will display; - But only one remains behind - If one we take away. - - -29. THE BARBER’S JOKE - -A barber placed prominently in his window the following notice:-- - - What do you think - I will shave you for nothing and give you a drink. - -Attracted by this, a man went into the shop, and was shaved, but instead -of receiving any liquid refreshment, he was surprised by a demand for -the usual payment. - -What was the barber’s explanation? - - -30. A FLIGHT OF FANCY - - +-------------------------+ - | G E N U I N E J A M | - | A | - | I C A R U M. | - +-------------------------+ - -This label, said to have been found among the ruins of old Rome, seems -to bear a very early reference to the birth of Icarus, the flying man; -or perhaps to some flying machine named after him, but not yet -perfected. Can this be so? - - -31. A SPELL - - Two _c_’s, an _h_, an _n_, a _p_, - Three _a_’s, a _u_, an _i_, an _e_, - Tell us what English word are we? - - -32. JOHNSON’S CAT - - Johnson’s cat went up a tree, - Which was sixty feet and three; - Every day she climbed eleven, - Every night she came down seven. - Tell me, if she did not drop, - When her paws would touch the top. - - -33. THE EXPANDING NINES - -Some of us may perhaps remember Titania’s promise to Bottom in _A -Midsummer Night’s Dream_: - - “I have a venturous fairy, that shall seek - The squirrel’s hoard, and fetch thee new nuts.” - -Here is a little puzzle so fresh and curious that it will tempt the -fancy of those who find it added to our hoard: - - A third of six behind them fix, - A third of six before; - Thus make two nines, when all combines, - Exactly fifty-four. - - -34. ACROSS THE MOAT - -Form a square with four matches. Outside this, at an equal distance all -round, form another square with twelve matches, just so far away that -the space between them cannot be spanned by a match. With two matches -only, form a firm bridge from the outer to the inner square. - - -35. IS IT BANTING? - - We start when the ninth hour is past, - Then there’s an end of you. - A vengeful goddess shows at last - What antifat will do. - - -36. QUITE A FAMILY PARTY - -The telephone-bell roused Mrs P.W. from her after-luncheon nap, and her -husband’s voice came to her ears, from his office in the city:--“I am -bringing home to dinner my father’s brother-in-law, my brother’s -father-in-law, my father-in-law’s brother, and my brother-in-law’s -father.” - -“Right!” she replied, knowing his quaint ways, “I shall be prepared.” -For how many guests did she provide? - - -37. THE WILY WAYFARER - -“Give me as much money as I have in my hand,” said Will Slimly to the -landlord of a country inn, “and I will spend sixpence with you.” This -was done, and repeated twice with the cash that was still in hand, and -then the traveller was penniless. How much had he at first, and how much -did the landlord contribute to Will’s refreshment? - - -38. A CLEVER CONSTRUCTION - -How can four triangles of equal size be formed with six similar matches? - - -39. A KNOTTY POINT - - When first the marriage knot was tied - Between my wife and me, - My age as oft repeated hers - As three times three does three; - - But when ten years and half ten years - We man and wife had been, - Her age came then as near to mine - As eight does to sixteen. - What age was hers, what age was mine, - When we were wed, from this divine. - - -40. A DIVISION SUM - -“Take this half-crown,” said the vicar at a village festival, “and -divide it equally between those two fathers and their two sons, but give -nothing of less value than a penny to either of them.” - -The schoolboy, who was a sharp lad, changed the half-crown, and divided -it equally among them. How was this possible? - - -41. A CROOKED ANSWER - -Tom (_yawning_) to Nell--“I wish we could play lawn-tennis!” - -Nell (_annoyed_).--“Odioso ni mus rem. Moto ima os illud nam?” - -Can you make head or tail, in Latin or in English, of her reply? - - -42. THE PEELER’S SMILE - -Two policemen stood behind a hedge, watching for motor-car scorchers. -One looked up the road, the other looked down it, so as to command both -directions. - -“Bill,” said one, without turning his head, “what are you smiling at?” -How could he tell that his mate was smiling? - - -43. THE NIMBLE NINES - - Twenty-seven with three nines - You and I can score; - Anyone one on other lines - Can extend them more. - Who can write them to be seen - Equal only to sixteen? - - -44. A TRYING SENTENCE - -That that is is that that is not is not is not that it it is. - - -45. SHORT AND SWEET - -What is this? - - A L L O. - - -46. SUPPLY THE CONSONANTS - -AN ENGLISH PROVERB - - i e a o a a a e a a i - - -47. IT LOOKS BLACK - - | | | | | | | | | | | | | - -Add thirteen more strokes, and make--what? - - -48. THE CORONER’S CHOICE - -Can a coroner, after signing his name, write his official position in -more ways than one? - - -HOW MANY PIPS? - -Here is a good and simple card trick. Ask anyone to choose three cards -from a pack, and to place them face downwards on the table. Then, -beginning to count with the number of pips on each card laid down, let -him place other cards upon these, one heap at a time, until in every -case he counts up to 15, adding mentally 1 as he places down each card. - -When he has completed the three heaps, take from him the remaining -cards, and count them. Their number, less 4, will always be the number -of pips on the three chosen cards. An ace counts 11, and a court card -10. - -Thus, if he has chosen a 7, a 10, and an ace (11), he must cap these -with 8, 5, and 4 cards respectively. There will then be 32 cards left, -and 32 - 4 = 28, which is the sum of 7, 10, and 11. - - -ROUND THE MONKEY - -Now for a few words about an old friend, familiar to most of us. If a -monkey sits on a post holding one end of a string, and continually moves -to face a man who holds the other end, and who walks round the post, -does that man walk round the monkey? - -R. A. Proctor, the astronomer, treated the question thus, some years ago -in _Knowledge_:--“In what way does going round a thing imply seeing -every side of it? Suppose a man shut his eyes, would that make any -difference? Or suppose the man stood still, and the monkey turned round, -so as to show the man its front and back, would the stationary man have -gone round the monkey?” - -We commend this ancient and puzzling subject of controversy to our -readers. Our own opinion is that the man _does_ walk round the monkey, -in the commonly accepted meaning of the words, but “who shall decide -when doctors disagree?” - - -BURIED ANIMALS - -Here are a few cleverly buried animals: - -“Come hither, mine friend,” said the monk, eyeing him kindly, “be a very -good boy, step through the furze bravely, and seek the lost riches.” - - _Ermine_; _monkey_; _beaver_; _zebra_; _ostrich_. - -We, as electricians, proclaim the electric motor cab a boon to London. - - _Weasel_; _baboon_. - - -QUESTIONS WELL ANSWERED - - What could not the cruet stand? - Seeing an apostle spoon. - - Why did the barmaid champagne? - Because the stout porter bitter. - - -A TABLE OF AFFINITY - -When it was reported that M. de Lesseps and his son were to marry -sisters, the _Rappel_ suggested these possible complications. Lesseps -the younger will be his father’s brother-in-law, and his wife will be -her own sister’s sister-in-law. - -If Lesseps the elder has a son, and Lesseps the younger has a daughter, -and these marry, then the daughter of Lesseps the younger will be her -father’s sister-in-law, and the son of Lesseps the elder will be the -son-in-law of his brother. The son of the second marriage will have two -grandfathers, Lesseps the elder and the younger, so that old Lesseps -will become his own son’s brother. - - -MARY QUITE CONTRARY - - Mary had a little lamb, - With feet as black as soot; - And into Mary’s bread and milk - He put his little foot. - Now Mary was an honest girl, - And scorned a hollow sham; - So the one word that Mary said - Was mother to the lamb! - - -MACARONIC VERSE - -LATIN - - “Is acer,” sed jacto his mas ter at te, - “Cantu passus sum jam?” “Notabit,” anser de; - “Mi jam potis empti, solis tento me, - For uva da lotas i vere vel se!” - -ENGLISH - - “I say, sir,” said Jack to his master at tea, - “Can’t you pass us some jam?” “Not a bit,” answered he, - “My jam pot is empty, so listen to me, - For you’ve had a lot as I very well see!” - - -HAM SANDWICHES - -We most of us know the good old double-barrelled riddle, “Why need we -never starve in the desert?” “Because of the sand which is there.” “How -did the sandwiches get there?” “Ham settled there, and his descendants -bred and mustered.” This clever metrical solution is by Archbishop -Whately:-- - - A traveller o’er the desert wild - Should ne’er let want confound him, - For he at any time can eat - The sand which is around him. - It might seem strange that he should find - Such palatable fare, - Did we not know the sons of Ham - Were bred and mustered there. - - -A GOOD MOTTO - -We know that Latin motto, with its clever double meaning, suggested for -a retired tobacconist, “_Quid rides_”--why do you smile?--or _quid_ -rides. Here is another, proposed many years ago, for a doctor of -indifferent repute:-- - - Take some device in your own way, - Neither too solemn, nor too gay; - Three ducks suppose, white, grey, and black, - And let your motto be “Quack! Quack!” - - -ON ONE NOTT - - There was a man who was Nott born, - His sire was Nott before him; - He did Nott live, he did Nott die, - His tombstone was Nott o’er him. - - -ON JOHN SO - - So died John So, - So, so, did he so? - So did he live, and So did he die, - So, so, did he so? - So let him lie! - - -STRANGE SIGHTS - -The importance of proper punctuation is very happily illustrated by the -following lines:-- - - I saw a peacock with a fiery tail - I saw a blazing comet pour down hail - I saw a cloud enwrapped with ivy round - I saw an oak tree swallow up a whale - I saw the boundless sea brimful of ale - I saw a Venice glass fifteen feet deep - I saw a well full of mens’ tears that weep - I saw wet eyes among the things that I saw - Were no sore eyes nor any other eye-sore. - - -A QUAINT INSCRIPTION - -There is a curiously constructed inscription over the door of the -cloister of the Convent of the Carmelites at Caen, which runs thus:-- - - D di Si scap ac ab as - um vus mon ulare cepit tris. - T sæ Dæ ul in in an - -The lines are in honour of one Simon Stock of that order, and they may -be freely rendered:-- - - W ho Si first beg pr - hen ly mon an his eaching. - T wi De howled to sc t - - -NONSENSE VERSE - - -IMPROMPTU, BY AN OLD DIVINE - - If down his throat a man should choose - In fun to jump or slide, - He’d scrape his shoes against his teeth, - Nor soil his own inside. - Or if his teeth were lost and gone, - And not a stump to scrape upon, - He’d see at once how very pat - His tongue lay there by way of mat, - And he would wipe his feet on that! - - -EDGAR POE’S RIDDLE - -Edgar A. Poe addressed the following puzzle-valentine to a lady, adding, -“You will not read the riddle, though you do the best you can do:”-- - - For her this rhyme is penned whose luminous eyes, - Brightly expressive as the twins of Leda, - Shall find her own sweet name, that nestling lies - Upon the page, enwrapped from every reader. - Search narrowly the lines--they hold a treasure - Divine--a talisman--an amulet - That must be worn at heart. Search well the measure. - -The first letter of the first line, the second of the second, the third -of the third, and so on spell the lady’s name--Frances. - - -AN ILLUSION OF TYPE - -A curious optical illusion is illustrated by printing a row of ordinary -capital letters and figures which are symmetrical, thus:-- - -[Illustration: SSSSSXXXXX3333388888] - -If we glance at them casually it does not strike us that their upper -parts are smaller than the lower, but if we turn the paper upside down -we are at once surprised to see how marked the difference really is. - - -AN EXCHANGE OF COMPLIMENTS - - At a tavern one night - Messrs More, Strange, and Wright - Met, good cheer and good thoughts to exchange. - Says More, “Of us three - The whole town will agree - There is only one knave, and that’s _Strange_!” - - “Yes,” says Strange, rather sore, - “I’m sure there’s one _More_, - A most terrible knave, and a bite, - Who cheated his mother, - His sister, and brother.” - “Oh yes,” replied More, “that is _Wright_!” - - -ΗΚΙΣΤΑ ΛΙΨ - -HE KISSED HER LIPS - -(_According to the daily Press, a good old-fashioned kiss lately lost -favour in some quarters._) - - Though a billiard player’s miss - Cannot meet or make a kiss; - Though a modern school of misses - Be not in the cue for kisses; - Chloe’s lips are not amiss, - Kismet! _I have_ met a kiss. - - -QUESTIONS WELL ANSWERED - -We must not fail to register these two Questions Well Answered, which it -is hard to match for excellence:-- - -Q.--Why did the fly fly? - -A.--Because the spider spied her! - -And - -Q.--Why did the lobster blush? - -A.--Because it saw the salad dressing! - -The following puzzling lines were the outburst of the wanton wit of a -lover, in his effort to play off one lady against another, and so retain -two strings to his bow:-- - - I don’t want the one that I don’t want to know - That I want the one that I want; - But the one that I do want wants me to go - And give up the one I don’t want. - - Why I don’t want the one that I don’t want to know - That I want the one that I want, - Is because, if the one that I want can’t be so, - I shall want the one I don’t want. - -Charles Lamb was responsible for the following ingenious perversion of -words, when the Whig associates of the Prince Regent were sore at not -obtaining office:-- - - Ye politicians tell me pray - Why thus with woe and care rent? - This is the worst that you can say, - Some wind has blown the wig away, - And left the hair apparent! - -We may assume that this was the germ of the riddle “What is the -difference between the Prince of Wales, a bald-headed man, and a -monkey?” One is the _heir-apparent_, the second has no _hair apparent_, -and the third is a _hairy parent_. - - -GRAMMAR OF A SORT - - When is whiskey an adverb? - _When it qualifies water._ - When does a cow become a pronoun? - _When it stands for Mary._ - -Can the conjunction “and” be used otherwise than as a connecting link? - -Yes, as in the puzzle sentence, “It was and I said not or,” which, if no -comma is placed after “said,” no one can read easily at sight. - - -A TONGUE TWISTER - -The tragedy “William Tell” was to be played many years ago at the old -Drury Lane Theatre, and an actor, familiarly known as Will, asked the -exponent of the part of Tell, on the eve of its production, whether he -thought the play would tell with the critics and the public. - -The following question and answer passed between them, in which only two -different words were used, in an intelligible sequence of twenty-five -words:-- - -_Will._--“The question has arisen Tell, ‘will Will Tell tell?’ Will Tell -tell Will ‘will Will Tell tell?’” - -_Tell._--“Tell _will_ tell Will ‘will Will Tell tell?’ ‘Will Tell _will_ -tell!’” - - -THE LADY AND THE TIGER - -Many of our readers will enjoy this very clever rendering of a -well-known Limerick:-- - - There was a young lady of Riga, - Who smiled as she rode on a tiger. - They returned from the ride - With the lady inside, - And the smile on the face of the tiger! - - Puella Rigensis ridebat, - Quam tigris in tergo vehebat; - Externa profecta, - Interna revecta, - Sed risus cum tigre manebat! - - -ANOTHER TONGUE TWISTER - - Six sieves of sifted thistles, - Six sieves of unsifted thistles, - And six thistle sifters. - -To be repeated six times rapidly and articulately. - - -NOVEL DEFINITION OF A MAN’S HAT - -Darkness that may be felt. - - -IS IT LATIN? - -The following cryptic notice was posted recently on the green baize -notice-board of a West-End Club:-- - - O nec ango in ab illi - Ardor pyram id contestata - Potor ac an non. - Si deis puto nat times - Ora res tu sed. - -For some time its message was a mystery, until the sharp eyes of a -member deciphered in what seemed to be real Latin, and was made up of -Latin words, this English sentence, appropriate to the place:--“One can -go in a billiard or pyramid contest at a pot or a cannon. Side is put on -at times, or a rest used.” - - -FOR THE CHILDREN - -A QUESTION - - How much wood would a wood-chuck chuck, - If a wood-chuck could chuck wood? - -THE REPLY - - The wood that a wood-chuck would chuck - Is the wood that a wood chuck could chuck, - If the wood-chuck that could chuck would chuck, - Or a wood-chuck could chuck wood! - - -A QUAINT CONCEIT - - The Capitol was saved of old - By geese with noisy bill; - More sage than silly, birds so bold - Should have a mission still. - - Time was when roving on the loose, - A goose would raise my dander; - But now I feel each proper goose - Should have her propaganda! - - -A LACK OF HOPS! - -A man fond of his joke, and speaking of Lenten fare to a friend in a -letter, wrote:-- - - I had a fish - In a dish - From an Archbish---- - -leaving it to his ingenuity to complete the broken line. The reply was a -clever solution to the puzzle:-- - - I had a fish - In a dish - From an Archbish---- - ’Op is not here - For he gave me no beer! - - -FOR THE CHILDREN - -The following simple calculation will be amusing to children:--If an -even number of coins or sweets are held in one hand, and an odd number -in the other, let the holder multiply those in the right hand by 2, and -those in the left hand by 3, and add together the two results. If this -is an even quantity the coins or sweets in the right hand are even, and -in the left odd; if it is odd the contrary is the case. - - -PETER PIPER’S WIFE - -(_To be read or said rapidly._) - - Betty bit a bit o’ butter, - Bitter bit! - But a better bit o’ butter - Betty bit! - - -PHONETIC VERSE - -“_A haunt each mermaid knows_” - - Eh horn teach myrrh made nose, - Buy seize wear awl groat ales; - Hear chilled wrens port inn rose, - Seek your gain steals oar wails. - - Sum son there yell oh hare, - Sums whim threw sigh leant baize; - Sow form sand fay says fare - Shy never knight sand daze. - - -PORSON’S EPIGRAM - -Porson wrote a Latin epigram on a Fellow of one of the Colleges who -always pronounced the _a_ of Euphrates short. This was wittily -translated thus:-- - - With fear on the Euphrates shore - The wild waves made him shiver. - But he thought to pass more quickly o’er, - So he _abridged_--the river! - - -ALL THE ALPHABET - -All the letters of the alphabet are used in these lines, which have such -an easy flow:-- - - “God gives the grazing ox his meat, - And quickly hears the sheep’s, low cry. - But man, who tastes his finest wheat, - Should joy to lift His praises high.” - - -A FRENCH TONGUE TWISTER - -A French mother, as she gives to her child a cup of tea to allay its -cough, says:-- - - “Ton thé t’a-t-il oté ta toux?” - - (Thy tea, has it removed thy cough?) - -This sentence, repeated rapidly, is warranted to tire the nimblest -tongue. - - -QUEER QUESTIONS AND QUAINT REPLIES - - Why does the cannon ball? - Because the Vickers Maxim - (the vicar smacks him!) - Why is the river Itchen? - Because there is a current in its bed. - - -WAS IT SCANDAL? - -Dick and Harry meet in a dim hotel passage:-- - - _Dick._--Did you hear that story about No. 288? - - _Harry_ (_all ears_).--No; what was it? - - _Dick._--Oh, it’s too gross, too gross entirely! - - _Harry._--Tell away. I’ll try to stand it. - - _Dick._--Well; 288 _is_ two gross, isn’t it? - - -AN INCONSEQUENT ECHO - -Byron in his “Bride of Abydos” is responsible for the following -strangely inconsequent echo:-- - - Hark to the hurried question of Despair, - “Where is my child?” and Echo answers, - “Where?” - -A well-conducted echo would assuredly have seconded the cry of Despair -by repeating the final syllables “my child!” - - -AN APPROPRIATE ANSWER - - Why did the Razorbill raise her bill? - To let the sea urchin see her chin! - - -CRICKET LATIN - - Bene audax. - _Well bowled!_ - - -MACARONIC VERSE - -Here is a modern specimen of Macaronic verse:-- - - Luce metat ipse sutor - (Cantas Orci madentes!) - “Qua forum an empti putor - Potor tria quarto pes!” - -Which reads into English thus:-- - - Lucy met a tipsy suitor - (Can’t a saucy maiden tease!) - “Quaff o’ rum an empty pewter - Pot, or try a quart o’ peas!” - - -MACARONIC PROSE - - -LATIN - -Puris agem, suetis a sylva bella vi olet indue mos is pura sueta far, -amar vel verre ex que sit. - - -ENGLISH READING - -Pure is a gem, sweet is a silver bell, a violet in dewy moss is purer, -sweeter far, a marvel very exquisite. - - -THE LONG AND THE SHORT OF IT - -These quaint lines were once addressed to a very tall barrister, named -Long, when he was briefless:-- - - “Longè longorum longissime, Longe, virorum, - Dic mihi, te quæso, num Breve quicquid habes?” - - -MOORE’S RIDDLE - -Thomas Moore, the poet, is responsible for the following rude riddle, -and its reply:-- - -Why is a pump like Viscount Castlereagh? - - Because it is a slender thing of wood, - That up and down its awkward arms doth sway, - And coolly spout, and spout, and spout away, - In one weak, washy, everlasting flood! - - -BIGGAR AND BIGGER - -Mrs Biggar had a baby. Which was the bigger? The baby was a little -Biggar! - -Which was the bigger, Mr Biggar or the baby? Mr Biggar was father -Biggar! - -Mr Biggar died; was the baby then bigger than Mrs Biggar? No, for the -baby was fatherless! - - -MAGIC CARD SQUARE - -Place the sixteen court cards from an ordinary pack in the form of a -square, so arranged that no row, no column, and neither of the diagonals -shall contain more than one card of each suit, and one of each rank. - -As the solution presents no difficulty, but merely calls for patience -and attention, we will leave it to the ingenuity of our readers. - - -THE ANNO DOMINI PUZZLE - -A Scottish tradesman had made, as he supposed, about £4,000, but his old -clerk produced a balance-sheet which plainly showed £6,000 to his -credit. It came upon the old gentleman as quite a disappointing shock -when presently the puzzle was solved by the discovery that in the -addition the year of Our Lord had been taken into account! - - -A PUBLIC SINK - -The following ingenious play upon words dates from the days when a -promise was made that the Thames pollution should cease in five years:-- - - In shorter time, kind sir, contrive - To purify our drink; - For while your figure is a Five - Our river is a Cinq! - - -ENGLISH AS SHE IS SPOKE - -“Mr Smith presents his compliments to Mr Brown, and I have got a hat -that is not his, and he has got a hat that is not yours, so no doubt -they are the expectant ones!” - - -PICKING FROM _PUNCH_ - -This play upon words appeared many years ago in the pages of _Punch_, -and is worth preserving:-- - - To win the maid the poet tries, - And sonnets writes to Julia’s eyes. - She likes a verse, but, cruel whim, - She still remains _averse_ to him. - - -FRENCH ALLITERATION - -“Si six scies scient six cigares, six cent six scies scient six cent six -cigares.” - -_To be said trippingly without a trip._ - -If 6 saws cut 6 cigars, 606 saws cut 606 cigars. - - -MIND YOUR STOPS! - -Here is a good illustration of the nonsense that may easily result from -the misuse of punctuation:-- - - Every lady in the land - Has twenty nails on each hand; - Five and twenty on hands and feet, - This is true without deceit. - - -A NOVEL DERIVATION - -“Yes,” said an Eton captain of the boats to his uncle, the admiral, “I -can quite believe that the British Jack Tar takes his name from that -Latin verb, which is so suggestive of a life on the ocean wave, -_jactari_, to be tossed about.” - - -AN AERATED BISHOP - -A bishop of Sodor and Man found himself entered in the visitor’s book of -a French hotel as “L’évêque du siphon et de l’homme!” - - -A HAPPY THOUGHT - - They cannot be complete in aught - Who are not humourously prone; - A man without a merry thought - Can hardly have a funny bone. - - -OUGH! - - Though the tough cough and hiccough - Make me hoarse, - Through life’s dark lough I plough - My patient course. - - -CUM GRANO SALIS - - I know Eno, you know too, - Fact is we all three know. - We know Eno, he knows you. - You know I know Eno! - - -OLD AND SOUND ADVICE - -NICHOLAS, 1828. - - He who a watch would wear - This must he do; - Pocket his watch, and watch - His pocket too! - - -COLD-DRAWN CONCLUSIONS - -Why is a lame dog like a blotting-pad? - - A lame dog is a slow pup. - - A slope up is an inclined plane. - - An ink-lined plane is a blotting-pad! - - -THE LAST OF MARY - - Mary had a little lamp, - Filled with benzoline; - Tried to light it at the fire, - Has not since benzine! - - -A BURIED WORD - -It is difficult to imagine that the very incarnation of what is wild and -forbidding is buried in those words of peace and promise, “On Christmas -Eve you rang out Angel peals,” until we find in them the consecutive -letters “ourangoutang!” - - -EVE’S APPLE - -How many apples were eaten by Adam and Eve? We know that Eve 81, and -that Adam 812, total 893. But Adam 8142 please his wife, and Eve 81242 -please Adam, total 89,384. Then again Eve 814240 fy herself, and Adam -8124240 fy himself, total 8,938,480! - - -U C I D K - -(_You see I decay!_) - - “Surely, good sir, you follow me? - It is as plain as A B C.” - “Repeat it in a treble clef, - For I am rather D E F!” - - -BURIED BY ACCIDENT - -Quite unconscious that he was burying a cat in his melodious lines Moore -wrote:-- - - “How sweet the answer Echo makes - To music at night...!” - - -A LAWYER’S PROPOSAL - - Fee simple and the simple fee, - And all the fees in tail, - Are nothing when compared with thee, - Thou best of fees, fe-male! - - -A BROAD GRIN - -“Sesquipedalia verba,” words a foot and a half long, were condemned by -Horace in his “Ars Poetica.” Had he known English, what would he have -said of “smiles,” a word so long that there is a mile between its first -and last letters? - - -SWISS HUMOUR - -A Swiss lad asked me, as I stopped quite breathless on an Alpine height, -“Do you prefer ‘monter’ to ‘descendre?’” I declared a preference for -downhill, but he most convincingly replied, “I prefer ‘mon thé’ to ‘des -cendres!’” (my tea to cinders). - - -QUESTIONS WELL ANSWERED - - Why did the penny stamp? - _Because the threepenny bit._ - Why did the sausage roll? - _Because it saw the apple turn-over._ - - -MEN OF LETTERS - - A budding author something new - Submitting, signed himself X Q. - The editor the essay read, - And begged he might be X Q Z! - - -PUZZLES ON THE PAVEMENT - -An angry street arab, who seems to have caught the infection of our -letter puzzles, was heard recently to call out to a gutter-snipe, “You -are a fifty-one ar!” (LIAR.) - - -PHONETIC ANSWERS - -Why may you pick an artist’s pocket?--Because he has _pictures_. - -What is the solace for a mind deprest?--_Deep rest_. - - -A FLIGHT OF FANCY - - There was a man from Yankeeland - Who round a walnut tree - Did run so fast--that lissome man-- - His own back he could see! - - -BURNS IN SABOTS - - “Guigne a beau de qui sabot de - Nid a beau de t’elle?” - - -DOG LATIN - -Here are all the elements of a rat hunt, expressed in Latin words:--“Sit -stillabit,” sed amanto hiscat, “sta redde, sum misi feror arat trito -unda minus, solet me terna ferret in micat.” They read into English, if -differently pointed, thus:--Sit still a bit, said a man to his cat, stay -ready, some mice I fear, or a rat try to undermine us, so let me turn a -ferret in, my cat. - - -EARLY RITUAL - -It is said that at first Adam thought Eve angelical, but there came a -time when they both took to vestments. - - -LEST WE FORGET - -If a man says that he forgets what he does not wish to remember, does he -mean to say that he does not remember what it is that he wishes to -forget; or that he is able to forget that which he does not wish to -remember? - - -QUAINT ANGLO-FRENCH QUESTION AND REPLY - - Pas qu’il ma, ou qu’il pas? - - _Marwood!_ - - -SOME POPULAR DEFINITIONS - - _Cricket._ _Lawn Tennis._ _Football._ - Lords Ladies Legs - Stumps Jumps Bumps. - - -REAL DOG LATIN - - Pax in bello. - - _The dogs of war._ - - -A QUAINT EPITAPH - - Here in S X I lies. - Killed by X S I dies. - - -A PHONETIC REPLY - -What is the French for teetotaler?--Thé tout à l’heure! - - -A FREE RENDERING - - Varietas pro Rege. - - _Change for a sovereign!_ - - -A FREE TRANSLATION - - “Splendide mendax.” - - Lying in State. - - -A WORD AND A BLOW - -When Dunlop, in playful mood, said that no one could make a good pun on -his name, a smart bystander at once exclaimed, “Lop off the end, and the -thing is done!” - - -DOG LATIN (FOR SCHOOLBOYS) - -Mitte meos super omnes ad candam aut esse homines mortui. - -The Dog Latin may be rendered thus: “Send my overalls to the tailor to -be mended.” - - -HIS L. E. G. - -Some printer’s devil must have been at work when the proof-reader found -“The Legend of the Cid,” set up in type as “The leg end of the Kid!” - - -SOLUTIONS - - -No. V.--THE MAKING OF A MAGIC SQUARE - -The perfect Magic Square, for which we have given the construction of -two preparatory squares, is formed by placing one of these over the -other, so that the numbers in their corresponding cells combine, as is -shown below. - -PREPARATORY SQUARE NO. 1. - - * - +--+--+--+--+--+ - | 1| 3| 5| 2| 4| - +--+--+--+--+--+ - | 5| 2| 4| 1| 3| - +--+--+--+--+--+ - | 4| 1| 3| 5| 2| - +--+--+--+--+--+ - | 3| 5| 2| 4| 1| - +--+--+--+--+--+ - | 2| 4| 1| 3| 5| - +--+--+--+--+--+ - -PREPARATORY SQUARE NO. 2. - - * - +--+--+--+--+--+ - | 5|15| 0|10|20| - +--+--+--+--+--+ - |10|20| 5|15| 0| - +--+--+--+--+--+ - |15| 0|10|20| 5| - +--+--+--+--+--+ - |20| 5|15| 0|10| - +--+--+--+--+--+ - | 0|10|20| 5|15| - +--+--+--+--+--+ - -THE PERFECT MAGIC SQUARE. - - +--+--+--+--+--+ - | 6|18| 5|12|24| - +--+--+--+--+--+ - |15|22| 9|16| 3| - +--+--+--+--+--+ - |19| 1|13|25| 7| - +--+--+--+--+--+ - |23|10|17| 4|11| - +--+--+--+--+--+ - | 2|14|21| 8|20| - +--+--+--+--+--+ - -No less than 57,600 Magic Squares can be formed with twenty-five cells -by varying the arrangement of these same figures, but not many are so -perfect as our specimen, in which sixty-five can be counted in -forty-two ways. These comprise each horizontal row; each perpendicular -row; main diagonals; blended diagonals from every corner (such as 6, -with 14, 17, 25, 3; or 15, 18, with 21, 4, 7); centre with any four -equidistant in outer cells; any perfect St George’s cross (such as 18, -22, 1, 15, 9); and any perfect St Andrew’s cross (such as 6, 22, 13, 5, -19). - - -No. XII.--A CENTURY OF CELLS - -Here is the solution of the ingenious Magic Square of 100 cells with 36 -cells unfilled. The rows, columns, and diagonals all add up to 505. - - +--+--+--+--+--+--+--+--+--+---+ - |91| 2| 3|97| 6|95|94| 8| 9|100| - +--+--+--+--+--+--+--+--+--+---+ - |20|82|83|17|16|15|14|88|89| 81| - +--+--+--+--+--+--+--+--+--+---+ - |21|72|73|74|25|26|27|78|79| 30| - +--+--+--+--+--+--+--+--+--+---+ - |60|39|38|64|66|65|67|33|32| 41| - +--+--+--+--+--+--+--+--+--+---+ - |50|49|48|57|55|56|54|43|42| 51| - +--+--+--+--+--+--+--+--+--+---+ - |61|59|58|47|45|46|44|53|52| 40| - +--+--+--+--+--+--+--+--+--+---+ - |31|69|68|34|35|36|37|63|62| 70| - +--+--+--+--+--+--+--+--+--+---+ - |80|22|23|24|75|76|77|28|29| 71| - +--+--+--+--+--+--+--+--+--+---+ - |90|12|13|87|86|85|84|18|19| 11| - +--+--+--+--+--+--+--+--+--+---+ - | 1|99|98| 4|96| 5| 7|93|92| 10| - +--+--+--+--+--+--+--+--+--+---+ - -Notice that the top and bottom rows contain all the numbers from 1 to 10 -and from 91 to 100; the two rows next to these range from 11 to 20 and -from 81 to 90; the two next from 21 to 30 and from 71 to 80; the two -next from 31 to 39 and 60 to 70, excluding 61, but including 41; and the -two central rows the numbers run from 42 to 59, with 40 and 61. - - -No. XXIII.--TWIN PUZZLE SQUARES - -The following diagram shows how the twin Magic Squares are evolved from -our diagram:-- - - +-+-+-+ +-+-+-+ - |1|5|6| |2|3|7| - +-+-+-+ +-+-+-+ - |2|6|7+====+3|4|8| - +-+-+-+ +-+-+-+ - |3|7|8| |4|5|9| - +-+-+-+ +-+-+-+ - -The sums of the corresponding rows in each square are now equal, and the -sums of the squares of the corresponding cells of these rows are equal. -The sums of the four diagonals are also equal, and the sum of the -squares of the cells in corresponding diagonals are equal. The sum of -any two numbers symmetrically placed with respect to the connecting link -between the 7 and the 3 is always 10. - - -No. XXX.--THE UNIQUE TRIANGLE - -The figures to be transposed in triangle A are 9 and 3 and 7 and 1. - - /\ /\ - / \ / \ - / 5 \ / 5 \ - / \ / \ - / 4 6 \ / 4 6 \ - / \ / \ - / 3 7 \ / 9 1 \ - / \ / \ - / 2 1 9 8 \ / 2 7 3 8 \ - ------------------ ------------------ - A B - -Then in triangle B, the sum of the side is in each case 20, and the sums -of the squares of the numbers along the sides is in each case 126. - - -No. XXXI.--MAGIC TRIANGLES - -The subjoined diagram shows the order in which the first 18 numbers can -be arranged so that they count 19, 38, or 57 in many ways, down, across, -or along some angles, 19 in 6 ways, 38 in 12, and 57 in 14 ways. - -[Illustration] - -Thus, for examples-- - - 7 + 12 = 14 + 5 = 4 + 15 = 19 - - 7 + 11 + 14 + 6 ------- = 38 - - 7 + 14 + 4 + 5 + 12 + 15 = 57 - - -No. XXXIV.--MAGIC HEXAGON IN A CIRCLE - -The figures in the Magic Hexagon must be arranged as is shown in this -diagram:-- - - 126 - 5 2 7 3 8 5 - 8 2 4 6 3 7 - 114 114 - 4 6 9 1 8 2 - 3 1 9 7 5 4 1 9 6 - 1 3 7 9 8 6 7 3 4 - 8 2 3 9 1 9 - 126 126 - 6 4 4 1 8 2 - 5 5 6 7 2 5 - 114 - -It will be seen that the sum of the four digits on each side of each -triangle is twenty, and that, while their arrangements vary, the total -of the added squares of the numbers on the alternate sides of the -hexagon are equal. - - -No. XXXVI.--A CHARMING PUZZLE - - ✦ ✦ ✦ - - ✦ ✦ ✦ - - ✦ ✦ ✦ - -To pass through these nine dots with four continuous straight lines, -start at the top right-hand corner, and draw a line along the top of -the square and _beyond its limits_, until its end is in line with the -central dots of the side and base. Draw the second line through these, -continuing it until its end is below and in line with the right-hand -side of the square; draw the third line up to the starting-point, and -the fourth as a diagonal, which completes the course. - - -No. XXXVII.--LEAP-FROG - -On a chess or draught-board three white men are placed on squares marked -_a_ and three black men on squares marked _b_ in the diagram-- - - +---+---+---+---+---+---+---+ - |_a_|_a_|_a_| |_b_|_b_|_b_| - +---+---+---+---+---+---+---+ - 1 2 3 4 5 6 7 - -Every _a_ can move from left to right one square at a time, and every -_b_ from right to left, and any piece can leap over one of another -colour on to an unoccupied square. They can reverse their positions -thus:-- - -If we number the cells or squares consecutively, and notice that at -starting the vacant cell is No. 4, then in the successive moves the -vacant cells will be 3, 5, 6, 4, 2, 1, 3, 5, 7, 6, 4, 2, 3, 5, 4. Of the -moves thus indicated six are simple, and nine are leaps. - - -No. XXXVIII.--SORTING THE COUNTERS - -The counters are changed in four moves only, moving two at a time as -follows:-- - - 1 2 3 4 5 6 7 8 9 10 - +---+---+---+---+---+---+---+---+---+---+ - | ○ | ● | ○ | ● | ○ | ● | ○ | ● | | | - +---+---+---+---+---+---+---+---+---+---+ - - 1 2 3 4 5 6 7 8 9 10 - +---+---+---+---+---+---+---+---+---+---+ - | | | ● | ● | ● | ● | ○ | ○ | ○ | ○ | - +---+---+---+---+---+---+---+---+---+---+ - - Move 2 and 3 to 9 and 10. - - „ 5 and 6 to 2 and 3. - - „ 8 and 9 to 5 and 6. - - „ 1 and 2 to 8 and 9. - - -No. XXXIX.--A TRANSFORMATION - -To change the ten-pointed star of wooden matches into one of five points -without touching it, let a little water fall into the very centre, as it -lies on quite a smooth surface, and in a few moments, under the action -of the water, it will gradually assume the shape shown in the second -diagram, of a five-pointed star. - -[Illustration] - -This is a very simple and effective after-dinner trick. Small matches -move best. - - -No. XLI.--FAST AND LOOSE - -The twelve counters or draughtsmen lying loosely at the bottom of a -shallow box can be arranged so that they wedge themselves together and -against the side thus:-- - -[Illustration] - -Place one for the moment in the centre, and six round it. Hold these -firmly in their places with the left hand, and fix the other five round -them, as is shown in the diagram. Then remove the temporary centre, and -fill in with it the vacant place. All will then be in firm contact, and -the box may be turned upside down without displacing them. - - -No. XLIII.--FOR CLEVER PENCILS - -This diagram, shows how a continuous course is possible without taking -pencil from paper, or going twice over any line. - -[Illustration] - -We have purposely left spaces wide enough to make the solution perfectly -clear. - - -No. XLVIII.--A BOTTLED BUTTON - -[Illustration] - -The diagram below shows how the thread within the bottle is severed so -that the button falls, without uncorking the bottle or breaking it. - -Nothing is needed but a lens to focus the rays of the sun, which pass -through the glass without heating it, and burn the thread. - - -No. XLIX.--CLEARING THE WAY - -In order to cause the coin to fall into the bottle without touching -coin, match, or bottle, let a drop or two of water fall upon the bent -middle of the match. - -[Illustration] - -Very soon, under the action of the water, the two ends of the match will -open out so that the coin which was resting on them falls between them -into the bottle. - - -No. LII.--BILLIARD MAGIC - -The diagram we give below shows the ingenious trick by which the plain -white, if struck gently with a cue, will, aided by the tumbler, pot the -spot white ball without in any way disturbing the red. - -[Illustration] - -The balls to start with are an eighth of an inch apart, and there is not -room for a ball to pass between the cushions and the red. Place the -tumbler close to spot white. - - -No. LIII.--THE NIMBLE COIN - -The most effective way to transfer the coin from the top of the circular -band of paper into the bottle is to strike a smart blow with a cane, or -any small stick, on the inside of the paper band. There is not time for -the coin to be influenced in the same direction, and it falls plumb into -the neck of the bottle. - -[Illustration] - - -No. LVIII.--WHAT WILL HAPPEN? - -When the boy shown in this picture blows hard at the bottle which is -between his mouth and the candle flame, the divided air current flows -round the bottle, reunites, and extinguishes the flame. - -[Illustration] - - -No. LX.--VIS INERTIÆ - -If, by a strong pull of my finger, I launch the draughtsman that is on -the edge of the table against the column of ten in front of it, the -black man, which is just at the height to receive the full force of the -blow, will be knocked clean out of its place, while the others will not -fall. This is another illustration of the _vis inertiæ_. - -[Illustration] - - -No. LXI.--CUT AND COME AGAIN - -A block of ice would _never_ be divided completely by a loop of wire on -which hangs a 5 ℔ weight. For as the wire works its way through, the -slit closes up by refreezing, and the weight falls to the ground with -the wire, leaving the ice still in a single block. - -[Illustration] - - -No. LXIII.--CATCHING THE DICE - -It is quite easy to throw the upper of this pair of dice into the air -and catch it in the cup, but the other is more elusive. As you throw it -upward with sufficient force you will also throw the die that has been -already caught out of the cup. - -[Illustration] - -The secret of success lies in dropping the hand and cup rapidly -downwards, quitting hold at the same moment of the die, which then falls -quietly into the cup held to receive it. - - -No. LXIV.--WILL THEY FALL? - -When the single domino shown in the diagram in front of the double -archway, is quite smartly tipped up by the forefinger carefully inserted -through the lower arch, the stone which lies flat below another _is -knocked clean out_, while none of the other stones fall, another -practical illustration of _vis inertiæ_. - -[Illustration] - -For this very curious trick, club dominoes, thick and large, should be -used. Some patience and experience is needed, but success at last is -certain. - - -No. LXV.--A TRANSPOSITION - -You will be able to place the shaded coin between the other two in a -straight line without touching one of these, and without moving the -other, if you place a finger firmly on the king’s head and then move the -shaded coin an inch or two to the right, and flick it back against the -coin you hold. The other “tail” coin will then spring away far enough to -allow the space that is required. - -[Illustration] - - -No. LXVI.--COIN COUNTING - -After reaching and turning the coin which you first call “four,” _miss -three coins_, and begin then a fresh set of four; repeat this process to -the end. - - -No. LXVIII.--NUTS TO CRACK - -Hold a cup of water so that it will wet the handle of the knife, then -remove it, and place the nut exactly on the spot where the drop of water -falls from the handle. - - -No. LXXI.--WHAT IS THIS? - -The photographic enlargement is simply a much magnified reproduction of -Mr Chamberlain’s eye and eyeglass, exactly as they appear in the picture -which we give below, taken from its negative. A strong condensing lens -will reproduce the original effect, which can also be obtained by -holding the enlargement at a distance. - -[Illustration] - -[Illustration] - - -No. LXXV.--THE SEAL OF MAHOMET - -[Illustration] - -This double crescent may be drawn by one continuous line, without -passing twice over any part, by starting at _A_, passing along the curve -_AGD_, from _D_ along _DEB_, from _B_ along _BFC_, and from _C_ along -_CEA_. - - -No. LXXVI.--MOVE THE MATCHES - -If fifteen matches are arranged thus-- - - --------| --------| -------| - | | | | | |\ | - | | | |-------| | \ | - | | | | | | \ | - |-------- |-------- |------- - -and six are removed, ten is the number that remains, thus-- - - ------- ------- |\ | - | | | \ | - | |------ | \ | - | | | \ | - | |------ | \| - -or one hundred may remain, thus:-- - - -------| -------| - | | | | | - | | | | | - | | | | | - | |------- |------- - - -No. LXXVII.--LINES ON AN OLD SAMPLER - -This diagram shows the arrangement in which seventeen trees can be -planted in twenty-eight rows, three trees in each row:-- - -[Illustration] - - -No. LXXXI.--COUNTING THEM OUT - -Here is an arrangement of dominoes which enables us to count out the -first twelve numbers, one after the other, by their spelling:-- - - +---+---+---+---+---+---+---+---+---+---+---+---+ - | 2 | 3 | 4 | 3 | 2 | 5 | 2 | 6 | 6 | 0 | 1 | 5 | - | | | | | | | | | | | | | - | 4 | 1 | 5 | 4 | 0 | 3 | 3 | 6 | 5 | 1 | 2 | 5 | - +---+---+---+---+---+---+---+---+---+---+---+---+ - -Start with the double five, and, touching each stone in turn, say o, n, -e, _one_; remove the stone with one pip, and go on, t, w, o, _two_; -remove the two, and say t, h, r, e, e, _three_, and so on till you -reach at last the twelve. - -Playing cards can be used, counting knave, queen, as eleven, twelve. It -makes quite a good trick if you place the cards face downwards in the -proper order, and then, saying that you will call up each number in -turn, move the cards one at a time to the other end, spelling out each -number as before, either aloud or not, and turning up and throwing out -each as you hit upon it. If you do not call the letters aloud it adds to -the mystery if you are blindfolded. - - -No. LXXXII.--TRICKS WITH DOMINOES - -This is the other combination of stones and their pips which fulfils the -conditions, and forms the word AGES. - - +---+-------+---+ +-------+-------+ +---+-------+---+ +-------+-------+ - | 6 | 6 5 | 5 | | 6 4 | 4 0 | | 1 | 1 1 | 1 | | 0 5 | 5 3 | - | +-------+ | +---+---+-------+ | +-------+ | +---+---+-------+ - | 0 | | 4 | | 6 | | 6 | | 4 | | 0 | - +---+---+---+---+ | | +-------+ +---+---+ +---+ | +-------+---+ - | 0 0 | 4 4 | | 3 | | 4 2 | | 6 6 | | 2 | 2 2 | 2 | - +---+---+---+---+ +---+ +---+---+ +---+---+ +---+ +---+-------+ | - | 0 | | 4 | | 3 | | 2 | | 6 | | 0 | | 5 | - | | | | | +-------+ | | +-------+ | +-------+---+---+ - | 1 | | 3 | | 3 | 3 1 | 1 | | 2 | 2 3 | 3 | | 1 5 | 5 5 | - +---+ +---+ +---+-------+---+ +---+-------+---+ +-------+-------+ - - +-------+-------+ +---+-------+ +---+-------+---+ +---+ +---+ - | 6 5 | 5 3 | | 1 | 1 5 | | 1 | 1 1 | 1 | | 5 | | 0 | - +---+---+-------+ | +---+---+ | +-------+ | | | | | - | 6 | | 0 | | 5 | | 6 | | 2 | | 4 | | 3 | - | | +---+ | | +---+ +---+ +---+ +---+ - | 0 +-------+ | 0 | | 2 | | 6 | | 4 +-------+ 3 | - +---+ 0 2 | | +---+---+ | | | | 4 3 | | - | 0 +-------+ | 4 | 4 2 | | 6 | | 4 +-------+ 3 | - | | +---+---+---+ +---+ +---+ +---+ +---+ - | 0 | | 4 | | 2 | | 6 | | 2 | | 4 | | 3 | - +---+---+-------+ | | | | | +-------+ | | | | | - | 0 5 | 5 5 | | 6 | | 6 | | 3 | 3 2 | 2 | | 1 | | 1 | - +-------+-------+ +---+ +---+ +---+-------+---+ +---+ +---+ - -In both cases a complete set of stones is used, which are arranged in -proper domino sequence, and everyone of the eight letters carries -exactly forty-two pips. - - -No. XCI--THE STOLEN PEARLS - -The dishonest jeweller reset the pearls in a cross so that its arms were -a stage higher up. It will be seen that by this arrangement nine pearls -can still be counted in each direction. - -[Illustration] - - -ENIGMAS - - -1. Self-assassin, a neddy. Saw an ass in an eddy! - - -2. To get her: Together. - - -3. A candle. - - -4. Liquorice. - - -5. A book. - - -6. One solver proposes _raven_, croaking before a storm; once an object -of worship; seldom seen; forbidden in Leviticus as food; alone with Noah -when its mate was sent forth; weighing about 3 lbs; the name of a small -South Carolina island, having as its first and last letters R and N; the -Royal Navy. - -Another finds in _K_ the key, as that letter with _no ar_ is alone in -_ark_. With much ingenuity he shows that the last line calls for a -second letter, and that the letters _K_ and _G_ can be traced -throughout almost all Hallam’s “lights;” _Kilogram_ being nearly 3 lbs., -and _Knot_ a mile; while either _K.G._ (Knight of the Garter) or _King_ -would fit the final line. - - -7. The lines become “rank treason” if the corresponding lines of the two -stanzas are read together, thus:-- - - The pomps of Courts and pride of Kings - I fain would banish far from hence, - -and so on throughout. - - -8. A pair of skates. - - -9. A shadow. - - -10. A chair. - - -11. The changes that are rung are one, eno, Noe, neo, eon, on, none. - - -12. Cares, caress. - - -13. Echo. - - -14. Strike. - - -15. A pair of spurs. - - -16. A.D.A.M.; Adam; a dam; Adam; a damson; a dam. - - -17. The CID, the Castilian hero whose fame was at its height in the -middle of the eleventh century. - - -18. A sigh. - - -19. Coxcomb. - - -20. Jack and Jill. - - -21. A man’s felt hat. - - -22. Measurable. - - -23. Chair, char, arch. - - -24. Sala (G.A.S.), which reversed is _alas_. - - -25. Page, (p)age. - - -26. C (sea), A (hay), T (tea). - - -27. A BROKEN TALE - - The deil jumped over the clouds so high - That he bounded almost right over the sky. - Over gates and fields, and under the trees - He dodged, with his tail dragging over all these, - But, alas! made a terrible blunder, - For a twist in his tail hooked under a rail, - And broke that appendage asunder. - - -28. Yesterday. _Most_ excludes Adam, and _ter_ is half of _terror_. - - -29. Donkey. - - -30. Mental, lament, mantle. - - -31. His heels. - - -32. Tares, tears, a rest. - - -33. Connecticut. - - -34. Grate, rate, rat, ate. - - -35. Mary, in fanciful mood, on her thirty-sixth birthday, decorated her -pincushion thus--XXXVI. - - -36. Opinionist. - - -37. Violin (LVII + on). - - -38. Trout (tr--out). - - -39. Post--stop. - - -40. A pair of scissors in a case. - - -41. Dog. - - -42. Mainland. - - -43. Changed. - - -44. The name of the Russian nobleman’s third son, the boy who went to -sea, was Yvan. As the name of the eldest, Rab, who became a lawyer, was -Bar reversed, and that of the soldier son Mary was Army as an anagram, -so Yvan’s name resolves itself into Navy, his profession. - - -45. VIVID. - - -46. Nothing. - - -47. London. - - -48. Rock, cork. - - -49. Place, lace, ace, lac. - - -50. a, e, i, o, u, y. - - -51. The solution of the enigma which begins:-- - - “Twice six is six, and so - Six is but three; - Three is just five you know, - What can we be?” - -is the number of letters of the alphabet used in spelling a number. Thus -twice six, or _twelve_, is composed of six letters, and so on. - - -52. A button. - - -53. LEVEL--MADAM. - - -54. An egg. - - -55. Vague. - - -56. - - A headless man had a letter to write, - (The letter O, i.e. _nothing_.) - He who read it had lost his sight, - (He read _nothing_.) - The dumb repeated it word for word, - (He said _nothing_.) - And deaf was he who listened and heard. - (He heard _nothing_.) - - -57. Highway. - - -58. A set of false teeth. - - -59. The “fearful fate” enigma is slaughter; cut off its head and we have -laughter; lop off its shoulders and we find aught. - - -60. Speculation--peculations. - - -61. The word “united” is “of fellowship the token,” and the requirement -“reverse it, and the bond is broken” refers only to the two central -letters. When this is reversed the word “untied” is formed. - - -62. Average. - - -63. German--manger. - - -64. Corkscrew. - - -65. _Tar_ is transformed by _Art_, and as a sailor is fond of port, and -blisters in the sun. When it turns to run it becomes _Rat_, and when it -doubles it is _Tartar_, and is caught. - - -66. - - A man with one eye two plums must have seen, - One perfectly ripe, the other quite green. - The former he took, and ate it with pleasure, - The other he left to ripen at leisure. - - -67. A widower who has lost two wives. - - -68. The grape-vine on the Marquis of Breadalbane’s estate, Killin, N.B., -which bears more than 5000 bunches of grapes, of which only 500, -properly thinned out, are allowed to mature, so that the fewer and -smaller bunches bear finer fruit. - - -69. Poe, poet, poetry. - - -70. Theatres. The articles _the_ and _a_ lead on to the other four -letters _tres_, and these form the word _rest_, if the _t_ is -transferred to the end. - - -71. Scold, cold, old. - - -72. Justice, (_just_--_ice_). - - -73. A shadow. - - -74. VI., IV., I. - - -75. The letter I. - - -76. The letter V. - - -77. An army. - - -78. _A rich table_; _chair_, _table_; _charitable_. - - -79. High-low. - - -80. Orange, pear, date, banana, peach, plum, lime, lemon, mango, apple. - - -81. Innuendo. - - -82. Snipe, of which _pines_ is an exact anagram. - - -83. - - None can locate the subject of my riddle, - For all the world would seek its place in vain, - Cut it asunder almost in the middle, - And in our very midst its place is plain - -is solved by _nowhere_, _now here_. - - -CHARADES - - -1. Good-night (knight). - - -2. Grandson. - - -3. Oyster. - - -4. Stay-lace. - - -5. Ann--ounce. - - -6. VOID, OVID. - - -7. Disconsolate (disc--on--so--late). - - -8. Ginger--Nigger. (G.E.R. Great Eastern Railway). - - -9. Honesty (hone, below the razor). - - -10. Nutmeg. - - -11. Waterloo. - - -12. Whether (whet--her). - - -13. Mendicant (mend I can’t). - - -14. Campbell. - - -15. Foxglove. - - -16. Anglesea. - - -17. Shewed. - - -18. Sparrow, often a gutter percher! - - -19. Dishonest (dish--one--st). - - -20. Dogmatism. - - -21. Anthem. - - -22. Gigantic (gig--antic). - - -23. Toad (_ad_ is Latin for _to_). - - -24. Cineraria (sinner--area). - - -25. Ignis--fatuus, or Will-o’-the-wisp (ignis, fire--fatuus, a fool). - - -26. Isis (sis in Latin, _thou mayest be_). - - -27. Capacity. - - -28. Scarcity. - - -29. Pardon. - - -30. Humbug. - - -31. Ramrod. - - -32. Dumpling. - - -33. Into. - - -34. Herring. - - -35. Dublin (bud--nil). - - -36. Peerless. - - -37. Beatrice. - - -38. Beam--_be_ is half of the word _verb_, _am_ is half of _same_, and -_be_ and _am_ are similar in sense. - - -39. Pulpit. - - -40. Spare--rib. - - -41. Usher. - - -42. The ship _Carmania_. - - -43. Candid. - - -44. Husbandman. - - -45. Hamlet. - - -46. Handcuff. - - -47. Sinecure. - - -48. Infancy. - - -49. Teachest. - - -50. Hippodrome. - - -51. Invalid. - - -52. Woman. - - -53. Kensington. - - -54. Benjamin. - - -55. Stipendiary. - - -56. Wonder. - - -57. Cabin. - - -58. Falstaff. - - -59. Periwinkle. - - -60. Nameless. - - -61. Fourscore. - - -62. Hatred. - - -63. Catsup. - - -64. Molestation. - - -65. Omen. - - -66. Isinglass. - - -67. Muffin. - - -68. Footman. - - -69. Sparrow-grass. - - -70. Matchless. - - -71. Planted. - - -72. Toast-rack. - - -73. Half-and-half, if properly punctuated. - - -RIDDLES AND CONUNDRUMS - - -1. Washerwoman. - - -2. - - “Call me an uncle, then you speak me fair, - Call me an _uncle_-_an_ uncle if you dare!” - - -3. Pluck the goose. - - -4. Also. - - -5. A lawsuit. - - -6. Because they are bargains. - - -7. A pair of shoes. - - -8. Because whenever he goes out he can put his portmanteaux (Portman -toes) into his boots. - - -9. FIVE. - - -10. Rail--liar. - - -11. Because it slopes with a flap! - - -12. In California they eat all the peaches they can, and can all they -can’t! - - -13. The utmost effort ever made by a piebald (or by any) horse at a high -jump is _four feet from the ground_! - - -14. Insatiate (in--sat--I--ate). - -The clever couplet-- - - Under my first my second stood. - That’s your riddle: mine’s as good! - -was intended to point out that the enigma - - In my first my second sat, - Then my third and fourth I ate - -was _understood_, and to frame at the same time a fresh one of similar -sort. - - -15. A gardener minds his peas, a billiard-marker his cues, a precise man -his p’s and q’s, and a verger his keys and pews. - - -16. A man with one eye can see more than a man with two, for in addition -to all else he can see the other man’s two eyes, which can only see his -one. - - -17. When you ask a policeman what o’clock it is, you are like the -Viceroy of India, because you are _as king for the time_. - - -18. “What does Y E S spell?” is the question to which “yes” is the only -possible reply. - - -19. An umbrella. - - -20. London for many years was a wonderful place for sound, for you could -laugh at 5 p.m. at Waterloo Junction, and by walking briskly across the -river be in time for the late Echo at Charing Cross. - - -21. Because it may be smelt! - - -22. The full reading of “1s. 6d. me a bloater” is “Bob Tanner sent me a -bloater.” - -_Note._--If any solver should ask, “But where is the ‘sent’?” we reply, -“The scent was in the bloater!” - - -23. The solution of the prime conundrum “Why is a moth flying round a -candle like a garden gate?” is--Because if it keeps on it singes its -wings (its hinges it swings). - - -24. (Twe)lve--twe(nty) = twenty. - - -25. Because it would be my newt (minute). - - -26. The steps by which, in paying my debt to a lawyer, a threepenny -piece swells to the needed six and eightpence are these:-- - - Three pence is one and two pence; - One and two pence is fourteen pence; - Fourteen pence is six and eight pence! - - -27. When the Vickers Maxim (vicar smacks him). - - -28. Children should go to bed soon after tea because when “t” is taken -away _night_ is _nigh_. - - -29. Scottish may be lighter than Irish men, for while Irishmen may be -men of Cork, Scotsmen may be men of Ayr. - - -30. Because barbers do not cut hair any longer! - - -31. Colenso. - - -32. This is Archbishop Whately’s riddle, and a solution, suggested long -after his offer of £50 had expired:-- - - When from the Ark’s capacious round - Mankind came forth in pairs, - Who was it that first heard the sound - Of boots upon the stairs? - - To him who cons the matter o’er, - A little thought reveals, - He heard it first who went before - Two pairs of soles and eels! - - -33. If Moses was the son of Pharaoh’s daughter, _he_ was the daughter of -Pharaoh’s son. - - -34. The word of three syllables which represents woman or man -alternately by three contractions is heroine--hero--her--he. - - -35. Solution to-morrow! - - -36. Wholesome. - - -37. They were jolly well tired! - - -38. The stocks. - - -39. Because it makes a far--thing present. - - -40. If I were in the sun, and you were out of it, it would be a _sin_. - - -41. COLD. - - -42. Take _off_--_ice_. - - -43. Enduring. - - -44. Uncross the “t” of “a foot,” and it becomes “a fool.” - - -45. A rabbit can run into a square wood with sides that each measures a -mile, keeping always in a straight line, _until it reaches the middle of -the wood_, when it must begin to run out of it! - - -46. To-morrow. - - -47. Scar--bo--rough. - - -48. - - Though I in time for lunch may be, - U cannot come till after T. - - -49. A wig. - - -50. Because _we_ cannot be _wed_ without it. - - -51. A spit. - - -52. Wit (double you--I--tea). - - -53. Holding up your hand you will see what you never have seen, never -can see, and never will see--namely, the little finger as long as the -finger next to it! - - -54. The Emperor of Russia issues manifestoes. An ill-shod beggar -manifests toes without his shoes! - - -55. To show Walsham How a good bishop is made. - - -56. There was certainly a tribe of Man--asses. - - -57. L. s. d. - - -58. A pillow. - - -59. Abused (a--b--used). - - -60. A settler. - - -61. Because John Burns. - - -62. It looks round! - - -63. A minute. - - -64. A deaf and dumb man cannot tickle nine persons, because he can only -gesticulate (just tickle eight!). - - -65. London always began with an _l_, and end always began with an _e_! - - -66. Season. - - -67. The new moon, for the full moon is much lighter. - - -68. Island (_la_ is the middle, _is_ is the beginning, _and_ is the -end!). - - -69. Because! (_bee caws_). - - -70. The reading of the Dark Rebus - - O - B =e= D - -is--a little blackie in bed with nothing over him. - - -71. If a monkey is placed before a cross it at once gets to the top, for -APE is then APEX. - - -72. The answer to this riddle, defined as “two heads and an -application,” is _a kiss_. - - -73. The Latin expression of encouragement “macte” may be applied in its -English equivalent _in-crease_ to a batsman when an umpire says of him -“not out” after a risky run. - - -74. The place which answers to the description “Half an inch (ch) before -the trees (elms), half a foot (fo), and half a yard (rd) after them -leads us to an English town,” is _Chelmsford_. - - -75. The subject of the riddle, which none can locate, is _nowhere_. Cut -asunder almost in the middle, it breaks into the opposite extreme, and -becomes _now here_! - - -76. The two letters which in nine letters describe the position of one -who has been left alone in his extremity are a _b_ and one _d_. -_Abandoned._ - - -77. Usher (us--her). - - -78. You can make a Maltese cross with less than twelve unbent and -unbroken matches, by striking only one match and dropping it down his -back. If the first fails, try another! - - -79. We may suppose that there were less vowels than we have now in the -early days of _Noe_, when _u_ and _i_ were not there. - - -80. An orange (or--ange). - - -81. The moral taught to us by the old emblem of a weathercock in the -shape of a fish on a church near Lewes is, “It is vain to aspire!” - - -82. FIDDLE. - - -83. The words “for the want of water we drank water, and if we had had -water we should have drank wine,” were spoken by the crew of a vessel -that could not cross the harbour bar for want of water, and who had no -wine on board. - - -84. - - The poor have two, the rich have none, - Millions have many, you have one, - -is solved by O. - - -85. Money. - - -86. Had _I_ been in Stanley’s place when Marmion cried “On, Stanley, -on!” the resulting word _on_-_i_-_on_ would have made the Scottish fray -seem more like Irish stew. - - -87. The figure O. - - -88. - - Let her be, or beat her, - Give her little ease; - Then in safety seat her - All among the bees, - -is solved by _A Queen Bee_. The _Bee_ is made up of the letter _b_, in -Greek called _beta_, and two little _e_s. - - -89. Its. - - -90. Inch--chin. - - -NUTS TO CRACK - - -1. CRAZY LOGIC - -Can you prove that madman = madam is solved thus:-- - -A madman is a man beside himself. Therefore a madman = two men. - -Madam is a woman. Woman is double you O man (w-o-man). Therefore madam = -two men. - -And as things which are equal to the same are equal to one another, -therefore madman = madam. - - Q. E. D. - (_Quite easily Done._) - - -2. A BIT OF BOTANY - -The water-plant is the _Frogbit_, which floats and spreads on the -surface of ponds and pools. - - -3. The six islands buried in the lines-- - - He set down the answer to that sum at random. - - By bold policy Prussia became a leading power. - - A great taste for mosaic has arisen lately. - - The glad news was swiftly borne over England. - - At dusk, year after year, the old man rambled home. - - The children cried, hearing such dismal tales. - -are Sumatra, Cyprus, Formosa, Borneo, Skye, Malta. - - -4. The seven geographical names “buried” in the sentence, “We could hide -a light royal boat with a man or two; the skipper, though, came to a -bad end,” are Deal, Troy, Witham, Esk, Perth, Baden, Aden. - - -5. The jumbled letter lines read thus:-- - - Let those who deal in mystic rhymes - This transposition trace; - And to _The Standard_ send betimes - Each letter in its place. - - -6. - - Three little articles all in a line - Lead to a thousand, expressing, - If with another all these you combine, - What can be never a blessing-- - -is solved by ANATHEMA (an-a-the-M-a). - - -7. - - Ask a policeman, possibly he knows - In uniformed array - If not, an added letter plainly shows - How little he can say-- - -is solved by adding n _to uniformed_--_uninformed_. - - -8. The Ruling letters in:-- - - We rule the world, we letters five, - We rule the world, we do! - And of our number three contrive - To rule the other two-- - -are B. U. T. (beauty), and Y. Z. (wise head). - - -9. Many might punctuate the sentence, “Maud like the pretty girl that -she was went for a walk in the meadows” by merely putting a full stop at -the end of it. But why not make a _dash after Maud_? - - -10. The answer by Echo to - - What were they who paid three guineas - To hear a tune of Paganini’s - -is _Pack o’ ninnies_! - - -11. The verse in which only five different letters are used is-- - - It is nineteen tennis nets, - Nine in tents in tints intense. - Ten sent in inset in sets, - See it, test it, it is sense! - - -12. The catch sentence: “If is is not is and is not is is what is it is -not is and what is it is is not if is not is is?” becomes intelligible -if it is punctuated thus: If “is” is not “is,” and “is not” is “is,” -what is it “is not” is, and what is it “is” is not, if “is not” is “is?” - - -13. The words on the placard were PALE ALE, and these through the steps -described become PA-LE AP-LE, APPLE. - - -14. The reading of “Time flies you cannot they pass at such irregular -intervals,” is as though it ran “You cannot time flies, they pass at -such irregular intervals.” - - -ROYAL MEMORIES - -15. I was reminded of Queen Victoria as I entered the South Kensington -Museum at _five minutes to one_, because I noticed that the hands of my -watch were so placed as to represent a very perfect V. - -When I left the building it was _twenty-five minutes and forty-five -seconds to six_, and then the hands, with the help of the seconds hand -which crossed it, formed a very perfect A, and so reminded me of Prince -Albert. - - -16. The solution of - - CCC - --- - SAW - -is “the season was backward.” - - -17. THE OLD LATIN LEGEND - - +------------------+ - | AMANS TAM ERAT | - | HI DESINT HERO | - |AD DIGITO UT MANDO| - +------------------+ - -reads off into excellent English thus:-- - -“A man’s tame rat hides in the road; dig it out man, do!” - - -18. The statement “I know that roseate hues preserve” does not imply -that there is any curative virtue in rose-coloured rays, but asserts “I -know that Rose ate Hugh’s preserve!” - - -19. The following exception was taken to Dr Fell’s diet for the sick of -all sops:-- - - “Sure the doctor’s wits are failing,” - Cried a saucy wag. - “Allsopp’s ale the sick and ailing - To their bier will drag.” - - -20. The English dislocated sentence formed by these thirty-six -letters:-- - - SAR BAB SAR BAB SAR BAB - SAR BAB SAR BAB SAR ARA - -is, “A bar as a barb bars Barbara’s Barabbas.” - - -21. The Wiltshire farmer’s sentence-- - - “Igineyvartydreevriswutts” - -when interpreted runs, “I gave him forty-three for his oats.” - - -22. Here is a tolerable rhyme to Chrysanthemum:-- - - Through gardens where appear - Beds of chrysanthemum, - We pass at eve to hear - Our choir their anthem hum. - - -23. This was, in brief, the pathetic tale of the three eggs--“_Two -bad!_” - - -24. THE ANCIENT LEGEND - - +--------------+ - |Doun tooth ers| - | A sy | - | Ouw ould bed | - | One by | - +--------------+ - -reads thus:--“Do unto others as you would be done by.” - - -25. There were but six persons in the vault which contained two -grandmothers and their two grand-daughters; two husbands and their two -wives; two fathers and their two daughters; two mothers and their two -sons; two maidens and their two mothers; two sisters and their two -brothers. Two widows had each one son, and each married the son of the -other, and had a daughter by the marriage. - - -26. The supposed charm-- - - ground - turn evil star - -given by the wise woman to a nervous couple, to counteract their evil -star, and account for mysterious noises, is merely “Rats live -underground,” _turn_ being a direction to the solver. - - -27. The word composed of five varied vowels of foreign sound, with but -one consonant between them, is oiseau, the French for bird. The three -letters which flow in four are eau, water, which flows in the River -Oise, and the other trio spell oie, a goose, which is found therein. - - -28. The Paradox-- - - What in his mind no man can find - Four symbols will display; - But only one remains behind - If one we take away-- - -is solved by _Bone_. - - -29. The barber who had placed in his window the notice-- - - “What do you think - I will shave you for nothing and give you a drink” - -explained, to the man who expected a free shave and a cool drink, that -the interpretation was really this:--“What? Do you think I will shave -you for nothing, and give you a drink?” - - -30. The curious Latin label-- - - +-------------------------+ - | G E N U I N E J A M | - | A | - | I C A R U M. | - +-------------------------+ - -has no reference to Icarus, or to flying machines. Its proper place was -on a cask of “Genuine Jamaica Rum.” - - -31. The puzzle word is ipecacuanha. - - -32. - - Johnson’s cat went up a tree, - Which was sixty feet and three; - Every day she climbed eleven, - Every night she came down seven. - Tell me, if she did not drop, - When her paws would touch the top-- - -is solved thus:--As each day and night the cat climbed up eleven feet, -and came down seven, the daily upward gain was four feet, and thirteen -days would bring her fifty-two feet up the tree. Then on the fourteenth -day she mounted the remaining eleven feet, and was at the top, so that -no coming down seven feet is to be taken into account, and she attains -her place _in fourteen days_. - - -33. - - A third of six behind them fix, - A third of six before; - Thus makes two nines, when all combines, - Exactly fifty-four-- - -is solved:-- - - IX NINE (the two nines.) - (S is a third of six) SIX NINES = 54. - - -34. To bridge the moat, or space between the two squares which one match -cannot span, place one match across one of the corners of the outer -square, and the other from this to the inner square. - - -35. - - We start when the ninth hour is past, - Then there’s an end of you. - A vengeful goddess shows at last - What Antifat will do-- - -is solved by _attenuate_ (at ten-u-Ate, goddess of vengeance). - - -36. Mrs P.W. had only one guest to provide for. Her husband had invited -his father’s brother-in-law, Jones, who was his brother’s father-in-law, -because Mr P.W.’s brother had married Jones’ daughter, and his -father-in-law’s brother, because he had himself married Jones’ niece, -and also his brother-in-law’s father, as Mr P.W.’s sister married Jones’ -son. - - -37. This sharp customer started with _fivepence farthing_, and gradually -extracted from the landlord’s pocket a shilling and three farthings -towards the eighteenpence which he spent in refreshments. - - -38. To form four triangles of equal size with six similar matches, place -three of them in a triangle on the table, and hold or balance the other -three above these, so as to form the skeleton of a pyramid. - - -39. The following couplet solves this question:-- - - Forty-five-years I had seen - When my bride was but fifteen - - -40. The lad gave tenpence each to a grandfather, his son, and his -grandson. - - -41. Nell’s reply to Tom, when he said, with a yawn, “I wish we could -play lawn-tennis!” “Odioso ni mus rem. Moto ima os illud nam,” was not -Latin, but good sound English. Read each word in its order _backwards_, -and you have-- “Oh! so do I in summer. Oh, Tom! am I so dull, I man?” - - -42. The policeman who was looking up the road for motor-car scorchers -was able to see that his mate, who was looking down the road, was -smiling, because they stood face to face. - - -43. - - Twenty-seven with three nines - You and I can score; - Anyone on other lines - Can extend them more. - Who can write them to be seen - Equal only to sixteen?-- - -is solved thus:--Two of the three nines are reversed, and then - - 96 - -- = 16. - 6 - - -44. The trying sentence, “that that is is that that is not is not is not -that it it is,” is cleared thus by proper punctuation:--That that is, -is; that that is not, is not. Is not that it? It is. - - -45. A L L O is “Nothing after all.” - - -46. The proverb with missing consonants is--Give a dog a bad name and -hang him. - - -47. If to the thirteen upright strokes-- - - | | | | | | | | | | | | | - -thirteen more are added, the word HOTTENTOT may be formed. - - -48. A coroner could, after signing his name, write down his official -position with _c or one r_. - - - - -=PART II.= - - -CONTENTS - - PAGE - - OPTICAL ILLUSIONS II-1 - - FREAKS OF FIGURES II-20 - - CHESS CAMEOS II-26 - - SCIENCE AT PLAY II-58 - - CURIOUS CALCULATIONS II-114 - - WORD AND LETTER PUZZLES II-147 - - SOLUTIONS II-167 - - -OPTICAL ILLUSIONS - - -No. I.--SWALLOWED! - -Take a small card and place it on its longer edge upon the dotted line. -Now set the picture in a good light on the table, and let your head drop -gradually towards the card until you almost touch it with your nose. You -will see the bird fly into the jaws of the snake! - -[Illustration] - - -AMUSING PROBLEMS - - -THE CARPENTER’S PUZZLE - -1. A carpenter was called in to mend a hole in a wooden floor. The gap -was two feet wide, and twelve feet long, while the only board at hand -was three feet wide, and eight feet long. - - +----------------+ - | Fig. 1. | - | | - | | - +----------------+ - - +------------------------+ - | Fig. 2. | - | | - +------------------------+ - -This had been put aside as useless, but, on catching sight of it, the -carpenter ran his rule over it and said that he could make a perfect -fit, and cover all the hole by cutting the board into two pieces. How -did he do this? - - -No. II.--AN ILLUSION OF ROTATION - -This most interesting optical illusion was devised by Professor Thompson -some years ago:-- - -[Illustration] - -[Illustration] - -If the illustration is moved by hand in a small circle on the level, -with such motion as is given in rinsing out a bowl, the circles of the -larger diagram will seem to revolve in the direction in which the paper -is moved, while the cogs of the smaller diagram will apparently turn -slowly in the opposite direction. - - -No. III.--WHIRLING WHEELS - -Here is another combination of the clever illusion of the whirling -wheels. - -[Illustration] - -If a rapid rotating motion is given to the diagram, each circle will -seem to revolve, and the cog wheel in the centre will appear to move -slowly round in the opposite direction. - - -GOLDEN PIPPINS - -2. A man leaves an orchard of forty choice apple trees to his ten sons. -On the first tree is one apple, on the second there are two, on the -third three, and so on to the fortieth, on which there are forty. - -Each son is to have four of the trees, and on them an equal number of -the apples. How can they thus apportion the trees, and how many apples -will each son have? Here is one way:-- - - 1 2 3 4 5 6 7 8 9 10 - 20 19 18 17 16 15 14 13 12 11 - 21 22 23 24 25 26 27 28 29 30 - 40 39 38 37 36 35 34 33 32 31 - ----------------------------- - 82 82 82 82 82 82 82 82 82 82 - -Can you find another perfect solution? - - -No. IV.--AN ILLUSION OF MOTION - -We call very particular attention to this fascinating illustration of -the fact that the mind and eye may receive and register false -impressions under quite simple conditions:-- - -[Illustration] - -Hold this at rather more than reading distance, upright, and move it -steadily up and down. The dark line will soon seem to slide up and down -upon the perpendicular line. It will be better seen if drawn to pattern -on a card. - - -No. V.--ARE THEY PARALLEL? - -As the eye falls upon the principal lines of this interesting diagram, -an immediate impression is formed that they are not parallel. - -[Illustration] - -This, however, is a most curious illusion, created in the mind entirely -by the short sloping lines, as is found at once by the simple test of -measurement. - - -AN AWKWARD FIX - -3. With no knowledge of the surrounding district, I was making my way to -a distant town through country roads, guided by the successive -sign-posts that were provided. - -Coming presently to four cross-roads I found to my dismay that some one -had in mischief uprooted the sign-post and thrown it into the ditch. In -this perplexing fix how could I find my way? A bright thought struck me. -What was it? - - -LINKED SWEETNESS LONG DRAWN OUT - -4. As I stood on the platform at a quiet country station, an engine, -coming along from my left at thirty miles an hour, began to whistle when -still a mile away from me. The shrill sound continued until the engine -had passed a mile and a half to my right. For how long was I hearing its -whistle? - - -No. VI.--ILLUSION OF LENGTH - -In this curious optical illusion the lines are exactly equal in length. - - \ / - \ / - >--------------------< - / \ - / \ - - - / \ - / \ - <--------------------> - \ / - \ / - - -The eye is misled by the effect which the lines drawn outward and inward -at their ends produce upon the mind and sight. - - -ELASTIC QUARTERS - -5. - - In room marked A two men were placed, - A third he lodged in B; - The fourth to C was next assigned, - The fifth was sent to D. - In E the sixth was tucked away, - F held the seventh man; - For eighth and ninth were G and H, - Then back to A he ran. - Thence taking one, the tenth and last, - He lodged him safe in I; - Thus in nine rooms ten men found place, - Now can you tell me why? - - -EXCLUDED DAYS - -6. Are there any particular days of the week with which no new century -can begin? - - -No. VII.--ILLUSION OF HEIGHT - -These straight lines, at right angles to each other, are, though they do -not seem to be, exactly equal in length. - -[Illustration] - -This and similar illusions are probably due to the variation of the -vague mental standard which we unconsciously employ, and to the fact -that the mind cannot form and adhere to a definite scale of measurement. - - -DRIVING POWER - -7. Why has a spliced cricket bat such good driving power? and why is the -“follow through” of the head of a golf club so telling in a driving -stroke? - - -THE BUSY BOOKWORM - -8. On my bookshelf in proper order stand two volumes. Each is two inches -thick over all, and each cover is an eighth of an inch in thickness. How -far would a bookworm have to bore in order to penetrate from the first -page of Vol. I. to the last page of Vol. II.? - - -No. VIII.--ILLUSION OF DIRECTION - -Can you decide at a glance which of the two lines below the thick band -is a continuation of the line above it? - -[Illustration] - -Make up your mind quickly, and then test your decision with a straight -edge. - - -A TERRIBLE TUMBLE - -9. From what height must a man fall out of an airship--screaming as he -goes overboard--so as to reach the earth before the sound of his cry? - -_N.B._--Resistance of the air, and the acoustical fact that sound will -not travel from a rare to a dense atmosphere, are to be disregarded. - - -IN A PREDICAMENT - -10. Imagine a man on a perfectly smooth table surface of considerable -size, in a vacuum, where there is no outside force to move him, and -there is no friction. He may raise himself up and down, slide his feet -about, double himself up, wave his arms, but his centre of gravity will -be always vertically above the same point of the surface. - -How could he escape from this predicament, if it was a possible one? - - -No. IX.--THINGS ARE NOT WHAT THEY SEEM - -It is difficult, even after measurement, to believe that these figures -are of the same size. - -[Illustration] - -But they will stand the test of measurement. - - -A CLIMBING MONKEY - -11. A rope passes over a single fixed pulley. A monkey clings to one end -of the rope, and on the other end hangs a weight exactly as heavy as the -monkey. The monkey presently starts to climb up the rope. Will he -succeed? - - -GAINING GROUND - -12. Seeing that the tension on a pair of traces tends as much to pull -the horse backward as it does to pull the carriage forward, why do the -traces move on at all? - - -No. X.--THE SHIFTING BRICK - -A very curious and interesting form of optical illusion is well -illustrated by what may be called “the shifting brick.” - -[Illustration] - -The central brick, drawn to show all its edges, as though it were made -of glass, will assume the form indicated by one or other of the smaller -bricks at its right and left, according to the way in which the eyes -accommodate themselves for the moment to one pattern or to the other. If -you do not see this at first, look steadily for awhile at the pattern -you desire. - - -ASK A CYCLIST - -13. Why does a rubber tyre leave a double rut in dust, and a single one -in mud? - - -TODHUNTER’S UNIQUE PUZZLE PROBLEM - -14. If two cats, on opposite sides of a sharply sloping roof, are on the -point of slipping off, which will hold on the longest? - - -No. XI.--AN ILLUSION WITH COINS - -If you place four coins in the positions shown at the top of this -diagram, and attempt, or challenge some one to attempt, without any -measuring, to move the single coin down in a straight line until the -spaces from C to D on either side exactly equal the distance from A to -B-- - -[Illustration] - -It must drop as far as is shown here, which seems to the unaided eye to -be too far. - -This excellent illusion can be shown as an after-dinner trick with four -napkin-rings. - - -No. XII.--THE FICKLE BARREL - -Here is another excellent optical illusion. Look attentively at the -diagram below, and notice in which direction you apparently look into -it, as though it were an open cask. - -[Illustration] - -Now shake the paper, or move it slightly, and you will find, more often -than not, that you seem to see into it in quite the opposite direction. - - -HEADS I WIN! - -15. I hold a penny level between my finger and thumb, and presently let -it fall from the thumb by withdrawing my finger. It makes exactly a -half-turn in falling through the first foot. If it starts “heads,” how -far must it fall to bring it “heads” to the floor? - - -HE DID IT! - -16. “They call these safety matches,” said Funnyboy at his club one day, -“and say that they strike only on the box. Don’t believe it! I can -strike them quite easily on my boot.” - -No sooner said than done. He took out a match, struck it on his boot, -and--phiz!--it was instantly alight. The box was handed round, and match -after match was struck by the bystanders on their boots, but not one of -them could succeed. - -“You don’t give the magic touch,” said Funnyboy, as he gaily struck -another. How did he do it? - - -No. XIII.--A STRANGE OPTICAL ILLUSION - -[Illustration] - -[Illustration] - -How many cubes can you see as you look at the large diagram? The two -smaller ones should be looked at first alternately, and they will assist -the eye to see at one time six, and at another time seven, very distinct -cubes. - - -No. XIV.--A CIRCULAR ILLUSION - -This curious optical illusion is not easily followed by eye to the -finish of the several lines. - -[Illustration] - -Each short line is, in fact, part of the circumference of a circle, and -the circles when completed will be found to be accurately concentric. It -would seem at first sight that the lines are taking courses which would -eventually meet at some point common to them all. - - -A CYCLE SURPRISE - -17. We commend this curious point to the special attention of -cyclists:-- - -A bicycle is stationary, with one pedal at its lowest point. If this -bicycle is lightly supported, and the bottom pedal is pulled backward, -what will happen? - - -No. XV.--THE GHOST OF A COIN - -[Illustration] - -A most remarkable optical illusion is produced by the blending of the -dark and light converging rays of this diagram. Stand with your back to -the light, hold the page, or better still, the diagram copied on a card, -by the lower right-hand corner, give it a continuous revolving movement -in either direction, and the visible ghost of a silver coin, sometimes -as large as sixpence, sometimes as large as a shilling, will appear! -Where can it come from? - - -ROUGH AND READY - -18. A merchant has a large pair of scales, but he has lost his weights, -and cannot at the moment replace them. A neighbour sends him six rough -stones, assuring him that with them he can weigh any number of pounds, -from 1 to 364. What did each stone weigh? - - -No. XVI.--A TAME GOOSE - -Here is a pretty form of our first illusion:-- - -[Illustration] - -Place the edge of a card on the dotted line, look down upon it in a good -light, and, as you drop your face till it almost touches the card, you -will see the goose _move towards the sugar_ in the little maiden’s hand. - - -REJECTED ADDRESSES - -19. A wheel is running along a level road, and a small clot of mud is -thrown from the hindermost part of the rim. What happens to it? Does it -ever renew its acquaintance with the wheel that has thus rejected it? - - -No. XVII.--ILLUSION OF LENGTH - -Here is another method by which an optical illusion of length is very -plainly shown:-- - - A B - +--------------+ - / \ - / \ - / \ - / \ - +------------------------+ - - A B - +--------------+ - \ / - \ / - \ / - \ / - +----+ - -Judged by appearances, the line A B in the larger figure is considerably -longer than the line A B below it, but tested by measurement they are -exactly equal. - - -THE CARELESS CARPENTER - -20. A village carpenter undertook to make a cupboard door. When he began -to put it in its place it was too big, so he took it back to his -workshop to alter it. Unfortunately he now cut it too little. What could -he do? He determined to cut it again, and it at once became a good fit. -How was this done? - - -No. XVIII.--PERPENDICULAR LINES - -Here is another excellent illustration that seeing is not always -believing. - -[Illustration] - -No one could suppose at first sight that these four lines are perfectly -straight and parallel, but they will stand the test of a straight edge. -The divergent rays distract the vision. - - -BY THE COMPASS - -21. If from the North Pole you start sailing in a south-westerly -direction, and keep a straight course for twenty miles, to what point of -the compass must you steer to get back as quickly as possible to the -Pole? - - -No. XIX.--ILLUSION OF PERSPECTIVE - -The optical illusion in the picture which we reproduce is due to the -defective drawing of the two men on the platform. In actual size upon -the paper the further man looks much taller than the other. - -[Illustration] - -Measurement, however, shows the figures to be exactly of a height. This -illusion is due to the fact that the head of the further man is quite -out of perspective. If he is about as tall as the other, and on level -ground, both heads should be about on the same line. As drawn, he is, in -fact, a monster more than eight feet high. - - -DICK IN A SWING - -22. If Dick, who is five feet in height, stands bolt-upright in a swing, -the ropes of which are twenty feet long, how much further in round -numbers do his feet travel than his head in describing a semi-circle? - - -No. XX.--OUR BLIND SPOT - -Here is an excellent and very simple illustration of a well-known -optical curiosity:-- - -[Illustration] - -Hold this picture at arm’s length in the right hand, hold the left hand -over the left eye, and draw the picture towards you gradually, looking -always at the black cross with the right eye. The black disc will -presently disappear, and then come into sight again as you continue to -advance the paper. - - -A POSER - -23. Can you name nine countries in Europe of which the initial letters -are the same as the finals? - - -FREAKS OF FIGURES - - -A HANDY SHORT CUT - -Here is a delightfully simple way in which market gardeners, or others -who buy or sell weighty produce, can check their invoices for potatoes -or what not. - -Say, for example, that a consignment weighs 6 tons, 10 cwts., 1 qr. -Then, since 20 cwts. are to a ton as 20s. are to a pound, and each -quarter would answer on these lines to 3d., we can at once write down £6 -10s. 3d., as the price at £1 the ton. On this sure basis any further -calculation is easily made. - - -No. XXI.--THE PERSISTENCE OF VISION - -[Illustration: HOW TO SEE THE GHOST] - -Look steadily, in a good light, for thirty seconds at the cross in the -eye of the pictured skull; then look up at the wall or ceiling, or look -fixedly at a sheet of paper for another thirty seconds, when a -ghost-like image of the skull will be developed. - - -NOT SO FAST! - -A gardener, when he had planted 100 trees on a line at intervals of 10 -yards, was able to walk from the first of these to the last in a few -seconds, for they were set _on the circumference of a circle_! - - -No. XXII.--THE PERSISTENCE OF VISION - -Here is another example of what is known as the persistence of vision:-- - -[Illustration] - -Look fixedly for some little time at this grotesque figure, then turn -your eyes to the wall or ceiling, and you will in a few seconds see it -appear in dark form upon a light ground. - - -A PUZZLE NUMBER - - The sum of nine figures a number will make, - Of which just a third will remain - If fifty away from the whole you should take, - Thus turning a loss to a gain. - -It needs something more than mere arithmetic to discover that the -solution to this puzzle is XLV, the sum of the nine digits, for if the L -is removed, XV, the third of XLV, remains. - - -No. XXIII.--ANOTHER PARALLEL FREAK - -Here is another curious illusion:-- - -[Illustration] - -The four straight lines are perfectly parallel, but the contradictory -herring-bones disturb the eye. - - -THE MAGIC OF FIGURES - -If our penny had been current coin in the first year of the -Christian era, and had been invested at compound interest at -five per cent., it would have amounted in 1905 to more than -£132,010,000,000,000,000,000,000,000,000,000,000,000. - -This gigantic sum would afford an income of £101,890,000,000,000,000,000 -every second to every man, woman, and child in the world, if we take its -population to be 1,483,000,000 souls! - -Absurdly small in contrast to these startling figures is the modest -eight shillings which the same penny would have yielded in the same time -at simple interest. - - -No. XXIV.--ILLUSION OF LENGTH - -Here in another form is shown the illusion of length. - -[Illustration] - -At first sight it seems that the two upright lines are distinctly longer -than the line that slopes, but it is not so. - - -WHAT IS YOUR AGE? - -Here is a neat method of discovering the age of a person older than -yourself:-- - -Subtract your own age from 99. Ask your friend to add this remainder to -his age, and then to remove the first figure and add it to the last, -telling you the result. This will always be the difference of your ages. -Thus, if you are 22, and he is 35, 99 - 22 = 77. Then 35 + 77 = 112. The -next process turns this into 13, which, added to your age, gives his -age, 35. - - -No. XXV.--THE HONEYCOMB ILLUSION - -In this diagram one hundred and twenty-one circular spots are grouped in -a diamond. - -[Illustration] - -If we half close our eyes, and look at this through our eye-lashes, we -find that it takes on the appearance of a section of honeycomb, with -hexagonal cells. - - -MULTIPLICATION NO VEXATION - -Here is a ready method for multiplying together any two numbers between -12 and 20. - -Take one of the two numbers and add it to the unit digit of the other. -Beneath the sum thus obtained, but one place to the right, put the -product of the unit digits of the two original numbers. - -The sum of these new numbers is the product of the numbers that were -chosen. Thus:-- - - 19 × 13. (19 + 3) = 22 - (9 × 3) = 27 - --- - 247 - - -No. XXVI.--CHESS CAMEO - -By Dr GOLD - -_A Chess Joke_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |.b.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| p |...| k |...| |.K.| | - +---+---+---+---+---+---+---+---+ - | |.n.| |.P.| |...| |...| - +---+---+---+---+---+---+---+---+ - |.P.| |...| p |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| N |...| N |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| B |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -Black has made an illegal move. He must replace this, and move his king -as the penalty. White then mates on the move. - - -[1]SHOT IN A PYRAMID - -Here is a method for determining the total number of balls in a solid -pyramid built up on a square base:-- - -Multiply the number of shot on one side of the base line by 2, add 3, -multiply by the number on the base line, add 1, multiply again by the -number on the base, and finally divide by 6. Thus, if the base line is -12-- - -12 × 2 + 3 = 27; 27 × 12 + 1 = 325; 325 × 12 = 3900; and 3900 ÷ 6 = 650, -which is the required number. - - [1] _N.B._--This title does not imply a tragedy. - - -No. XXVII.--CHESS CAMEO - -By A. CYRIL PEARSON - -_A Chess Puzzle_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |.p.| |...| |.p.| p | - +---+---+---+---+---+---+---+---+ - | |.P.| |.P.| |.k.| |...| - +---+---+---+---+---+---+---+---+ - |...| |.p.| K |.N.| P |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| p |...| R |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.N.| |...| | - +---+---+---+---+---+---+---+---+ - | |.q.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White might have given mate on the last move. White now to retract his -move, and mate at once. - -_Show by analysis the mating position._ - - -No. XXVIII.--CHESS CAMEO - -By J. G. CAMPBELL - -_A very Clever Device_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| p |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.P.| |.p.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| K |...| p |...| |.B.| | - +---+---+---+---+---+---+---+---+ - | P |...| |.P.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.p.| p | - +---+---+---+---+---+---+---+---+ - | |.P.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| K |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play and draw. - - -COMIC ARITHMETIC - -“Now, boys,” said Dr Bulbous Roots to class, “you shall have a -half-holiday if you prove in a novel way that 10 is an even number.” - -Next morning, when the doctor came into school, he found this on the -blackboard:-- - - SIX = 6 - IX = 9 - --------- - By subtraction S = -3 - - SEVEN = 7 - S = -3 - ------------ - Therefore EVEN = 10 - - Q. E. D. - (_Quite easily done!_) - -The half-holiday was won. - - -No. XXIX.--CHESS CAMEO - -By E. B. COOK - -_A Fine Example_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |.k.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.R.| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | K |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| p |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and draw. - - -No. XXX.--CHESS CAMEO - -By A. F. MACKENZIE - -_A Prize Problem_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |.r.| |...| |.b.| - +---+---+---+---+---+---+---+---+ - |.p.| |...| |...| |.P.| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |.q.| - +---+---+---+---+---+---+---+---+ - |.N.| b |...| |...| |...| K | - +---+---+---+---+---+---+---+---+ - | p |.P.| |.k.| P |...| R |...| - +---+---+---+---+---+---+---+---+ - |...| |.p.| P |.p.| |.B.| R | - +---+---+---+---+---+---+---+---+ - | |...| n |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.N.| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in two moves. - -There are twelve variations in this beautiful problem. - - -MAGIC MULTIPLICATION - -It will interest all who study short cuts and contrivances to know that -a novice at arithmetic who has mastered simple addition, and can -multiply or divide by 2, but by no higher numbers, can, by using all -these methods, multiply any two numbers together easily and accurately. - -This is how it is done:-- - -Write down the numbers, say 53 and 21, divide one of them by 2 as often -as possible, omitting remainders, and multiply the other by 2 the same -number of times; set these down side by side, as in the instance given -below, and wherever there is an _even_ number on the division side, -strike out the corresponding number on the multiplication side. Add up -what remains on that side, and the sum is done. Thus:-- - - 53 21 - 26 (42) - 13 84 - 6 (168) - 3 336 - 1 672 - ------ - 1113 - - which is 53 multiplied by 21. - - -No. XXXI.--CHESS CAMEO - -BY A. W. GALITZKY - -_A Prize Problem_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.B.| q |.n.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| p | - +---+---+---+---+---+---+---+---+ - | |...| N |...| R |...| P |.P.| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| k |...| | - +---+---+---+---+---+---+---+---+ - | |...| b |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| n |...| |...| |.K.| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in two moves. - - -No. XXXII.--CHESS CAMEO - -BY S. LOYD - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.N.| |.p.| |.p.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.p.| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |.k.| N |.q.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.n.| |...| | - +---+---+---+---+---+---+---+---+ - | |.K.| |...| |.B.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in two moves. - - -No. XXXIII.--CHESS CAMEO - -BY B. G. LAWS - -_A Prize Problem_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.q.| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| n |.p.| |.p.| p |...| k | - +---+---+---+---+---+---+---+---+ - | N |...| P |...| k |.b.| |.R.| - +---+---+---+---+---+---+---+---+ - |...| n |...| |.B.| |...| R | - +---+---+---+---+---+---+---+---+ - | |...| |.r.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in two moves. - - -PERFECT NUMBERS - -The following particulars about a very rare property of numbers will be -new and interesting to many of our readers:-- - -The number 6 can only be divided without remainder by 1, 2, and 3, -excluding 6 itself. The sum of 1 + 2 + 3 is 6. The only exact divisors -of 28 are 1, 2, 4, 7, and 14, and the sum of these is 28; 6 and 28 are -therefore known as perfect numbers. - -The only other known numbers which fulfil these conditions are 496; -8128; 33,550,336; 8,589,869,056; 137,438,691,328; and - - 2,305,843,008,139,952,128. - -This most remarkable rarity of perfect numbers is a symbol of their -perfection. - - -No. XXXIV.--CHESS CAMEO - -BY EMIL HOFFMANN - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| q |...| |.B.| - +---+---+---+---+---+---+---+---+ - |.R.| |...| |...| |.Q.| n | - +---+---+---+---+---+---+---+---+ - | |...| |...| k |...| |...| - +---+---+---+---+---+---+---+---+ - |.b.| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |.R.| |...| |...| - +---+---+---+---+---+---+---+---+ - |.p.| |...| B |...| n |...| b | - +---+---+---+---+---+---+---+---+ - | K |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in two moves. There are no less than twelve -variations! - - -No. XXXV.--CHESS CAMEO - -BY J. POSPICIL - -_A Prize Problem_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |.N.| |...| - +---+---+---+---+---+---+---+---+ - |...| N |...| |...| |...| p | - +---+---+---+---+---+---+---+---+ - | |...| n |...| B |.p.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.k.| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.K.| |...| |...| P |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| P |.n.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.Q.| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in two moves. - - -AMICABLE NUMBERS - -Somewhat akin to perfect numbers are what are known as amicable numbers, -of which there is a still smaller quantity in the realm of numbers. - -The number 220 can be divided without remainder only by 1, 2, 4, 5, 10, -11, 22, 44, 55, and 110, and the sum of these divisors is 284. The only -divisors of 284 are 1, 2, 4, 71, and 142, and the sum of these is 220. - -The only other pairs of numbers which fulfil this curious mutual -condition, that the sum of the divisors of each number exactly equals -the other number, are 17,296 with 18,416, and 9,363,584 with 9,437,056. -No other numbers, at least below ten millions, are in this way -“amicable.” - - -No. XXXVI.--CHESS CAMEO - -BY H. J. C. ANDREWS - -_A Prize Problem_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| K |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.Q.| | - +---+---+---+---+---+---+---+---+ - | |.B.| |...| |...| |.R.| - +---+---+---+---+---+---+---+---+ - |...| |...| k |.N.| |.b.| R | - +---+---+---+---+---+---+---+---+ - | P |...| |...| |...| P |...| - +---+---+---+---+---+---+---+---+ - |...| k |...| p |...| |...| | - +---+---+---+---+---+---+---+---+ - | B |...| |.P.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in two moves. - - -No. XXXVII.--CHESS CAMEO - -BY ALFRED DE MUSSET - -_A Gem of the First Water_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| n | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| N |...| |.k.| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |.N.| |...| |.K.| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.R.| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -A SWARM OF ONES - - 1 × 9 + 2 = 11 - 12 × 9 + 3 = 111 - 123 × 9 + 4 = 1111 - 1234 × 9 + 5 = 11111 - 12345 × 9 + 6 = 111111 - 123456 × 9 + 7 = 1111111 - 1234567 × 9 + 8 = 11111111 - 12345678 × 9 + 9 = 111111111 - - -No. XXXVIII.--CHESS CAMEO - -BY FRANK HEALEY - -_A Masterpiece_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.B.| N |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.P.| |...| |.p.| |.p.| | - +---+---+---+---+---+---+---+---+ - | |...| K |...| k |.b.| P |...| - +---+---+---+---+---+---+---+---+ - |.Q.| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.n.| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -DIVINATION BY FIGURES - -There is a pleasant touch of mystery in the following method of -discovering a person’s age:--Ask any such subjects of your curiosity to -write down the tens digit of the year of their birth, to multiply this -by 5, to add 2 to the product, to multiply this result by 2, and finally -to add the units digit of their birth year. Then, taking the paper from -them, subtract the sum from 100. This will give you their age in 1896, -from which their present age is easily determined. - - -No. XXXIX.--CHESS CAMEO - -BY FRANK HEALEY - -_The “Bristol Prize Problem”_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| n |...| |...| N |.p.| | - +---+---+---+---+---+---+---+---+ - | |.N.| |...| |...| Q |...| - +---+---+---+---+---+---+---+---+ - |...| b |.k.| P |...| |...| | - +---+---+---+---+---+---+---+---+ - | p |...| p |...| |.p.| |...| - +---+---+---+---+---+---+---+---+ - |.P.| |.P.| |...| R |...| | - +---+---+---+---+---+---+---+---+ - | |...| |.P.| |...| P |.K.| - +---+---+---+---+---+---+---+---+ - |.B.| |...| R |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -FUR AND FEATHERS - -As I came in after a day among the birds and rabbits, the keeper asked -me--“Well, sir, what sport?” I replied, “36 heads and 100 feet.” It took -him some time to calculate that I had accounted for 22 birds and 14 -rabbits. - - -No. XL.--CHESS CAMEO - -BY J. E. CAMPBELL - -_Splendid Strategy_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |.N.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| p |.p.| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.B.| |.k.| p |.P.| |.n.| Q | - +---+---+---+---+---+---+---+---+ - | |...| p |.N.| |.P.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| B |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| K |.R.| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -JUGGLING WITH THE DIGITS - -The nine digits can be arranged to form fractions equivalent to - - 1 1 1 1 1 1 1 - - - - - - - - - 3 4 5 6 7 8 9 - -thus:-- - - 5823 1 7956 1 2973 1 2943 1 5274 1 - ----- = - ----- = - ----- = - ----- = - ----- = - - 17469 3 31824 4 14865 5 17658 6 36918 7 - - 9321 1 8361 1 - ----- = - ----- = - - 74568 8 75249 9 - - -No. XLI.--CHESS CAMEO - -BY W. GRIMSHAW - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.N.| |...| K |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.b.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| k |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.P.| p |.p.| p |.P.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.P.| P | - +---+---+---+---+---+---+---+---+ - | |.Q.| |...| |...| R |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -No. XLII.--CHESS CAMEO - -BY S. LOYD - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| P |...| - +---+---+---+---+---+---+---+---+ - |...| |.K.| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |.p.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.p.| | - +---+---+---+---+---+---+---+---+ - | |.Q.| |...| |.N.| k |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -A MOTOR PROBLEM - -This motor problem will be new and amusing to many readers:-- - -Let _m_ be the driver of a motor-car, working with velocity _v_. If a -sufficiently high value is given to _v_, it will ultimately reach _pc_. -In most cases _v_ will then = _o_. For low values of _v_, _pc_ may be -neglected; but if _v_ be large it will generally be necessary to square -_pc_, after which _v_ will again assume a positive value. - -By a well-known elementary theorem, _pc_ + _lsd_ = (_pc_)², but the -squaring may sometimes be effected by substituting _x_³ (or × × ×) for -_lsd_. This is preferable, if _lsd_ is small with regard to _m_. If -_lsd_ be made sufficiently large, _pc_ will vanish. - -Now if _jp_ be substituted for _pc_ (which may happen if the difference -between _m_ and _pc_ be large) the solution of the problem is more -difficult. No value of _lsd_ can be found to effect the squaring of -_jp_, for, as is well-known, (_jp_)² is an impossible quantity. - - -No. XLIII.--CHESS CAMEO - -BY J. G. CAMPBELL - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| p |...| Q | - +---+---+---+---+---+---+---+---+ - | |...| |.k.| N |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.N.| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| P |...| B |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.P.| p |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |.K.| |.B.| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -No. XLIV.--CHESS CAMEO - -BY FRANK HEALEY - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |.K.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |.R.| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |.P.| k |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |.Q.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -A NEAT METHOD OF DIVISION - -To divide any sum easily by 99, cut off the two right-hand figures of -the dividend and add them to all the others. Set down the result of this -in line below, and then repeat this process until no figures remain on -the left to be thus dealt with. - -Now draw a line down between the tens and hundreds columns, and add all -up on the left of it, thus:-- - - 8694 | 32 120 | 78 - 87 | 26 1 | 98 - 1 | 13 | 99 - | 14 ------------ - ------------- 121 and 99 over. - 8782 and 14 over. In other words, 122. - -The last number on the right of the lines shows always the remainder. If -this should appear as 99 (as in the second example above), add one to -the number on the left. - - -No. XLV.--CHESS CAMEO - -BY BLUMENTHAL AND KUND - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| K |...| |.R.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| B |...| |...| | - +---+---+---+---+---+---+---+---+ - | p |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.r.| n |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | k |...| p |...| |...| |.Q.| - +---+---+---+---+---+---+---+---+ - |...| |...| N |...| |...| | - +---+---+---+---+---+---+---+---+ - | b |.P.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -No. XLVI.--CHESS CAMEO - -BY A. F. MACKENZIE - -_A Prize Problem_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |.R.| |...| - +---+---+---+---+---+---+---+---+ - |...| |.p.| |.B.| |...| Q | - +---+---+---+---+---+---+---+---+ - | n |...| |.R.| |...| |.b.| - +---+---+---+---+---+---+---+---+ - |.p.| |.k.| P |...| |...| | - +---+---+---+---+---+---+---+---+ - | K |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.n.| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -A SMART SCHOOLBOY - -The question, “How many times can 19 be subtracted from a million?” was -set by an examiner, who no doubt expected that the answer would be -obtained by dividing a million by 19. One bright youth, however, filled -a neatly-written page with repetitions of - - 1,000,000 1,000,000 1,000,000 - 19 19 19 - --------- --------- --------- - 999,981 999,981 999,981 - -and added at the foot of the page, “_N.B._--I can do this as often as -you like.” - -There was a touch of unintended humour in this, for, after all, the boy -gave a correct answer to a badly worded question. - - -No. XLVII.--CHESS CAMEO - -BY A. CYRIL PEARSON - - BLACK - +---+---+---+---+---+---+---+---+ - | |.N.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| r |.n.| |...| n |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |.R.| |...| - +---+---+---+---+---+---+---+---+ - |...| |.P.| k |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| p |.P.| |...| |...| - +---+---+---+---+---+---+---+---+ - |.Q.| |.P.| |.K.| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| P |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -No. XLVIII.--CHESS CAMEO - -BY FRANK HEALEY - -_Quite a Gem_ - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |.b.| - +---+---+---+---+---+---+---+---+ - |...| |...| n |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.K.| |...| |...| |.Q.| | - +---+---+---+---+---+---+---+---+ - | |.P.| |.k.| b |...| P |...| - +---+---+---+---+---+---+---+---+ - |.R.| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | B |...| |...| |.P.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -LEWIS CARROLL’S SHORT CUT - -Here is a very smart and very simple method of dividing any multiple of -9 by 9, from the fertile brain of Lewis Carroll:--Place a cypher over -the final figure, subtract the final figure from this, place the result -above in the tens place, subtract the original tens figure from this, -and so on to the end. Then the top line, excluding the intruded cypher, -gives the result desired. Thus:-- - - 36459 ÷ 9 = 4051,0 - = 4051. - 36459 - - -No. XLIX.--CHESS CAMEO - -BY A. BAYERSDORFER - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| K |...| | - +---+---+---+---+---+---+---+---+ - | |...| |.k.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |.p.| B |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| Q |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -ANOTHER FREAK OF FIGURES - - 1 × 8 + 1 = 9 - 12 × 8 + 2 = 98 - 123 × 8 + 3 = 987 - 1234 × 8 + 4 = 9876 - 12345 × 8 + 5 = 98765 - 123456 × 8 + 6 = 987654 - 1234567 × 8 + 7 = 9876543 - 12345678 × 8 + 8 = 98765432 - 123456789 × 8 + 9 = 987654321 - - -No. L.--CHESS CAMEO - -BY J. DOBRUSKY - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.n.| |...| |...| B |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| q |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| k |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.R.| N |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| K |.R.| |...| |...| | - +---+---+---+---+---+---+---+---+ - | Q |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.n.| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -DIVINATION BY NUMBERS - -Here is one of the methods by which we can readily discover a number -that is thought of. The thought-reader gives these directions to his -subject: “Add 1 to three times the number you have thought of; multiply -the sum by 3; add to this the number thought of; subtract 3, and tell me -the remainder.” This is always ten times the number thought of. Thus, if -6 is thought of--6 × 3 + 1 = 19; 19 × 3 = 57; 57 + 6 - 3 = 60, and 60 ÷ -10 = 6. - - -No. LI.--CHESS CAMEO - -BY KONRAD BAYER - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | p |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.k.| |.K.| |...| |...| | - +---+---+---+---+---+---+---+---+ - | b |.p.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.P.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.R.| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -COINCIDENCES - -Here is a curious rough rule for remembering distances and sizes:-- - -The diameter of the earth multiplied by 108 gives approximately the -sun’s diameter. The diameter of the sun multiplied by 108 gives the mean -distance of the earth from the sun. The diameter of the moon multiplied -by 108 gives the mean distance of the moon from the earth. - - -No. LII.--CHESS CAMEO - -BY J. BERGER - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| B |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| p |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| k |...| |...| - +---+---+---+---+---+---+---+---+ - |.B.| Q |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.p.| |.K.| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -PERSONAL ARITHMETIC - - Says Giles, “My wife and I are two, - Yet faith I know not why, sir.” - Quoth Jack, “You’re ten, if I speak true, - She’s one, and you’re a cypher!” - - -No. LIII.--CHESS CAMEO - -BY H. F. L. MEYER - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| R |...| |...| - +---+---+---+---+---+---+---+---+ - |...| k |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | b |.p.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| p |...| P |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.K.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.B.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| Q |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -DIVISION BY SUBTRACTION - -Here is a curious and quite uncommon method of dividing any multiple of -11 by 11. - -Set down the multiple of 11, place a cypher under its last figure, draw -a line, and subtract, placing the first remainder under the tens place. -Subtract this from the next number in order, and so on throughout, -adding in always any number that is carried. Thus:-- - - 363 56408 375034 - 0 0 0 - --- ----- ------ - 33 5128 34094 - - -No. LIV.--CHESS CAMEO - -BY FRANK HEALEY - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.B.| |...| |...| |...| p | - +---+---+---+---+---+---+---+---+ - | |.r.| p |.p.| |...| b |...| - +---+---+---+---+---+---+---+---+ - |...| |.k.| n |...| |.Q.| | - +---+---+---+---+---+---+---+---+ - | P |...| |...| p |...| |...| - +---+---+---+---+---+---+---+---+ - |.K.| |...| |.P.| |...| N | - +---+---+---+---+---+---+---+---+ - | B |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -LUCK IN ODD NUMBERS - -Perhaps the old saying, “there is luck in odd numbers,” may have some -connection with the curious fact that the sum of any quantity of -consecutive odd numbers, beginning always with 1, is the square of that -number. Thus:-- - - 1 + 3 + 5 = 9 = 3 × 3. - 1 + 3 + 5, etc., up to 17 = 81 = 9 × 9. - 1 + 3 + 5, etc., up to 99 = 2500 = 50 × 50. - - -No. LV.--CHESS CAMEO - -BY FRANK HEALEY - - BLACK - +---+---+---+---+---+---+---+---+ - | |.K.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |.n.| |...| |.p.| |...| | - +---+---+---+---+---+---+---+---+ - | |.N.| |.k.| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |.N.| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |.P.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |.n.| Q |.P.| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -THE VERSATILE NUMBER - -In the number 142857, if the digits which belong to it are in succession -transposed from the first place to the end, the result is in each case a -multiple of the original number. Thus:-- - - 285714 = 142857 × 2 - 428571 = 142857 × 3 - 571428 = 142857 × 4 - 714285 = 142857 × 5 - 857142 = 142857 × 6 - - -No. LVI.--CHESS CAMEO - -BY J. E. CAMPBELL - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |.p.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| p |...| p |...| B | - +---+---+---+---+---+---+---+---+ - | |...| |...| |.k.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| K |...| N |...| | - +---+---+---+---+---+---+---+---+ - | |...| |...| |...| |.P.| - +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.R.| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in three moves. - - -A PARADOX - -By the following simple method, a plausible attempt is made to prove -that 1 is equal to 2:-- - -Suppose that _a_ = _b_, then - - _ab_ = _a_² - - ∴ _ab_ - _b_² = _a_² - _b_² - - ∴ _b_(_a_ - _b_) = (_a_ + _b_)(_a_ - _b_) - - ∴ _b_ = _a_ + _b_ - - ∴ _b_ = 2_b_ - - ∴ 1 = 2 - -This process only proves in reality that 0 × 1 = 0 × 2, which is true. - - -No. LVII.--CHESS CAMEO - -_Double First Prize_ - -BY A. CYRIL PEARSON - - BLACK - +---+---+---+---+---+---+---+---+ - | |...| b |...| |...| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| p |.K.| |...| p | - +---+---+---+---+---+---+---+---+ - | |...| p |...| |.p.| |...| - +---+---+---+---+---+---+---+---+ - |...| |...| B |.k.| |...| | - +---+---+---+---+---+---+---+---+ - | |.b.| |...| |...| P |...| - +---+---+---+---+---+---+---+---+ - |.N.| |.N.| |.P.| |...| | - +---+---+---+---+---+---+---+---+ - | |.R.| |.P.| |.R.| |...| - +---+---+---+---+---+---+---+---+ - |.b.| q |...| |...| |...| | - +---+---+---+---+---+---+---+---+ - WHITE - -White to play, and mate in four moves. - - -QUICK CALCULATION - -Few people know a very singular but simple method of calculating rapidly -how much any given number of pence a day amounts to in a year. The rule -is this:--Set down the given number of pence as pounds; under this place -its half, and under that the result of the number of original pence -multiplied always by five. Take, for example, 7d a day:-- - - £7 0 0 - 3 10 0 - 2 11 - --------- - £10 12 11 - --------- - -The reason for this is evident as soon as we remember that the 365 days -of a year may be split up into 240, 120, and 5, and that 240 happens to -be the number of pence in a pound. - - -SCIENCE AT PLAY - - -No. LVIII.--THE GEARED WHEELS - -A small wheel with ten teeth is geared into a large fixed wheel which -has forty teeth. This small wheel, with an arrow mark on its highest -cog, is revolved completely round the large wheel. How often during its -course is the arrow pointing directly upwards? Here is a diagram of the -starting position. - -[Illustration] - - -No. LIX.--ADVANCING BACKWARDS - -Here is a most curious and interesting question:--When an engine is -drawing a train at full speed from York to London, what part of the -train at any given moment is moving _towards York_? - -At any time, when the engine is drawing a train at full speed from York -to London, that part of the flange of each wheel which is for the moment -at its lowest is actually _moving backwards towards York_. - -[Illustration] - -For any point, such as A, on the circumference of the tyre, describes in -running along a series of curves, as shown by _full_ lines in the -diagram; and any point, B, on the outer edge of the flange, follows a -path shown by the _dotted_ curves. - -If these lines are followed round with a pencil in the direction of the -arrows, it will be found that the point on the flange actually moves -_backwards_ as it passes _below the track_, while the point A, as it -completes each curve, is _at rest_ for the instant on the track, just -before it starts afresh. The speed of the train does not affect these -very curious facts. - - -No. LX.--THE FIFTEEN BRIDGES - -In the subjoined diagram A and B represent two islands, round which a -river runs as is indicated, with fifteen connecting bridges, that lead -from the islands to the river’s banks. - -[Illustration] - -Can you contrive to pass in turn over all these bridges without ever -passing over the same one twice? - - -ARRANGING THE DIGITS - -In a school where two boys were taught to think out the bearings of -their work, a sharp pupil remarked that 100 is represented on paper by -the smallest digit and two cyphers, which are in themselves symbols of -nothing. The master, quick to catch any signs of mental activity, took -the opportunity to propound to his class the following ingenious -puzzle:--How can the sum of 100 be represented exactly in figures and -signs by making use of all the nine digits in their reverse order? This -is how it is done:-- - - 9 × 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 100. - -Another ingenious method of using the nine digits, so that by simple -addition they sum up to exactly 100, and each is used once only, is -this:-- - - 15 + 36 + 47 = 98 + 2 = 100 - -Here is another arrangement by which the nine digits written in their -inverse order can be made to represent exactly 100:-- - - 98 - 76 + 54 + 3 + 21 = 100. - -Here is yet another way of arriving at 100 by using each of the digits, -this time with an 0:-- - - 40¹⁄₂ - 59³⁸⁄₇₆ - -------- - 100 - - -No. LXI.--LOOPING THE LOOP - -Here is quite a pretty scientific experiment, which any one of a handy -turn can construct and arrange:-- - -[Illustration] - -The spiral track is formed of two wires bent, and connected by curved -cross-pieces. The upper twist is turned so that the ball starts on a -horizontal course. - -During the accelerated descent the ball acquires momentum enough to keep -it on the vertical track, held outwardly against the wires by -centrifugal force. - -Convenient proportions are: height of spiral two feet, diameter six -inches, and wire rails three-quarters of an inch apart. - - -No. LXII.--A MECHANICAL BIRD - -A close approach to an ideal flying machine can be made with a little -ingenuity. Two Y-shaped standards, secured to the backbone rod, support -two wires which carry wings of thin silk, provided with light stays, and -connected at their inner corners with the backbone by threads. - -[Illustration] - -Rubber bands are attached to a loop on the inner end of the crank shaft, -and secured to a post at the rear. These are twisted by turning the -shaft with the cross wire, and when the tension is released the wings -beat the air and carry the bird forward. It is known as Penaud’s -mechanical bird, and has been sold as an attractive toy. - - -No. LXIII.--LINE OF SWIFTEST DESCENT - -A simple apparatus constructed on the lines of this illustration will -give an interesting proof of the laws which govern falling bodies on an -inclined plane or on a curved path. - -[Illustration] - -In the case of the inclined plane the ball is governed by the usual law -which controls falling bodies. In that of the concave circular curve, as -it is accelerated rapidly at the start, it makes its longer journey in -quicker time. In the case of the cycloidal curve it acquires a high -velocity. This curve has therefore been called “the curve of swiftest -descent,” as a falling body passes over it in less time than upon any -path except the vertical. - - -No. LXIV.--A CENTRIFUGAL RAILWAY - -Here is another very simple and pretty illustration of the natural -forces which come into play in “looping the loop.” - -[Illustration] - -This scientific toy on a small scale may be easily made, if care is -taken that the height of the higher end of the rails is to the height of -the circular part in a greater ratio than 5 to 4. - -A ball started at the higher end follows the track throughout, and at -one point is held by centrifugal force against the under side of the -rails, against the force of gravity. - - -No. LXV.--A QUESTION OF GRAVITY - -If a ball is fired point blank from a perfectly horizontal gun, and -travels half a mile over a level plain before it touches ground, and -another similar ball is at the same moment dropped from the same height -by some mechanical means, the two balls will touch ground -simultaneously. The flight, however long, of one through the air has no -influence upon the force of gravity, which draws it earthward at the -same resistless rate as it draws the other that is merely dropped. - -[Illustration] - - -A SHORT CUT - -A quick method of multiplying any number of figures by 5 is to divide -them by 2, annexing a cypher to the result when there is no remainder, -and if there is any remainder annexing a 5. Thus:-- - - 464 × 5 = 2320; 464 ÷ 2 = 232, annex 0, = 2320. - 753 × 5 = 3765; 753 ÷ 2 = 376, annex 5, = 3765. - - -No. LXVI.--A DUCK HUNT - -A duck begins to swim round the edge of a circular pond, and at the same -moment a water spaniel starts from the middle of the pond in pursuit of -it. - -[Illustration] - -If both swim at the same pace, how must the dog steer his course so that -he is sure in any case to overtake the duck speedily? - - -THE MAGIC OF DATES - -LOUIS NAPOLEON, EMPEROR 1852 - - 1852 1852 1852 - date 1 date 1 date 1 - of 8 of 8 of 8 - his 0 Empress’s 2 their 5 - birth 8 birth 6 marriage 3 - ---- ---- ---- - 1869 1869 1869 - -Thus, by a most remarkable series of coincidences, the principal dates -of the Emperor and Empress of the French added, as is shown above, to -the year of the Emperor’s accession, express in each instance the year -before his fall. - - -No. LXVII.--GEOMETRY WITH DOMINOES - -In this domino diagram we have a pretty and practical proof that the -squares of the sides containing the right angle in any right-angled -triangle are together equal to the square of the side opposite to the -right angle. - -[Illustration] - -Each stone forms two squares, and it is easily seen that the number of -squares which make up the whole square on the line opposite the right -angle are equal to the number of those which make up the two whole -squares on the lines which contain that angle. - -A second point to be noticed is that the number of pips on the large -square are equal to the number on the other two squares combined, an -arrangement of the stones which forms quite a game of patience to -reproduce, if this pattern is not at hand. - - -No. LXVIII.--TO COLOUR MAPS - -Four colours at most are needed to distinguish the surfaces of separate -districts on any plane map, so that no two with a common boundary are -tinted alike. - -[Illustration] - -On this diagram A, B, and C, are adjoining districts, on a plane -surface, and X borders, in one way or another, upon each. - -It is clearly impossible to introduce a fifth area which shall so adjoin -these four districts as to need another tint. - - -A FREAK OF FIGURES - -Here is another freak of figures:-- - - 9 × 1 - 1 = 8 - 9 × 21 - 1 = 188 - 9 × 321 - 1 = 2888 - 9 × 4321 - 1 = 38888 - 9 × 54321 - 1 = 488888 - 9 × 654321 - 1 = 5888888 - 9 × 7654321 - 1 = 68888888 - 9 × 87654321 - 1 = 788888888 - 9 × 987654321 - 1 = 8888888888 - - -No. LXIX.--THE TETHERED BIRD - -A bird made fast to a pole six inches in diameter by a cord fifty feet -long, in its flight first uncoils the cord, _keeping it always taut_, -and then recoils it in the reverse direction, rewinding the coils close -together. If it starts with the cord fully coiled, and continues its -flight until it brings up against the pole, how far does it fly in its -double course? - -[Illustration] - - -STRIKE IT OUT - -Ask a person to write down in a line any number of figures, then to add -them all together as units, and to subtract the result from the sum set -down. Let him then strike out any one figure, and add the others -together as units, telling you the result. - -If this has been correctly done, the figure struck out can always be -determined by deducting the final total from the multiple of 9 next -above it. If the total happens to be a multiple of 9, then a 9 was -struck out. - - -No. LXX.--THE MOVING DISC AND THE FLY - -A fly, starting from the point A, just outside a revolving disc, and -always making straight for its mate at the point B, crosses the disc in -four minutes, while the disc is revolving twice. What effect has the -revolution of the disc on the path of the fly? - -[Illustration] - - -A MAGIC SQUARE - -This Magic Square is so arranged that the product of the continued -multiplication of the numbers in each row, column, or diagonal is 4096, -which is the cube of the central 16. - - +---+---+---+ - | 8|256| 2| - +---+---+---+ - | 4| 16| 64| - +---+---+---+ - |128| 1| 32| - +---+---+---+ - - -No. LXXI.--A SHUNTING PUZZLE - -The railway, D E F, has two sidings, D B A and F C A, connected at A. -The rails at A, common to both, are long enough to hold a single wagon -such as P or Q, but too short to admit the whole of the engine R, which, -if it runs up either siding, must return the same way. - -[Illustration] - -How can the engine R be used to interchange the wagons P and Q without -allowing any flying shunts?--From _Ball’s Mathematical Recreations_. - - -No. LXXII.--A CURIOUS FACT - -It is a little known and very interesting fact that an equilateral -triangle can easily be drawn by rule of thumb in the following -way:--Take a triangle of any shape or size, and on each of its sides -erect an equilateral triangle. Find and join the centres of these, and a -fourth equilateral triangle is always thus formed, as shown by the -dotted lines. - -[Illustration] - -These centres are _centres of gravity_, and they are symmetrically -distributed around the centre of gravity of the original triangle. - -The figure formed by joining them must therefore be symmetrical, and, as -in this case, it is a triangle, it _must be_ always equilateral. - - -No. LXXIII.--TRY THIS EXPERIMENT - -There can be no better instance of how the eye may be deceived than is -so strikingly afforded in these very curious diagrams:-- - -[Illustration] - -The square which obviously contains sixty-four small squares, is to be -cut into four parts, as is shown by the thicker lines. When these four -pieces are quite simply put together, as shown in the second figure, -there seem to be sixty-five squares instead of sixty-four. - -This phenomena is due to the fact that the edges of the four pieces, -which lie along the diagonal A B, do not exactly coincide in direction. -In reality they _include a very narrow diamond_, not easily detected, -whose area is just equal to that of one of the sixty-four small squares. - - -FIGURES IN SWARMS - -Very curious are the results when the nine digits in reverse order are -multiplied by 9 and its multiples up to 81. Thus:-- - - 987654321 × 9 = 8888888889 - × 18 = 17777777778 - × 27 = 26666666997 - × 36 = 35555555556 - × 45 = 44444444445 - × 54 = 53333333334 - × 63 = 62222222223 - × 72 = 71111111112 - × 81 = 80000000001 - -It will be seen that the figures by which the reversed digits are -multiplied reappear at the beginning and end of each result except the -first, and that the figures repeated between them are to be found by -dividing the divisors by 9 and subtracting the result from 9. Thus, 54 ÷ -9 = 6, and 9 - 6 = 3. - - -No. LXXIV.--A TRIANGLE OF TRIANGLES - -[Illustration] - -In this nest of triangles there are no less than six hundred and -fifty-three distinct triangles of various shapes and sizes. - - -No. LXXV.--PHARAOH’S SEAL - -In a chamber of the Great Pyramid an ancient Egyptian jar was found, -marked with the device now known as Pharaoh’s seal. - -[Illustration] - -Can you count the number of triangles or pyramids, of many sizes, but -all of similar shape that are expressed on it? Solvers should draw the -figure on a larger scale. - - -MAKING CUBES - -It is interesting to note that the repeated addition of odd numbers to -one another can be so arranged as to produce cube numbers in due -sequence. Thus:-- - - 1 = 1 × 1 × 1 - 3 + 5 = 2 × 2 × 2 - 7 + 9 + 11 = 3 × 3 × 3 - 13 + 15 + 17 + 19 = 4 × 4 × 4 - 21 + 23 + 25 + 27 + 29 = 5 × 5 × 5 - -and so on, to any extent. - - -No. LXXVI.--ROUND THE GARDEN - -In a large old-fashioned garden walks were arranged round a central -fountain in the shape of a Maltese cross. - -[Illustration] - -If four persons started at noon from the fountain, walking round the -four paths at two, three, four and five miles an hour respectively, at -what time would they meet for the third time at their starting-point, if -the distance on each track was one-third of a mile? - - -A NICE SHORT CUT - -When the tens of two numbers are the same, and their units added -together make ten, multiply the units together, increase one of the tens -by unity, and multiply it by the other ten. The result is the product of -the two original numbers, if the first result follows the other. Thus:-- - - 43 × 47 = 2021. - - -No. LXXVII.--A JOINER’S PUZZLE - -Can you cut Fig. A into two parts, and so rearrange these that they form -either Fig. B or Fig. C? - - +--------------+ - | | - +--------------+ | +--+ - | | | | - | | +-----------------+ | | - | | | | | | - | | | | | | - | | | | | | - | | | | | | - | | | | | | - | | | | | | - | | | | | | - | | | | +--+ | - | | | | | | - +--------------+ +-----------------+ +--------------+ - A B C - -The two parts of A must not be _turned round_ to form B or C, but must -retain their original direction. - - -A CALCULATION - -Coal may fail us, but we can never run short of material for “words that -burn.” It has been calculated that if a man could read 100,000 words in -an hour, and there were 4,650,000 men available, they could not -pronounce the possible variations which could be formed from the -alphabet in 70,000 years! - - -A PARADOX - -It is possible, in a sense, by the following neat method, to take 45 -from 45, and find that 45 remains:-- - - 987654321 = 45. - 123456789 = 45. - --------- - 864197532 = 45. - - -No. LXXVIII.--THE BROKEN OCTAGON - -Cut out in stiff cardboard four pieces shaped as Fig. 1, four as Fig. 2, -and four as Fig. 3, taking care that they are all exactly true to -pattern in shape and proportion to one another. - -[Illustration] - -Now see whether you can put the twelve pieces together so as to form a -perfect octagon. - - -PROPERTIES OF SEVEN - -Here is a proof that 7, if it cannot rival the mystic 9, has quaint -properties of its own:-- - - 15873 × 7 = 111111 - 31746 × 7 = 222222 - 47619 × 7 = 333333 - 63492 × 7 = 444444 - 79365 × 7 = 555555 - 95238 × 7 = 666666 - 111111 × 7 = 777777 - 126984 × 7 = 888888 - 142857 × 7 = 999999 - - -A SWARM OF EIGHTS - -Here is an arithmetical curiosity:-- - - 9 × 9 + 7 = 88 - 9 × 98 + 6 = 888 - 9 × 987 + 5 = 8888 - 9 × 9876 + 4 = 88888 - 9 × 98765 + 3 = 888888 - 9 × 987654 + 2 = 8888888 - 9 × 9876543 + 1 = 88888888 - 9 × 98765432 + 0 = 888888888 - - -No. LXXIX.--AT A DUCK POND - -A farmer’s wife kept a pure strain of Aylesbury ducks for market on a -square pond, with a duck-house at each corner. As trade grew brisk she -found that she must enlarge her pond. An ingenious neighbour undertook -to arrange this without altering the shape of the pond, and without -disturbing the duck-houses. What was his plan? - - ○-------------○ - | | - | | - | | - | | - | | - | | - ○-------------○ - - -STRANGE SUBTRACTION - -It would seem impossible to subtract 69 from 55, but it can be arranged -thus, with six as a remainder:-- - - SIX IX XL - IX X L - ------------- - S I X - ============= - - -No. LXXX.--ALL ON THE SQUARE - -Cut out in cardboard twenty triangular pieces exactly the size and shape -of this one, and try to place them together so that they form a perfect -square. - -[Illustration] - - -ANOTHER MYSTIC NUMBER - -The decimal equivalent of ¹⁄₁₃ is .076923. This (omitting the point), -multiplied by 1, 3, 4, 9, 10, or 12, yields results in which the same -figures appear in varied order, but similar sequence, and multiplied by -2, 5, 6, 7, 8, or 11, it yields a different series, with similar -characteristics. Thus:-- - - 76923 × 1 = 76923 - × 3 = 230769 - × 4 = 307692 - × 9 = 692307 - × 10 = 769230 - × 12 = 923076 - - 76923 × 2 = 153846 - × 5 = 384615 - × 6 = 461538 - × 7 = 538461 - × 8 = 615384 - × 11 = 846153 - - -DON’T BUY IT TO TRY IT - -A kaleidoscope cylinder contains twenty small pieces of coloured glass. -As we turn it round, or shake it, so as to make ten changes of pattern -every minute, it will take the inconceivable space of time of -462,880,899,576 years and 360 days to exhaust all the possible -symmetrical variations. (The 360 days is good!) - - -No. LXXXI.--PINS AND DOTS - -Here is an amusing little exercise for the ingenuity of our solvers. - - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - -Take six sharp pins, and puzzle out how to stick them into six of the -black dots, so that no two pins, are on the same line, in any direction, -vertical, horizontal, or diagonal. - - -No. LXXXII.--A TRICKY COURSE - -The middle of a large playground was paved with sixty-four square -flagstones of equal size, which are numbered on this diagram from one to -sixty-four. - - +----+----+----+----+----+----+----+----+ - | _1_| _9_|_17_|_25_|_33_|_41_|_49_|_57_| - +----+----+----+----+----+----+----+----+ - | _2_|_10_|_18_|_26_|_34_|_42_|_50_|_58_| - +----+----+----+----+----+----+----+----+ - | _3_|_11_|_19_|_27_|_35_|_43_|_51_|_59_| - +----+----+----+----+----+----+----+----+ - | _4_|_12_|_20_|_28_|_36_|_44_|_52_|_60_| - +----+----+----+----+----+----+----+----+ - | _5_|_13_|_21_|_29_|_37_|_45_|_53_|_61_| - +----+----+----+----+----+----+----+----+ - | _6_|_14_|_22_|_30_|_38_|_46_|_54_|_62_| - +----+----+----+----+----+----+----+----+ - | _7_|_15_|_23_|_31_|_39_|_47_|_55_|_63_| - +----+----+----+----+----+----+----+----+ - | _8_|_16_|_24_|_32_|_40_|_48_|_56_|_64_| - +----+----+----+----+----+----+----+----+ - -One of the schoolmasters, who had a head for puzzles, took his stand -upon the square here numbered 19, and offered a prize to any boy who, -starting from the square numbered 46, could make his way to him, passing -through every square once, and only once. It was after many vain -attempts that the course was at last discovered. Can you work it out? - - -No. LXXXIII.--FOR THE CHILDREN - -Place twelve draughtsmen, or buttons, in a square, so that you count -four along each side of it, thus:-- - - ● ● ● ● - ● ● - ● ● - ● ● ● ● - -Now take the same men or buttons, and arrange them so that they form -another square, and you can count five along each side of it. - - -A GAME OF NINES - -Here is a good specimen of the eccentricities and powers of numbers:-- - - 153846 × 13 = 1999998 - 230769 × 13 = 2999997 - 307692 × 13 = 3999996 - 384615 × 13 = 4999995 - 461538 × 13 = 5999994 - 538461 × 13 = 6999993 - 615384 × 13 = 7999992 - 692307 × 13 = 8999991 - - -No. LXXXIV.--TELL-TALE TABLES - -She was quite an old maid, and her age was a most absolute secret. -Determined to discover it, her scapegrace nephew, on Christmas Eve, -produced these tables, and asked her with well simulated innocence on -which of them she could see the number of her age. - - +--+--+--+ +--+--+--+ +--+--+--+ - | 1|23|45| | 2|23|46| |16|27|54| - +--+--+--+ +--+--+--+ +--+--+--+ - | 3|25|47| | 3|26|47| |17|28|55| - +--+--+--+ +--+--+--+ +--+--+--+ - | 5|27|49| | 6|27|50| |18|29|56| - +--+--+--+ +--+--+--+ +--+--+--+ - | 7|29|51| | 7|30|51| |19|30|57| - +--+--+--+ +--+--+--+ +--+--+--+ - | 9|31|53| |10|31|54| |20|31|58| - +--+--+--+ +--+--+--+ +--+--+--+ - |11|33|55| |11|34|55| |21|48|59| - +--+--+--+ +--+--+--+ +--+--+--+ - |13|35|57| |14|35|58| |22|49|60| - +--+--+--+ +--+--+--+ +--+--+--+ - |15|37|59| |15|38|59| |23|50|61| - +--+--+--+ +--+--+--+ +--+--+--+ - |17|39|61| |18|39|62| |24|51|62| - +--+--+--+ +--+--+--+ +--+--+--+ - |19|41| | |19|42| | |25|52| | - +--+--+ A| +--+--+ B| +--+--+ C| - |21 43| | |22 43| | |26|53| | - +--+--+--+ +--+--+--+ +--+--+--+ - - +--+--+--+ +--+--+--+ +--+--+--+ - | 8|27|46| | 4|23|46| |32|43|54| - +--+--+--+ +--+--+--+ +--+--+--+ - | 9|28|47| | 5|28|47| |33|44|55| - +--+--+--+ +--+--+--+ +--+--+--+ - |10|29|56| | 6|29|52| |34|45|56| - +--+--+--+ +--+--+--+ +--+--+--+ - |11|30|57| | 7|30|53| |35|46|57| - +--+--+--+ +--+--+--+ +--+--+--+ - |12|31|58| |12|31|54| |36|47|58| - +--+--+--+ +--+--+--+ +--+--+--+ - |13|40|59| |13|36|55| |37|48|59| - +--+--+--+ +--+--+--+ +--+--+--+ - |14|41|60| |14|37|60| |38|49|60| - +--+--+--+ +--+--+--+ +--+--+--+ - |15|42|61| |15|38|61| |39|50|61| - +--+--+--+ +--+--+--+ +--+--+--+ - |24|43|62| |20|39|62| |40|51|62| - +--+--+--+ +--+--+--+ +--+--+--+ - |25|44| | |21|44| | |41|52| | - +--+--+ D| +--+--+ E| +--+--+ F| - |26|45| | |22|45| | |42|53| | - +--+--+--+ +--+--+--+ +--+--+--+ - -From her answer he was able to calculate that the old lady was -fifty-five. - -The tell-tale tables disclosed her age thus:--As it appeared in tables -A, B, C, E, and F, he added together the numbers at the top left-hand -corners, and found the total to be fifty-five. This rule applies in all -cases. - - -No. LXXXV.--A PAPER PUZZLE - -Of the many paper-cutting tricks which appeal to us none is more simple -and attractive than this:-- - - +---+ - | | - | | - +-----+ +-----+ - | | - +-----+ +-----+ - / \ | | / \ - \ / | | \ / - +-+ | | +-+ - | | | | | | - | | | | | | - | | | | | | - | | +---+-+-+---+ | | - +-+ | | | +-+ - +---+ | +-+-+ | +---+ - | +---+---+-+-+---+---+ | - | | | - +-------------+-------------+ - -Take a piece of paper, say 5 inches by 3 inches, but any oblong shape -and size will do, and after folding it four times cut it lengthways up -the centre. Unfold the pieces, and to your surprise you will find a -perfect cross and other pieces in pairs of the shapes shown above. The -puzzle is how to fold the paper. - - +--------------+----------+ - |b d¦ | - | ¦ | - | ¦ | - | e¦ | - | ¦ | - | ¦ | - |a c¦ | - +--------------+----------+ - -The paper must be folded first so that B comes upon C, then so that A -comes upon D, then from D to C, and lastly from E to C. If it is now cut -lengthways exactly along the centre the figures shown on the original -diagram will be formed, which resemble a cross and lighted candles on an -altar. - - -No. LXXXVI.--A HOME-MADE PUZZLE - -Take a thin board, about eight inches square, and mark it out into -thirty-six equal parts; bore a hole in the centre of each part, and then -fit in a small wooden peg, leaving about a quarter inch above the -surface, as is shown in Fig. 1, the section below the diagram. - -[Illustration] - -Prepare thirty-six pieces of white or coloured cardboard of the length A -to B, and place them over the pegs in any direction in which they will -fit so as to form some such symmetrical pattern as is given on the -second diagram, putting two holes only on each peg. Chess-players will -see that this is the regular knight’s move. - -[Illustration] - -Quite a number of beautiful designs can be thus formed, and those who -have not the means at hand for making a complete set can enjoy the -puzzle by merely marking out thirty-six squares, and drawing lines from -centre to centre of the exact length from A to B, with black or coloured -pencils. - - -No. LXXXVII.--LOYD’S MITRE PROBLEM - -[Illustration] - -Divide this figure into four similar and equal parts. - - -A PRETTY PROBLEM - -The solution of the pretty little problem: place three twos in three -different groups, so that twice the first group, or half the third group -equals the second group, is this:-- - - 2 1 2 2 + 2 - ----- = - 2 - - = 1 ----- = 2 - 2 + 2 2 2 2 - - -No. LXXXVIII.--CONTINUOUS LINES - -The following figure, which represents part of a brick wall, cannot be -marked out along all the edges of the bricks in less than six continuous -lines without going more than once over the same line:-- - -[Illustration] - -Here, in strong contrast to the simple figure given above, which could -not be traced without lifting the pen six times from the paper, is an -intricate design, the lines of which, on the upper or on the lower half, -can be traced without any break at all. - -[Illustration] - -The general rule that governs such cases is, that where an uneven number -of lines meet a fresh start has to be made. In the diagram now given the -only such points are at the extremities of the upper and lower halves of -the figure at A and X. At all other points two, or four, or six lines -converge, and there is no break of continuity in a tracing of the -figure. - - -No. LXXXIX.--CUT OFF THE CORNERS - -Can you suggest quite a simple and practical way to fix the points on -the sides of a square which will be at the angles of an octagon formed -by cutting off equal corners of the square, as shown below? - - A E F B - +------+--------+------+ - | / \ | - | / \ | - |/ \| - M+ +G - | | - | | - | | - L+ +H - |\ /| - | \ / | - | \ / | - +------+--------+------+ - C K I D - - -MYSTIC FIGURES - -Very interesting and curious are the properties of the figures 142857, -used in varied order but always in similar sequence, in connection with -7 and 9:-- - - 142857 × 7 = 999999 ÷ 9 = 111111 - 285714 × 7 = 1999998 ÷ 9 = 222222 - 428571 × 7 = 2999997 ÷ 9 = 333333 - 571428 × 7 = 3999996 ÷ 9 = 444444 - 714285 × 7 = 4999995 ÷ 9 = 555555 - 857142 × 7 = 5999994 ÷ 9 = 666666 - - -No. XC.--THE FIVE TRIANGLES - -The subjoined diagram shows how a square with sides that measure each 12 -yards can be divided into five triangles, no two of which are of equal -area, and of which the sides and areas can be expressed in yards by -whole numbers:-- - -[Illustration] - -The areas of these triangles are 6, 12, 24, 48, and 54 square yards -respectively, and the sum of these, 144 square yards, is the area of the -square. - - -CURIOUS COINCIDENCES - -Our readers may remember the remarkable fact that the figures of the -sum, £12, 12s. 8d., when written thus, 12,128, exactly represent the -number of farthings it contains. Now this, so far as we know, is the -only instance of the peculiarity, but there are at least five other -cases which come curiously near to it. They are these:-- - - £ s. d. - 9 9 6 = 9096 farthings - 6 6 4 = 6064 „ - 3 3 2 = 3032 „ - 10 10 6¹⁄₂ = 10106 „ - 13 13 8¹⁄₂ = 13138 „ - - -No. XCI.--PLACING A LADDER - -If a ladder, with rungs 1 foot apart, rests against a wall, and its -thirteenth rung is 12 feet above the ground, the foot of the ladder is -25 feet from the wall. - -[Illustration] - -_Proof._--Drop a perpendicular from A to B. Then, as A B C is a right -angle, and the squares on A C, A B, are 169 feet and 144 feet, the -square on C B must be 25 feet, and the length of C B is 5 feet. We thus -move 5 feet towards the wall in going 13 feet up the ladder, and in -mounting 65 feet (five times as far) we must cover 25 feet. - - -No. XCII.--GRACEFUL CURVES - -A prettily ingenious method of dividing the area of a circle into -quarters, each of them a perfect curve, with perimeter (or enclosing -line) equal to the circumference of the circle, and with which four -circles can be formed, is clearly shown by the subjoined diagrams:-- - -[Illustration] - - -NIGHTS AT A ROUND TABLE - -The host of a large hotel at Cairo noticed that his Visitors’ Book -contained the names of an Austrian, a Brazilian, a Chinaman, a Dane, an -Englishman, a Frenchman, a German, and a Hungarian. Moved by this -curious alphabetical list, he offered them all free quarters and the -best of everything if they could arrange themselves at a round -dining-table so that not one of them should have the same two neighbours -on any two occasions for 21 successive days. - -The following is one of many ways in which this arrangement can be made, -and it seems to be the simplest of them all. - -Number the persons 1 to 8; and for our first day set them down in -numerical order _except that the two centre ones (4 and 5) change -places_: - - (1st day)--1 2 3 5 4 6 7 8 - -Keep the 1 and the 7 unaltered but double each of the other numbers. -When the product is greater than 8, divide by 7, and only set down the -remainder. Thus we get: - - (8th day)--1 4 6 3 8 5 7 2 - -(Here the fourth figure 3 is 5 × 2 ÷ 7, giving _remainder_ 3, and so -on.) - -Repeat this operation once more: - - (15th day)--1 8 5 6 2 3 7 4 - -To fill in the intermediate days we have only to keep 1 unchanged and -let the remaining numbers run downwards in _simple numerical order_, -following 8 with 2, 2 with 3, and so on. Thus:-- - - 1st day--1 2 3 5 4 6 7 8 - 2nd day--1 3 4 6 5 7 8 2 - 3rd day--1 4 5 7 6 8 2 3 - 4th day--1 5 6 8 7 2 3 4 - 5th day--1 6 7 2 8 3 4 5 - 6th day--1 7 8 3 2 4 5 6 - 7th day--1 8 2 4 3 5 6 7 - ------------------------- - 8th day--1 4 6 3 8 5 7 2 - 9th day--1 5 7 4 2 6 8 3 - 10th day--1 6 8 5 3 7 2 4 - 11th day--1 7 2 6 4 8 3 5 - 12th day--1 8 3 7 5 2 4 6 - 13th day--1 2 4 8 6 3 5 7 - 14th day--1 3 5 2 7 4 6 8 - ------------------------- - 15th day--1 8 5 6 2 3 7 4 - 16th day--1 2 6 7 3 4 8 5 - 17th day--1 3 7 8 4 5 2 6 - 18th day--1 4 8 2 5 6 3 7 - 19th day--1 5 2 3 6 7 4 8 - 20th day--1 6 3 4 7 8 5 2 - 21st day--1 7 4 5 8 2 6 3 - -This completes the schedule. It will be found on examination that every -number is between every pair of the other numbers once, and once only. - -In order to reduce our first-day ring to exact numerical order we have -only to interchange the numbers 4 and 5 throughout. The first three -lines for example would then become: - - 1 2 3 4 5 6 7 8 - 1 3 5 6 4 7 8 2 - 1 5 4 7 6 8 2 3, etc. - -or, by putting letters for figures, - - A B C D E F G H - A C E F D G H B - A E D G F H B C, etc. - -An arrangement of the guests is thus arrived at for twenty-one -successive days, so that not one of them has the same two neighbours on -any two occasions. - - -No. XCIII.--MAKING MANY SQUARES - -Can you apply the two oblongs drawn below to the two concentric squares, -so as to produce thirty-one perfect squares? - - +------+ +------+ - | | | | - | | | | - +----------------------------------+ +------+ +------+ - | | | | | | - | | | | | | - | +--------------------+ | +------+ +------+ - | | | | | | | | - | | | | | | | | - | | | | +------+ +------+ - | | | | | | | | - | | | | | | | | - | | | | +------+ +------+ - | | | | | | | | - | | | | | | | | - | +--------------------+ | +------+ +------+ - | | | | | | - | | | | | | - +----------------------------------+ +------+ +------+ - | | | | - | | | | - +------+ +------+ - - -No. XCIV.--CUT ACROSS - -Take a piece of cardboard in the form of a Greek cross with arms, as -shown here, and divide it by two straight cuts, so that the pieces when -reunited form a perfect square. - - +------+ - | | - | | - +------+ +------+ - | | - | | - +------+ +------+ - | | - | | - +------+ - - -No. XCV.--A PRETTY PUZZLE - -The diagrams which we give below show how a hollow square can be formed -of the pieces of three-quarters of another square from which a corner -has been cut away:-- - - +-------+ +-------+ +-------+-------+ - | | | | | | | - | | | +---+ | +---+---+ | - | | | | | | | | | - | +-------+ +---+ +---+---+ +---+ +---+ - | | | | | | | | | | - | | | +---+---+ | | +---+---+ | - | | | | | | - +---------------+ +---------------+ +---------------+ - - -No. XCVI.--A FIVE-FOLD SQUARE - -The subjoined diagram shows how a square of paper or cardboard may be -cut into nine pieces which, when suitably arranged, form five perfect -squares. - -[Illustration] - - -THE SOCIABLE SCHOOLGIRLS - -On how many days can fifteen schoolgirls go out for a walk so arranged -in rows of three, that no two are together more than once? - -Fifteen schoolgirls can go out for a walk on seven days so arranged in -rows of three that no two are together more than once. - -It is said, on high authority, that there are no less than -15,567,522,000 different solutions to this problem. Here is one of them, -given in _Ball’s Mathematical Recreations_, in which _k_ stands for one -of the girls, and _a_, _b_, _c_, _d_, _e_, _f_, _g_, in their -modifications, for her companions on the seven different days:-- - - +---------+---------+---------+---------+---------+---------+--------+ - | Sunday | Monday | Tuesday |Wednesday| Thursday| Friday |Saturday| - +---------+---------+---------+---------+---------+---------+--------+ - |_ka₁a₂_ |_kb₁b₂_ |_kc₁c₂_ |_kd₁d₂_ |_ke₁e₂_ |_kf₁f₂_ |_kg₁g₂_ | - |_b₁d₁f₁_ |_a₁d₂e₂_ |_a₁d₁e₁_ |_a₂b₂c₂_ |_a₂b₁c₁_ |_a₁b₂c₁_ |_a₁b₁c₂_| - |_b₂e₁g₁_ |_a₂f₂g₂_ |_a₂f₁g₁_ |_a₁f₂g₁_ |_a₁f₁g₂_ |_a₂d₂e₁_ |_a₂d₁e₂_| - |_c₁d₂g₂_ |_c₁d₁g₁_ |_b₁d₂f₂_ |_b₁e₁g₂_ |_b₂d₁f₂_ |_b₁e₂g₁_ |_b₂d₂f₁_| - |_c₂e₂f₂_ |_c₂e₁f₁_ |_b₂e₂g₂_ |_c₁e₂f₁_ |_c₂d₂g₁_ |_c₂d₁g₂_ |_c₁e₁f₂_| - +---------+---------+---------+---------+---------+---------+--------+ - -It is an excellent game of patience, for those who have time and -inclination, to place the figures 1 to 15 inclusive in seven such -columns, so as to fulfil the conditions. - - -No. XCVII.--THE THREE CROSSES - -It is possible from a Greek cross to cut off four equal pieces which, -when put together, will form another Greek cross exactly half the size -of the original, and by this process to leave a third Greek cross -complete. - -[Illustration] - -This is how to do it:-- - -Bisect _C D_ at _N_, _F G_ at _O_, _K L_ at _P_, and _B I_ at _Q_. - -Join _N H_, _O M_, _P A_, _Q E_, intersecting at _R_, _S_, _T_, _U_. - -Bisect _A R_ at _V_, _E S_ at _W_, _T H_ at _X_, and _M U_ at _Y_. - -Join _V Q_, _N Y_, _W P_, _O X_, _N W_, _V O_, _Q X_, _Y P_. - -Carefully cut out from the original Greek cross the newly-formed Greek -cross, and the odd pieces from around it can be arranged to form another -Greek cross. - - -No. XCVIII.--THE HAMMOCK - -The greatest number of plane figures that can be formed by the union of -ten straight lines is thirty-six. - -[Illustration] - -The two equal lines at right angles are first drawn, and each is divided -into eight equal parts. The other eight straight lines are then drawn -from _a_ to _a_, from _b_ to _b_, and so on, until the hammock-shaped -network of thirty-six plane figures is produced. - - -No. XCIX.--CUTTING A CRUMPET - -It will be seen on the diagram below that seven straight vertical cuts -with a table-knife will divide a crumpet into twenty-eight parts. - -[Illustration] - -BALANCE THE SCALES - -The nine digits can be so adjusted as to form an equation, or, if taken -as weight, to balance the scales. Thus:-- - - 9, 6¹⁄₂ = 3, 5, 7⁴⁄₈ - - -TRUE STRETCHES OF IMAGINATION - -How large is the sea? This is a bold big question, and any possible -answer involves a considerable stretch of the imagination. Here is a -startling illustration of its vast volume:-- - -If the water of the sea could be gathered into a round column, reaching -the 93,000,000 miles which separate us from the sun, the diameter of -this column would be nearly two miles and a half! - -It is perhaps even more difficult to realise that this mighty mass of -waters could be dissipated in a few moments, if the column we have -imagined could become ice, and if the entire heat of the sun could be -concentrated upon it. All would be melted in _one second of time_, and -converted into steam in eight seconds! - - -No. C.--TO MAKE AN ENVELOPE - -Many of our readers may be glad to know an easy way to make an envelope -of any shape or size. - -[Illustration] - -This diagram speaks for itself. When the lines _A B_, _A C_, _D B_, _D -C_ have been drawn, the corners of the rectangle, _H E G F_, are folded -over, as shown by the dotted lines, after the corners have been rounded, -and the margins touched with gum. - - -No. CI.--SQUARING AN OBLONG - -The diagrams below will show how a piece of paper, 15 inches long and 3 -inches wide, can be cut into five parts, and rearranged to form a -perfect square. - -[Illustration] - - -A PLAGUE OF BLOW-FLIES - -The following astounding calculation is answer enough to a question put -by one of the authors of “Rejected Addresses:”--“Who filled the -butchers’ shops with big blue flies?” - -A pair of blow-flies can produce ten thousand eggs, which mature in a -fortnight. If every egg hatches out, and there are equal numbers of -either sex, which forthwith increase and multiply at the same rapid -rate, and if their descendants do the like, so that all survive at the -end of six months, it has been calculated that, if thirty-two would fill -a cubic inch of space, the whole innumerable swarm would cover the -globe, land and sea, half a mile deep everywhere. - - -No. CII.--BY RULE OF THUMB - -Here is quite a neat way to make an equilateral triangle without using -compasses:-- - -[Illustration] - -Take a piece of paper exactly square, which we will call _A B C D_, fold -it across the middle, so as to form the crease _E F_; unfold it, and -fold it again so that the corner _D_ falls upon the crease _E F_ at _G_, -and the angle at _G_ is exactly divided. Again unfold the square, and -from _G_ draw the straight lines _G C_ and _G D_. Then _G C D_ is the -equilateral triangle required. - - -THE VALUE OF A FRENCHWOMAN - -How can we be sure that the value of a Frenchwoman is just 1 franc 8 -centimes? - -We can be sure that the exact value of a Frenchwoman is 1 franc 8 -centimes, for - - Two Frenchwomen = Deux Françaises. - Deux Françaises = deux francs seize. - (2 francs 16). - Therefore, One Frenchwoman = 1 franc 8! - - -No. CIII.--CLEARING THE WALL - -If a 52-feet ladder is set up so as just to clear a garden wall 12 feet -high and 15 feet from the building, it will touch the house 48 feet from -the ground. - -[Illustration] - -Our diagram shows this, and also, by a dotted line, the only other -possible position in which it could fulfil the conditions, if it were -then of any practical use. - - -A BURDEN OF PINS - -If one pin could be dropped into a vessel this week, two the next, four -the next, and so on, doubling each time for a year, the accumulated -quantity would be 4,503,599,627,370,495, and their weight, if we reckon -200 pins to the ounce, would amount to 628,292,358 tons, a full load for -27,924 ships as large as the _Great Eastern_, whose capacity was 22,500 -tons. - - -No. CIV.--MEMORIES OF EUCLID - -When at the signpost which said “To _A_ 4 miles, to _B_ 9 miles” on one -arm, and on the other “To _C_ 3 miles, to _D_ ---- miles,” and the boy -whom I met could only tell me that the farm he worked at was equidistant -from _A_, _B_, _C_, and _D_, and nearer to them than to the signpost, -and that all the roads ran straight, I found, thanks to memories of -Euclid, that I was 12 miles from _D_. - -[Illustration] - -Since _B A_ and _D C_ intersect outside the circle at the signpost _E_, - - therefore _A E_ × _E B_ = _C E_ × _E D_. - but _A E_ × _E B_ = 4 × 9 = 36, - therefore _C E_ × _E D_ = 36, - and _C E_ = 3, therefore _E D_ = 12. - - _Q.E.D._ - - -No. CV.--A TRANSFORMATION - -This seems to be quite a poor attempt at a Maltese cross, but there is -method in the madness of its make. - -[Illustration] - -It is possible by two straight cuts to divide this uneven cross into -four pieces which can be arranged together again so that they form a -perfect square. Where must the cuts be made, and how are the four pieces -rearranged? - - -BREVITY IS THE SOUL OF WIT - -We all remember that splendidly terse message of success sent home to -the authorities by Napier when he had conquered the armies of -Scinde--“Peccavi!” (I have sinned). - -History had an excellent opportunity for repeating itself when Admiral -Dewey defeated the Spaniel fleet, for he might have conveyed the news of -his victory by the one burning word--“Cantharides”--“The Spanish fly!” - - -No. CVI--SHIFTING THE CELLS - -In the diagram below a square is subdivided into twenty-five cells. - - +-----------+-----------+-----------+-----------+-----------+ - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - |/ \|/ \|/ \|/ \|/ \| - | | | | | | - | | | | | | - +-----------+-----------+-----------+-----------+-----------+ - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - |/ \|/ \|/ \|/ \|/ \| - | | | | | | - | | | | | | - +-----------+-----------+-----------+-----------+-----------+ - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - |/ \|/ \|/ \|/ \|/ \| - | | | | | | - | | | | | | - +-----------+-----------+-----------+-----------+-----------+ - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - |/ \|/ \|/ \|/ \|/ \| - | | | | | | - | | | | | | - +-----------+-----------+-----------+-----------+-----------+ - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - |/ \|/ \|/ \|/ \|/ \| - | | | | | | - | | | | | | - +-----------+-----------+-----------+-----------+-----------+ - -Can you, keeping always on the straight lines, cut this into four -pieces, and arrange these as two perfect squares, in which every -semicircle still occupies the upper half of its cell? - - -A HOME-MADE MICROSCOPE - -The following very simple recipe for a home-made microscope has been -suggested by a Fellow of the Royal Microscopical Society:-- - -Take a piece of black card, make a small pinhole in it, put it close to -the eye, and look at some small object closely, such as the type of a -newspaper. A very decided magnifying power will be shown thus. - - -No. CVII.--IN A TANGLE - -Where on this diagram must we place twenty-one pins or dots so that they -fall into symmetrical design and form thirty rows, with three in each -row? - -[Illustration] - - -ON ALL FOURS - -Those who are fond of figures will find it a most interesting exercise -to see how far they are able to represent every number, from one up to a -hundred, by the use of four fours. Any of the usual signs and symbols of -arithmetic may be brought into use. Here are a few instances of what may -thus be done:-- - - 4 + 4 + 4 4 - 3 = ---------; 9 = 4 + 4 + -; - 4 4 - - 4 - 36 = 4(4 + 4) + 4; 45 = 44 + -; - 4 - - 52 = 44 + 4 + 4; 60 = 4 × 4 × 4 - 4. - - -No. CVIII.--STILL A SQUARE - -This figure, which now forms a square, and the quarter of that square, -can be so divided by two straight lines that its parts, separated and -then reunited, form a perfect square. How is this done? - - +------+------+------+ - | | | | - | | | | - +------+------+------+ - | | | - | | | - +------+------+ - - -A MAGIC SQUARE - -Here we have arranged five rows of five cards each, so that no two -similar cards are in the same lines. Counting the ace as eleven, each -row, column, and diagonal adds up to exactly twenty-six. - - /-------\ /-------\ /-------\ /-------\ /-------\ - | ♣ | | ♥ | | ♠ ♠ | | ♥ ♥ | | ♣ ♣ | - | | | | | | | ♥ | | ♣ ♣ | - | | | ♥ | | ♠ | | ♥ | | ♣ | - | | | | | | | ♥ | | ♣ ♣ | - | ♣ | | ♥ | | ♠ ♠ | | ♥ ♥ | | ♣ ♣ | - \-------/ \-------/ \-------/ \-------/ \-------/ - - /-------\ /-------\ /-------\ /-------\ /-------\ - | ♦ ♦ | | ♠ ♠ | | ♦ ♦ | | | | ♦ | - | | | ♠ | | ♦ ♦ | | | | | - | ♦ | | ♠ | | ♦ ♦ | | ♠ | | ♦ | - | | | ♠ | | ♦ ♦ | | | | | - | ♦ ♦ | | ♠ ♠ | | ♦ ♦ | | | | ♦ | - \-------/ \-------/ \-------/ \-------/ \-------/ - - /-------\ /-------\ /-------\ /-------\ /-------\ - | ♥ ♥ | | | | ♠ | | ♥ ♥ | | ♣ ♣ | - | ♥ ♥ | | | | | | | | ♣ | - | ♥ | | ♣ | | ♠ | | ♥ | | ♣ ♣ | - | ♥ ♥ | | | | | | | | ♣ | - | ♥ ♥ | | | | ♠ | | ♥ ♥ | | ♣ ♣ | - \-------/ \-------/ \-------/ \-------/ \-------/ - - /-------\ /-------\ /-------\ /-------\ /-------\ - | ♣ | | ♥ ♥ | | ♣ ♣ | | ♦ ♦ | | | - | | | | | ♣ | | ♦ ♦ | | | - | ♣ | | ♥ ♥ | | ♣ | | ♦ | | ♥ | - | | | | | ♣ | | ♦ ♦ | | | - | ♣ | | ♥ ♥ | | ♣ ♣ | | ♦ ♦ | | | - \-------/ \-------/ \-------/ \-------/ \-------/ - - /-------\ /-------\ /-------\ /-------\ /-------\ - | ♦ ♦ | | ♠ ♠ | | | | | | ♣ ♣ | - | ♦ | | ♠ ♠ | | | | ♠ ♠ | | | - | ♦ | | ♠ | | ♦ | | | | ♣ | - | ♦ | | ♠ ♠ | | | | ♠ ♠ | | | - | ♦ ♦ | | ♠ ♠ | | | | | | ♣ ♣ | - \-------/ \-------/ \-------/ \-------/ \-------/ - -After you have looked at this Magic Square, and set it out on the table, -shuffle the cards, and try to re-arrange them so as to give the same -results. - - -No. CIX.--A TRANSFORMATION - -Cut a square of paper or cardboard into seven such pieces as are marked -in this diagram. - -[Illustration] - -Can you rearrange them so that they form the figure 8. - - -A SECRET REVEALED - -There are several ways in which strange juggling with figures and -numbers is to be done, but none is more curious than this:-- - -Ask someone, whose age you do not know, to write down secretly the date -and month of his birth in figures, to multiply this by 2, to add 5, to -multiply by 50, to add his age last birthday and 365. He then hands you -_this total only_ from this you subtract 615. This reveals to you at a -glance his age and birthday. - -Thus, if he was born April 7 and is 23, 74 (the day and the month) × 2 = -148; 148 + 5 = 153; 153 × 50 = 7650; 7650 + 23 (his age) = 7673; and -7673 + 365 = 8038. If from this you subtract 615, you have 7423, which -represents to you the _seventh day of the fourth month, 23 years age_! -This rule works out correctly in all cases. - - -No. CX.--TO MAKE AN OBLONG - -Cut out in stiff paper or cardboard two pieces of the shape and size of -the small triangle, and four pieces of the shapes and sizes of the other -three patterns--fourteen pieces in all. - -[Illustration] - -The puzzle is to fit these pieces together so that they form a perfect -oblong. - - -SLEEPERS THAT SLIP AND SLEEP - -Here is a string of sentences, which may be used as stimulating mental -gymnastics when we leave the “Land of Nod.” - -A sleeper runs on sleepers, and in this sleeper on sleepers sleepers -sleep. As this sleeper carries its sleepers over the sleepers that are -under the sleeper, a slack sleeper slips. This jars the sleeper and its -sleepers, so that they slip and no longer sleep. - - -DAYS THAT ARE BARRED - -Clever calculation has established a fact which we shall not be able to -verify by personal experience. Whatever else may happen, the first day -of a century can never fall on Sunday, Wednesday, or Friday. - - -No. CXI.--SQUARES ON THE CROSS - -On this cross there are seventeen distinct and perfect squares marked -out at their corners by asterisks. - - *-----------* - | | - | | - | | - | | - | | - *-----------* - /| \ / |\ - / | \ / | \ - / | * | \ - / | / \ | \ - / | / \ | \ - *-----------*-----------*-----------*-----------*-----------* - | | \ / | \ / | \ / | | - | | \ / | \ / | \ / | | - | | * | * | * | | - | | / \ | / \ | / \ | | - | | / \ | / \ | / \ | | - *-----------*-----------*-----------*-----------*-----------* - \ | \ / | / - \ | \ / | / - \ | * | / - \ | / \ | / - \| / \ | / - *-----------* - | | - | | - | | - | | - | | - *-----------* - -How few, and which, of these can you remove, so that not a single -perfect square remains? - - -STANDING ROOM FOR ALL - -On a globe 2 feet in diameter the Dead Sea appears but as a small -coloured dot. If it were frozen over there would be standing room on its -surface for the whole human race, allowing 6 square feet for each -person; and if they were all suddenly engulfed, it would merely raise -the level of the lake about 4 inches. - - -No. CXII.--A CHINESE PUZZLE - -Here is quite a good exercise for ingenious brains and fingers. Cut a -piece of stiff paper or cardboard into such a right-angled triangle as -is shown below. - - + - | \ - | \ - | \ - | \ - | \ - | \ - | \ - | \ - | \ - | \ - | \ - | \ - | \ - | \ - +----------------------------+ - - +----+ - | | - +--+ +--+ - | | - +--+ +--+ - | | - +--+ +--+ - | | - +--+ +--+ - | | - +--+ +--+ - | | - +--+ +--+ - | | - +----+ - -Can you divide this into only three pieces, which, when rearranged, will -form the design given as No. 2? - - -A DEAL IN ROSES - -I sent an order for dwarf roses to a famous nursery-garden, asking for a -parcel of less than 100 plants, and stipulating that if I planted them 3 -in a row there should be 1 over; if 4 in a row 2 over; if 5 in a row 3 -over, and if 6 in a row 4 over, as a condition for payment. - -The nurseryman was equal to the occasion, charged me for 58 trees, and -duly received his cheque. - - -No. CXIII.--FIRESIDE FUN - -This puzzle is not so easy of solution as it may seem at first sight. - -Take a counter, or a coin, and place it on one of the points; then push -it across to the opposite point, and leave it there. Do this with a -second counter or coin, starting on a vacant point, and continue this -process until every point is covered, as we place the eighth counter or -coin on the last point. - - A+ +B - | \ / | - | \ / | - | + | - | / \ | - | / \ | - H+-----------+-----------+-----------+C - \ / | | \ / - \ / | | \ / - + | | + - / \ | | / \ - / \ | | / \ - G+-----------+-----------+-----------+D - | \ / | - | \ / | - | + | - | / \ | - | / \ | - F+ +E - - -A NOVEL EXERCISE - -“Write down,” said a schoolmaster, “the nine digits in such order that -the first three shall be one third of the last three, and the central -three the result of subtracting the first three from the last.” - -The arrangement which satisfies these conditions is, 219, 438, 657. - - -CURIOUS CALCULATIONS - - -1. There is a sum of money of such sort that its pounds, shillings, and -pence, written down as one continuous number, represent exactly the -number of farthings which it contains. What is it? - - -THE SLIP CARRIAGE - -2. If on a level track a train, running all the time at 30 miles an -hour, slips a carriage, which is uniformly retarded by the brakes, and -which comes to rest in 200 yards, how far has the train itself then -travelled? - - -3. A traveller said to the landlord of an inn, “Give me as much money as -I have in my hand, and I will spend sixpence with you.” This was done, -and the process was twice repeated, when the traveller had no money -left. How much had he at first? - - -4. How can we obtain eleven by adding one-third of twelve to four-fifths -of seven? - - -FILL IN THE GAPS - -5. Can you replace the missing figures in this mutilated long division -sum? - - 215)*7*9*(1** - *** - ----- - *5*9 - *5*5 - ----- - *4* - *** - ===== - - -6. I buy as many heads of asparagus in the market as can be contained by -a string 1 foot long. Next day I take a string 2 feet long, and buy as -many as it will gird, offering double the price that I have given -before. Was this a reasonable offer? - - -ALIKE FROM EITHER END - -7. As “one good turn deserves another,” first reverse me, then reverse -my square, then my cube, then my fourth power. When all this is done no -change has been made. What am I? - - -THE SEALED BAGS - -8. How can a thousand pounds be so conveniently stored in ten sealed -bags that any sum in pounds from £1 to £1000 can be paid without -breaking any of the seals? - - -9. This is at once a problem and a puzzle:-- - - Though you twist and turn me over, - Yet no change can you discover. - Take me thrice, and cut in twain, - You will find but one remain. - - -10. Three gamblers, when they sit down to play, agree that the loser -shall always double the sum of money that the other two have before -them. After each of them has lost once, it is found that each has eight -sovereigns on the table. How much money had each at starting? - - -FIND THE MULTIPLIER - -11. When Tom’s back was turned, the boy sitting next to him rubbed out -almost all his sum. Tom could not remember the multiplier, and only -this remained on his slate-- - - 345 - .. - ----- - .... - .... - ----- - ..76. - -Can you reconstruct the sum? - - -JUGGLING WITH THE DIGITS - -12. The sum of the nine digits is 45. Can you hit upon other -arrangements of 1, 2, 3, 4, 5, 6, 7, 8, 9, writing each of them once -only, which will produce the same total. Of course fractions may be -used. - - -A BRAIN TWISTER - -13. The combined ages of Mary and Ann are forty-four years. Mary is -twice as old as Ann was when Mary was half as old as Ann will be when -Ann is three times as old as Mary was when Mary was three times as old -as Ann. How old, then, is Mary? - - -14. Mr Oldboy was playing backgammon with his wife on the eve of his -golden wedding, and could not make up his mind whether he should leave a -blot where it could be taken up by an ace, or one which a tré would hit. - -His grandson, at home from Cambridge for the Christmas vacation, solved -the question for him easily. What was his decision? - - -“ASK WHERE’S THE NORTH?”--_Pope._ - -15. I am aboard a steamer, anchored in a bay where the needle points due -north, and exactly 1200 miles from the North Pole. If the course is -perfectly clear, and I steam continuously at the rate of 20 miles an -hour, always steering north by the compass needle, how long will it take -me to reach the North Pole? - - -16. Three persons, _A_, _B_, and _C_, share twenty-one wine casks of -equal capacity, of which seven are full, seven are half full, and seven -are empty. How can these be so apportioned that each person shall have -an equal number of casks, and an equal quantity of wine, without -transferring any of it from cask to cask? - - -17. A hungry mouse, in search of provender, came upon a box containing -ears of corn. He could carry three ears home at a time, and only had -opportunity to make fourteen journeys to and fro. How many ears could he -add to his store? - - -18. Take exactly equal quantities of lard and butter; mix a small piece -of the butter intimately with all the lard. From this blend take a piece -just as large as the fragment removed from the butter, and mix this -thoroughly with the butter. Is there now more lard in the butter or more -butter in the lard? - - -WHERE IS THE FALLACY? - -19. Here is an apparent proof that 2 = 3:-- - - 4 - 10 = 9 - 15 - - 4 - 10 + ²⁵⁄₄ = 9 - 15 + ²⁵⁄₄ - -and the square roots of these:-- - - 2 - ⁵⁄₂ = 3 - ⁵⁄₂ - -therefore - - 2 = 3. - - -PARCEL POST LIMITATIONS - -20. Our Parcel Post regulations limit the length of a parcel to 3 feet 6 -inches, and the length and girth combined to 6 feet. What is the largest -parcel of any size that can be sent through the post under these -conditions? - - -21. How can we show, or seem to show, that either four, five, or six -nines amount to one hundred? - - -TEST YOUR SKILL - -22. Can you arrange nine numbers in the nine cells of a square, the -largest number 100, and the least 1, so that the product by -multiplication of each row, column and diagonal is 1000? - - -CATCHING CRABS - -23. Seven London boys were at the seaside for a week’s holiday, and -during the six week-days they caught four fine crabs in pools under the -rocks, when the tide was out at Beachy Head. - -Hearing of this, the twenty-one boys of a school in the neighbourhood -determined to explore the pools; but with the same rate of success they -only caught one large crab. For how long were they busy searching under -the seaweed? - - -SETTING A WATCH - -24. On how many nights could a watch be set of a different trio from a -company of fifteen soldiers, and how often on these terms could one of -them, John Pipeclay, be included? - - -“IMPERIAL CÆSAR” - -25. If Augustus Cæsar was born on September 23rd, B.C. 63, on what day -and in what year did he celebrate his sixty-third birthday, and by what -five-letter symbol can we express the date? - - -26. _A_ was born in 1847, _B_ in 1874. In what years have the same two -digits served to express the ages of both, if they are still living? - - -THIS SHOULD “AMUSE” - - 27. A hundred and one by fifty divide, - To this let a cypher be duly applied; - And when the result you can rightly divine, - You find that its value is just one in nine. - - -OVER THE FERRY - -28. A man started one Monday morning with money in his purse to buy -goods in a neighbouring town. He paid a penny to cross the ferry, spent -half of the money he then had, and paid another penny at the ferry on -his return home. - -He did exactly the same for the next five days, and on Saturday evening -reached home with just one penny in his pocket. How much had he in his -pocket on Monday before he reached the ferry? - - -THE MEN, THE MONKEY, AND THE MANGOES - -29. Three men gathered mangoes, and agreed that next day they would give -one to their monkey and divide the rest equally. The first who arrived -gave one to the monkey, and then took his proper share; the second came -later and did likewise, and the third later still, neither knowing that -any one had preceded him. Finally they met, and, as there were still -mangoes, gave one to the monkey, and shared the rest equally. How many -mangoes at least must there have been if all the divisions were -accurate? - - -30. I look at my watch between four and five, and again between seven -and eight. The hands have, I find, exactly changed places, so that the -hour-hand is where the minute-hand was, and the minute-hand takes the -place of the hour-hand. At what time did I first look at my watch? - - -A LARGE ORDER - -31. There is a number consisting of twenty-two figures, of which the -last is 7. If this is moved to the first place, the number is increased -exactly sevenfold. Can you discover this lengthy number? - - -32. A farmer borrowed from a miller a sack of wheat, 4 feet long and 6 -feet in circumference. He sent in repayment two sacks, each 4 feet long -and 3 feet in circumference. Was the miller satisfied? - - -THE FIVE GAMBLERS - -33. Five gamblers, whom we will call _A_, _B_, _C_, _D_, and _E_, play -together, on the condition that after each hazard he who loses shall -give to all the others as much as they then have in hand. - -Each loses in turn, beginning with _A_, and when they leave the table -each has the same sum in hand, thirty-two pounds. How much had each at -first? - - -34. Knowing that the square of 87 is 7569, how can we rapidly, without -multiplication, determine in succession the squares of 88, 89, and 90? - - -NOT WHOLE NUMBERS - - 35. Two numbers seek which make eleven, - Divide the larger by the less, - The quotient is exactly seven, - As all who solve it will confess. - - -AN AMPLE CHOICE - -36. If there are twenty sorts of things from which -^99999999999999999999^ different selections can be made, how many of -each sort are there? - - -37. Three women, with no money, went to market. The first had -thirty-three apples, the second twenty-nine, the third twenty-seven. -Each woman sold the same number of apples for a penny. They all sold -out, and yet each received an equal amount of money. How was this? - - -SIMPLE SUBTRACTION - - 38. Take five from five, oh, that is mean! - Take five from seven, and this is seen. - - -39. If a bun and a half cost three halfpence, how many do you buy for -sixpence? - - -40. How many times in a day would the hands of a watch meet each other, -if the minute-hand moved backward and the hour-hand forward? - - -41. How can half-a-crown be equally divided between two fathers and two -sons so that a penny is the coin of smallest value given to them? - - -SIZE AND SPEED - -42. If the number of the revolutions of the wheel of a bicycle in six -seconds is equal to the number of miles an hour at which it is running, -what is the circumference of the wheel? - - -43. Hearing a clock strike, and being uncertain of the hour, I asked a -policeman. He had a turn for figures, and replied: “Take half, a third, -and a fourth of the hour that has just struck, and the total will be one -larger than that hour.” What o’clock was it? - - -AFTER LONG YEARS - - 44. If cash is lent at five per cent. - To those who choose to borrow, - How soon shall I be worth a pound - If I lend a crown to-morrow? - - -ON THE JUMP - -45. If I jump off a table with a 20-lb. dumb-bell in my hand, what is -the pressure upon me of its weight while I am in the air? - - -AT A BAZAAR - -46. In charitable mood I went recently to a bazaar where there were four -tents arranged to tempt a purchaser. At the door of each tent I paid a -shilling, and in each tent I spent half of the money remaining in my -purse, giving the door-keepers each another shilling as I came out. - -It took my last shilling to pay the fourth door-keeper. How much money -had I at first, and what did I spend in each tent? - - -OUT IN THE RAIN - -47. Rain is falling vertically, at a speed of 5 miles an hour. I am -walking through it at 4 miles an hour. At what angle to the vertical -must I hold my umbrella, so that the raindrops strike its top at right -angles? - - -A MONKEY PUZZLER - -48. The following interesting problem, translated from the original -Sanscrit, is given by Longfellow in his “Kavanagh”:-- - -“A tree, 100 cubits high, is distant from a well 200 cubits. From the -top of this tree one monkey descends, and goes to the well. Another -monkey leaps straight upwards from the top, and then descends to the -well by the hypotenuse. Both pass over an equal space. How high does the -second monkey leap?” - - -49. A steamboat 105 miles east of Tynemouth Lighthouse springs a leak. -She puts back at once, and in the first hour goes at the rate of 10 -miles an hour. - -More and more water-logged, she decreases her speed each succeeding hour -at the rate of one-tenth of what it has been during the previous hour. -When will she reach the lighthouse? - - -50. If a hen and a half lays an egg and a half in a day and a half, how -many eggs will twenty-one hens lay in a week? - - -51. If the population of Bristol exceeds by two hundred and thirty-seven -the number of hairs on the head of any one of its inhabitants, how many -of them at least, if none are bald, must have the same number of hairs -on their heads? - - -52. A benevolent uncle has in his pocket a sovereign, a half-sovereign, -a crown, a half-crown, a florin, a shilling, and a threepenny piece. In -how many different ways can he tip his nephew, using only these coins, -and how is this most easily determined? - - -53. Here is a prime problem, in more senses than one, which will tax the -ingenuity of our solvers:--I am a prime number of three figures. -Increased by one-third, ignoring fractions, I become a square number. -Transpose my first two figures and increase me by one-third, and again -I am a square number. Put my first figure last, and increase me by -one-third, and I am another square number. Reverse my three figures, and -increase as before by one-third, and for a fourth time I become a square -number. What are my original figures? - - -54. In how many different ways can six different things be divided -between two boys? - - -55. What is quite the highest number that can be scored at six card -cribbage by the dealer, if he has the power to select all the cards, and -to determine the order in which every card shall be played? - - -COVERING THE WALLS - -56. A fanciful collector, who bought pictures with more regard to -quantity than quality, gave instructions that the area of each frame -should exactly equal that of the picture it contained, and that the -frames should be of the same width all round. - -At an auction he picked up a so-called “old master,” unframed, which -measured 18 inches by 12 inches. What width of frame will fulfil his -conditions? - - -A FAMILY REGISTER - -57. Our family consists of my mother, a brother, a sister, and myself. -Our average age is thirty-nine. My mother was twenty when I was born; my -sister is two years my junior, and my brother is four years younger than -she is. What are our respective ages? - - -58. A spider in a dockyard unwittingly attached her web to a mechanical -capstan 1 foot in diameter, at the moment when it began to revolve. To -hold her ground she paid out 73 feet of thread, when the capstan -stopped, and she found herself drained of silk. - -To make the best of a bad job she determined to unwind her thread, -walking round and round the capstan at the end of the stretched thread. -When she had gone a mile in her spiral path she stopped, tired and in -despair. How far was she then from the end of her task? - - -59. A mountebank at a fair had six dice, each marked only on one face 1, -2, 3, 4, 5, or 6, respectively. He offered to return a hundredfold any -stake to a player who should turn up all the six marked faces once in -twenty throws. How far was this from being a fair offer? - - -CATS’-MEAT FOR DOGS - - 60. If ninety groats for twenty cats - Will furnish three weeks’ fare, - How many hounds for forty pounds, - Less one, may winter there? - - Just ninety days and one assume - The winter’s space to be; - And note that what five cats consume - Will serve for dogs but three. - -(A groat = 4d.) - - -61. Two wineglasses of equal size are respectively half and one-third -full of wine. They are filled up with water, and their contents are then -mixed. Half of this mixture is finally poured back into one of the -wineglasses. What part of this will be wine and what part will be -water? - - -62. A legend goes that on a stout ship on which St Peter was carried -with twenty-nine others, of whom fourteen were Christians and fifteen -Jews, he so arranged their places, that when a storm arose, and it was -decided to throw half of the passengers overboard, all the Christians -were saved. The order was that every ninth man should be cast into the -sea. How did he place the Christians and the Jews? - - -A PROLIFIC COW - -63. Farmer Southdown was the proud possessor of a prize cow, which had a -fine calf every year for sixteen years. Each of these calves when two -years old, and their calves also in their turn, followed this excellent -example. How many head did they thus muster in sixteen years? - - -64. A shepherd was asked how many sheep he had in his flock. He replied -that he could not say, but he knew that if he counted them by twos, by -threes, by fours, by fives, or by sixes, there was always one over, but -if he counted them by sevens, there was no remainder. What is the -smallest number that will answer these conditions? - - -READY RECKONING - -65. If a number of round bullets of equal size are arranged in rows one -above another evenly graduated till a single bullet crowns the flat -pyramid, how can their number be readily reckoned, however long the base -line may be? - - -THE TITHE OF WAR - - 66. Old General Host - A battle lost, - And reckoned on a hissing, - When he saw plain - What men were slain, - And prisoners, and missing. - - To his dismay - He learned next day - What havoc war had wrought; - He had, at most, - But half his host - Plus ten times three, six, ought. - - One-eighth were lain - On beds of pain, - With hundreds six beside; - One-fifth were dead, - Captives, or fled, - Lost in grim warfare’s tide. - - Now, if you can, - Tell me, my man, - What troops the general numbered, - When on that night - Before the fight - The deadly cannon slumbered? - - -67. A farmer sends five pieces of chain, of three links each, to be made -into one continuous length. He agrees to pay a penny for each link cut, -and a penny for each link joined. What was the blacksmith entitled to -charge if he worked in the best interest of the _farmer_? - - -68. In a parcel of old silver and copper coins each silver piece is -worth as many pence as there are copper coins, and each copper coin is -worth as many pence as there are silver coins, and the whole is worth -eighteen shillings. How many are there of each? - - -A FEAT WITH FIGURES - -69. Take the natural numbers 1 to 11, inclusive, and arrange them in -five groups, not using any of them more than once, so that these groups -are equal. Any necessary signs or indices may be used. - - -HOW OLD WAS JOHN? - -70. John Bull passed one-sixth of his life in childhood and one-twelfth -as a youth. When one-seventh of his life had elapsed he had a son who -died at half his father’s age, and John himself lived on four years -more. How old was he at the last? - - -FIGURE IT OUT - -71. There are two numbers under two thousand, such that if unity is -added to each of them, or to the half of each, the result is in every -case a square number. Can you find them? - - -72. A cheese in one scale of a balance with arms of unequal length seems -to weigh 16 lbs. In the other scale it weighs but 9 lbs. What is its -true weight? - - -“DIVISION IS AS BAD!” - -73. Can you divide 100 into two such parts that if the larger is divided -by the lesser the quotient is also 100? - - -74. I have marbles in my two side pockets. If I add one to those in the -right-hand pocket, and multiply its increased contents by the number it -held at first, and then deal in a similar way with those in the other -pocket, the difference between the two results is 90. If, however, I -multiply the sum of the two original quantities by the square of their -difference, the result is 176. How many marbles had I at first in each -pocket? - - -A SURFEIT OF BRIDGE - -75. A friendly circle of twenty-one persons agreed to meet each week, -five at a time, for an afternoon of bridge, so long as they could do so -without forming exactly the same party on any two occasions. - -As a central room had to be hired, it was important to have some idea as -to the length of time for which they would require it. How long could -they keep up their weekly meetings? - - -76. A herring and a half costs a penny and a half; what is the price of -a dozen? - - -77. What sum of money is in any sense seen to be the double of itself? - - -COMIC ARITHMETIC - -78. At the close of his lecture upon unknown quantities, Dr Bulbous -Roots, in playful mood, wrote this puzzle on his blackboard:-- - -Divide my fifth by my first and you have my fourth; subtract my first -from my fifth and you have my second; multiply my first by my fourth -followed by my second, and you have my third; place my second after my -first and you have my third multiplied by my fourth. What am I? - - -DROPPED THROUGH THE GLOBE - -79. If we can imagine the earth at a standstill for the purpose of our -experiment, and if a perfectly straight tunnel could be bored through -its centre from side to side, what would be the course of a cannon ball -dropped into it from one end, under the action of gravity? - - -LOVE LETTERS - - 80. A lady to her lover cried, - “How many notes have you of mine?” - “Six more I’ve sent,” the youth replied, - “Than I have had of thine.” - - “But if from one pound ten you take - The pennies we on stamps have spent, - One eighth their cost you thus will make.” - How many had they had and sent? - - -81. A man, on the day of his marriage, made his will, leaving his money -thus:--If a son should be born, two-thirds of the estate to that son and -one-third to the widow. If a daughter should be born, two-thirds to the -widow and one-third to that daughter. In the course of time twins were -born, a boy and a girl. The man fell sick and died without making a -fresh will. How ought his estate to be divided in justice to the widow, -son, and daughter? - - -82. My carpet is 22 feet across. My stride, either backwards or -forwards, is always 2 feet, and I make a stride every second. If I take -three strides forwards and two backwards continuously until I cross the -carpet, how long does it take me to reach the end of it? - - -NO TIME TO BE LOST - -83. A merchant at Lisbon has an urgent business call to New York. Taking -these places to be, as they appear on a map of the world, on the same -parallel of latitude, and at a distance measured along the parallel, of -some 3600 miles, if the captain of a vessel chartered to go there sails -along this parallel, will he be doing the best that he can for the -impatient merchant? - - -ROUND THE ANGLES - -84. Two schoolboys, John and Harry, start from the right angle of a -triangular field, and run along its sides. John’s speed is to Harry’s as -13 is to 11. - -They meet first in the middle of the opposite side, and again 32 yards -from their starting point. How far was it round the field? - - -AN ECHO FROM THE PAST - -85. The following question is given and spelt exactly as it was -contributed to a puzzle column by “John Hill, Gent.,” in 1760:-- - -“A vintner has 2 sorts of wine, viz. A and B, which if mixed in equal -parts a flagon of mixed will cost 15 pence; but if they be mixed in a -_sesqui-alter_ proportion, as you should take two flagons of A as often -as you take three of B, a flagon will cost 14 pence. Required the price -of each wine singly.” - - -PROMISCUOUS CHARITY - -86. A man met a beggar and gave him half the money he had in his pocket, -and a shilling besides. Meeting another he gave him half of what was -left and two shillings, and to a third, he gave half of the remainder -and three shillings. This left a shilling in his pocket. How much had he -at first? - - -87. A young clerk wishes to start work at an office in the City on -January 1st. He has two promising offers, one from _A_ of £100 a year, -with a yearly rise of £20, the other from _B_ of £100 a year with a -half-yearly rise of £5. Which should he accept, and why? - - -HOW CAN I PAY MY BILL? - -88. I have an abundance of florins and half-crowns, but no other coins. -In how many different ways can I pay my tailor £11, 10s. without -receiving change? - - -89. A monkey climbing up a greased pole ascends 3 feet and slips down 2 -feet in alternate seconds till he reaches the top. If the pole is 60 -feet high, how long does it take him to arrive there? - - -“SAFE BIND, SAFE FIND” - -90. Old Adze, the village carpenter, who kept his tools in an open -chest, found that his neighbours sometimes borrowed and forgot to return -them. - -To guard against this, he secured the lid of the chest with a letter -lock, which carried six revolving rings, each engraved with twelve -different letters. What are the chances against any one discovering the -secret word formed by a letter on each ring, which will open the lock, -and be the only key to the puzzle? - - -91. Five merry married couples happened to meet at a Swiss hotel, and -one of the husbands laughingly proposed that they should dine together -at a round table, with the ladies always in the same places so long as -the men could seat themselves each between two ladies, but never next to -his own wife. How long would their nights at the round table be -continued under these conditions? - - -SOUNDING THE DEPTH - -92. In calm water the tip of a stiff rush is 9 inches above the surface -of a lake. As a steady wind rises it is gradually blown aslant, until at -the distance of a yard it is submerged. Can you decide from these data -the depth of the water in which the rush grows? - - -AMINTA’S AGE - -93. - - If to Aminta’s age exact - Its square you add, and eighteen more, - And from her age its third subtract, - And to the difference add three score, - The latter to the former then - Will just the same proportion bear - As eighteen does to nine times ten. - Can you Aminta’s age declare? - - -ONE FOR THE PARROT - -94. A bag of nuts was to be divided thus among four boys:--Dick took a -quarter, and finding that there was one over when he made the division, -gave it to the parrot. Tom dealt in exactly the same way with the -remainder, as did Jack and Harry in their turns, each finding one nut -from the reduced shares to spare for the parrot. The final remainder -was equally divided among the boys, and again there was one for the -bird. How many nuts, at the lowest estimate, did the bag contain? - - -95. Here is an easy one:-- - - If five times four are thirty-three, - What will the fourth of twenty be? - - -96. What fraction of a pound, added to the same fraction of a shilling, -and the same fraction of a penny, will make up exactly one pound? - - -MENTAL ARITHMETIC - -97. “Now, boys!” said Dr Tripos, “I think of a number, add 3, divide by -2, add 8, multiply by 2, subtract 2, and thus arrive at twice the number -I thought of.” What was it? - - -98. Two club friends, _A_ and _B_, deposit similar stakes with _C_, and -agree that whoever first wins three games at billiards shall take the -whole of them. _A_ wins two games and _B_ wins one. Upon this they -determine to divide the stakes in proper shares. How must this division -be arranged? - - -99. Not so simple as it sounds is the following compact little -problem:--If I run by motor from London to Brighton at 10 miles an hour, -and return over the same course at 15 miles an hour, what is my average -speed? - - -100. “I can divide my sheep,” says Farmer Hodge, who from his schooldays -had a turn for figures, “into two unequal parts, so that the larger part -added to the square of the smaller part shall be equal to the smaller -part added to the square of the larger part.” - -How many sheep had the farmer? - - -A HELPFUL BURDEN - -101. The following question was proposed in an old book of Mathematical -Curiosities published more than a hundred years ago:-- - -“It often happens that if we take two horses, in every respect alike, -yet, if both are put to the draught, that horse which is most loaded -shall be capable of performing most work; so that the horse which -carries the heavier weight can draw the larger load. How is this?” - - -102. In the king’s treasury were six chests. Two held sovereigns, two -shillings, and two pence, in equal numbers of these coins. “Pay my -guard,” said the king, “giving an equal share to each man, and three -shares to the captain; give change if necessary.” “It may not be -possible,” replied the treasurer, “and the captain may claim four -shares.” “Tut, tut,” said the king, “it can be done whatever the amount -of the treasure, and whether the captain has three shares or four.” - -Was the king right? If so, how many men were there in the guard? - - -NUTS TO CRACK - -103. I bought a parcel of nuts at forty-nine for twopence. I divided it -into two equal parts, one of which I sold at twenty-four, the other at -twenty-five for a penny. I spent and received an integral number of -pence, but bought the least possible number of nuts. How many did I buy? -What did they cost? What did I gain? - - -MONEY MATTERS - -104. My purse contained sovereigns and shillings. After I had spent half -of its contents there were as many pounds left as I had shillings at -first. With what sum did I start? - - -A DELICATE QUESTION - -105. A lady was asked her age in a letter, and she replied by postcard -thus:-- - - If first my age is multiplied by three, - And then of that two-sevenths tripled be, - The square root of two-ninths of this is four, - Now tell my age, or never see me more! - -What was her age? - - -106. If cars run at uniform speed on the twopenny tube, from Shepherd’s -Bush to the Bank at intervals of two minutes, how many shall I meet in -half an hour if I am travelling from the Bank to Shepherd’s Bush? - - -PAYMENT BY RESULTS - -107. What would it cost me to keep my word if I were to offer my -greengrocer a farthing for every different group of ten apples he could -select from a basket of a hundred apples? - - -108. If the minute-hand of a clock moves round _in the opposite -direction_ to the hour-hand, what will be the real time between three -and four, when the hands are exactly together? - - -109. Two monkeys have stolen some filberts and some walnuts. As they -begin their feast they see the owner of the garden coming with a stick. -It will take him two and a half minutes to reach them. There are twice -as many filberts as walnuts, and one monkey finishes the walnuts at the -rate of fifteen a minute in four-fifths of the time and bolts. The other -manages to finish the filberts just in time. - -If the walnut monkey had stopped to help him till all was finished, when -would they have got away if they ate filberts at equal rates? - - -110. A cashier, in payment for a cheque, gives by mistake pounds for -shillings and shillings for pounds. The receiver spends half-a-crown, -and then finds that he has twice as much as the cheque was worth. What -was its value? - - -111. What five uneven figures can be added together so as to make up 14? - - -112. Three posts which vary in value are vacant in an office. In how -many ways can the manager fill these up from seven clerks who apply for -the appointments? - - -113. “It is now ⁵⁄₁₁ of the time to midnight,” said the fasting man, who -began his task at noon. What time was it? - - -A STRIKING TIME - -114. If a clock takes six seconds to strike six how long will it take to -strike eleven? - - -WHAT ARE THE ODDS? - -115. How would you arrange twenty horses in three stalls so as to have -an odd number of horses in each stall? - - -116. Here is a pretty little problem, which has at any rate an Algebraic -form, and is exceedingly ingenious:-- - -Given _a_, _b_, _c_, to find _q_. - - -WHEN WAS HE BORN? - -117. Tom Evergreen was asked his age by some men at his club on his -birthday in 1875. “The number of months,” he said, “that I have lived -are exactly half as many as the number which denotes the year in which I -was born.” How old was he? - - -118. Draw three circles of any size, and in any position, so long as -they do not intersect, or lie one within another. How many different -circles can be drawn touching all the three? - - -119. We have seen that the nine digits can be so dealt with, using each -once, as to add up to 100. How can 1, 2, 3, 4, 5, 6, 7, 8, 9, 0 be -arranged so that they form a sum which is equal to 1? - - -120. How is it possible, by quite a simple method, to find the sum of -the first fifty numbers without actually adding them together? - - -121. Two tram-cars, _A_ and _B_, start at the same time. _A_ runs into a -“lie by” in four minutes, and waits there five minutes, when _B_ meets -and passes it. Both complete the whole course at the same moment. In -what time can _A_ complete it without a rest? - - -A CURIOUS DEDUCTION - -122. Take 10, double it, deduct 10, and tell me what remains. - - -123. The average weight of the Oxford crew is increased by 2 lbs., when -one of them, who weighs 12 stone, is replaced by a fresh man. What is -the fresh man’s weight? - - -ASK ANY MOTORIST - -124. A motor car is twice as old as its tyres were when it was as old as -its tyres are. When these tyres are as old as the car is now, the -united ages of car and tyres will be two years and a quarter. What are -their respective ages now? - - -125. _A_ and _B_ on the edge of a desert can each carry provisions for -himself for twelve days. How far into the desert can an advance be made, -so that neither of them misses a day’s food? - - -126. A bottle of medicine and its cork cost half-a-crown, but the bottle -and the medicine cost two shillings and a penny more than the cork. What -did the cork cost? - - -IN A FIX - -127. A boat’s crew are afloat far from land with no sail or oars. How -can they, without making any use of wind or stream, and without any -outside help, regain the shore by means of a coil of rope which happens -to be at hand. - - -128. What is the largest sum in silver that I can have in my pockets -without being able to give change for a half-sovereign. - - -129. I have apples in a basket. Without cutting an apple I give half of -the number and half an apple to one person; half of what then remains -and half an apple to another, and half of what are still left and half -an apple to a third. One apple now remains in the basket. How many were -there at first? - - -A QUEER DIVISION - - 130. A third of twelve divide - By just a fifth of seven; - And you will soon decide - That this must give eleven. - - -131. A motor goes 9 miles an hour uphill, 18 miles an hour downhill, and -12 miles an hour on the level. How long will it take to run 50 miles and -return at once over the same course? - - -132. In firing at a mark _A_ hits it in two out of three shots, _B_ in -three out of four, and _C_ in four out of five. The mark was hit 931 -times. If each fired the same number of shots, how many hits did each -make, and how many shots were fired? - - -133. If a cat and a dog, evenly matched in speed, run a race out and -back over a course 75 yards in all, and the dog always takes 5 feet at a -bound and the cat 3 feet, which will win? - - -IN A FOG - -134. In a fog a man caught up a wagon going in the same direction at 3 -miles an hour. If the wagon was just visible to him at a distance of 55 -yards, and he could see it for five minutes, at how many miles an hour -was he walking? - - -135. Three horses start in a race. In how many different ways can they -be placed by the judge? - - -NEW ZEALAND FOOTBALL - -136. The New Zealanders, winning a match against Oxbridge, scored 34 -points, from tries and tries converted into goals. - -If every try had been converted they would have made four-fifths of the -maximum which a score of 34 points from tries and goals can yield. - -What is this maximum, and what was their actual score? - - -137. What is the smallest number, of which the alternate figures are -cyphers, that is divisible by 9 and by 11? - - -138. Here is an interesting little problem:--_A_, with 8d. in his hand, -meets _B_ and _C_, who have five and three loaves respectively. In -hungry mood they all agree to share the loaves equally, and to divide -the money fairly between _B_ and _C_. How much does each receive? - - -THE MONEY-BOXES - -139. When four money-boxes, containing pennies only, were opened and -counted, it was found that the number in the first with half those in -all the others, in the second with a third of all the others, in the -third with a fourth of all the others, and in the fourth with a fifth of -all the others, amounted in each case to 740. How much money did the -boxes contain, and how was it divided? - - -140. Two steamers start together to make a trip to a far-off buoy and -back. Steamer _A_ runs all the time at 10 miles an hour. Steamer _B_ -does the passage out at 8 miles an hour, and the return at 12 miles. -Will they regain port together? - - -141. A golf player has two clubs mended in London. One has a new head, -the other a new leather face. The head costs four times as much as the -face. At St Andrews it costs five times as much, and the leather face at -St Andrews is half the London price. Including a shilling for a ball he -pays twice the St Andrews charges for these repairs. What is the London -charge for each? - - -FROM TWO WRONGS TO MAKE A RIGHT - -142. Two children were asked to give the total number of animals in a -pasture, where sheep and cattle were grazing. They were told the numbers -of sheep and of cattle, but one subtracted, and gave 100 as the answer, -and the other arrived at 11,900 by multiplication. What was the correct -total? - - -THE STONE CARRIER - -143. Fifty-two stones are placed at intervals along a straight road. The -distance between the first and the second is 1 yard, between the second -and the third it is 3 yards, between the next two 5 yards, and so on, -the intervals increasing each time by 2 yards. - -How far would a tramp have to travel to earn five shillings promised to -him when he had brought them one by one to a basket placed at the first -stone? - - -144. On a division in the House of Commons, if the Ayes had been -increased by fifty from the Noes, the motion would have been carried by -five to three. If the Noes had received sixty votes from the Ayes, it -would have been lost by four to three. Did the motion succeed? How many -voted? - - -A WATCH PUZZLE - -145. How many positions are there on the face of a watch in which the -places of the hour and minute-hands can be interchanged so as still to -indicate a possible time? - - -CRICKET SCORES - -146. In a cricket match the scores in each successive innings are a -quarter less than in the preceding innings. The match was played out, -and the side that went in first won by fifty runs. What was the complete -score? - - -HOW HIGH CAN YOU THROW? - -147. A boy throws a cricket ball vertically upwards, and catches it as -it falls just five seconds later. How high from his hands does the ball -go? - - -MEASURE THE CARPET - -148. It may be said of a section of the gigantic carpet at Olympia that -had it been 5 feet broader and 4 feet longer it would have contained 116 -more feet; but if 4 feet broader and 5 longer the increase would have -been but 113 feet. What were its actual breadth and length? - - -149. In estimating the cost of a hundred similar articles, the mistake -was made of reading pounds for shillings and shillings for pence in each -case, and under these conditions the estimated cost was £212 18s. 4d. in -excess of the real cost. What was the true cost of the articles? - - -SQUARES IN STREETS - -150. The square of the number of my house is equal to the difference of -the squares of the numbers of my next door neighbour’s houses on either -side. - -My brother, who lives in the next street, can say the same of the number -of his house, though his number is not the same as mine. How are our -houses numbered? - - -151. Two men of unequal strength are set to move a block of marble which -weighs 270 lbs., using for the purpose a light plank 6 feet long. The -stronger man can carry 180 lbs. How must the block be placed so as to -allow him just that share of the weight? - - -152. A man has twenty coins, of which some are shillings and the rest -half-crowns. If he were to change the half-crowns for sixpences and the -shillings for pence he would have 156 coins. How many shillings has he? - - -COUNT THE COINS - -153. Some coins are placed at equal distances apart on a table, so that -they form the sides of an equilateral triangle. - -From the middle of each side as many are then taken as equal the square -root of the number on that side, and placed on the opposite corner coin. -The number of coins on each side is then to the original number as 5 is -to 4. How many coins are there in all? - - -PUTTING IN THE POSTS - -154. A gardener, wishing to fence round a piece of ground with some -light posts, found that if he set them a foot apart there would be 150 -too few, but if placed a yard apart there would be 70 to spare. How many -posts had he? - - -155. _A_ gives _B_ £100 to buy 100 animals, which must be cows at £5 -each, sheep at £1, and geese at 1s. How many of each sort can he buy? - - -156. John is twice as old as Mary was when he was as old as Mary is. -John is now twenty-one. How old is Mary? - - -157. In a cricket match _A_ made 35 runs; _C_ and _D_ made respectively -half and one-third as many as _B_, and _B_’s score was as much below -_A_’s as _C_’s was above _D_’s. What did _B_, _C_, and _D_ each score? - - -SETTLED BY REMAINDERS - -158. What is the least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9, -or 10, leaves respectively as remainders 1, 2, 3, 4, 5, 6, 7, 8, and 9? - - -TABLE TURNING - -159. A square table stands on four legs, which are set at the middle -point of its sides. What is the greatest weight that this table can -uphold upon one of its corners? - - -BRIBING THE BOYS - -160. Well pleased with the inspector’s report, the rector of a country -parish came into his school with 99 new pennies in his pocket, and said -that he would give them to the five boys in Standard VII. if they could, -within an hour, show him how to divide them so that the first share -should exceed the second by 3, be less than the third by 10, be greater -than the fourth by 9, and less than the fifth by 16. What was the answer -which would satisfy these conditions? - - -SHEEP-STEALING - -161. Some Indian raiders carried off a third of a flock of sheep, and a -third of a sheep. Another party took a fourth of what remained, and a -fourth of a sheep. Others took a fifth of the rest and three-fifths of a -sheep. What was the number of the full flock, if there were then 409 -left? - - -162. Three boys begin to fill a cistern. _A_ brings a pint at the end of -every three minutes, _B_ a quart every five minutes, and _C_ a gallon -every seven minutes. If the cistern holds fifty-three gallons, in what -time will it be filled, and who will pour in the last contribution? - - -ESTIMATE OF AGE - -163. A man late in the last century said that his age was the square -root of the year in which he was born. In what year did he say this? - - -A DEAL IN CHINA - -164. A dealer in Eastern curios sold a Satzuma vase for £119, and on -calculation found that the number which expressed his profit per cent. -expressed also the cost price in pounds of the vase. What was this -number? - - -165. What is the chance of throwing at least one ace in a single throw -with a pair of dice? - - -166. A thief starts running from a country house as fast as he can. Four -minutes later a policeman starts in pursuit. If both run straight along -the road, and the policeman gets over the ground one-third faster than -the thief, how soon will he catch him? - - -167. Twenty-seven articles are exposed for sale on one of the stalls of -a bazaar. What choice has a purchaser? - - -VERY PERSONAL - -168. “How old are _you_, dad?” said Nellie on her birthday, as her -father gave her as many shillings as she was years old. His answer was -quite a puzzle for a time, but with the help of her schoolfellows Nellie -worked it out. - -This is what he said:-- - - “I was twice as old as you are - The day that you were born. - You will be just what I was then - When fourteen years are gone.” - -How old was Nellie, and how old was her dad? - - -WORD AND LETTER PUZZLES - - -A MAGIC COCOON - -This Magic Cocoon is so cleverly spun that the word can be traced and -read in many ways. - - N - N O N - N O O O N - N O O C O O N - N O O C O C O O N - N O O C O C O C O O N - N O O C O C O O N - N O O C O O N - N O O O N - N O N - N - -How many readings can you discover starting from one or other of the Cs, -and passing up and down or sideways, but not diagonally, and never over -the same letter twice in a reading? There are 756! - - -THE CHRONOGRAM - -The Chronogram, severely classed by Addison as “a species of false wit” -is a sentence in which the salient letters represent in Roman numerals -some particular year. A good English specimen is this: “My Day Closed Is -In Immortality.” The capital letters in these words give MDCIII., or -1603, the year in which Queen Elizabeth died. - - -A FRENCH CHRONOGRAM - -The battle-cry at Montlhéry in 1465 was:--“à CheVaL, à CheVaL, -gendarMes, à CheVaL!” Taking the letters printed in capitals-- - - M = 1000 - CCC = 300 - LLL = 150 - VVV = 15 - ---- - we have the date of the battle 1465 - - -A NOTABLE CHRONOGRAM - - QVI CHRISTI IAVDES CANTANT - SANCTÆ PASSIONIS SVÆ VIRTVTE - IN IPSO ET PATRE VNVM SINT. - -This curious inscription is placed over the organ at Ober Ammergau. Add -together its Roman numerals and they give the date at which the organ -was dedicated. The English of it is:-- - -May those who sing the praises of Christ be by virtue of His Sacred -Passion one in The Father and in Himself. - - -A PERFECT CHRONOGRAM - -On a damaged inscription to Bishop Berkeley in Winchester Cathedral are -the words--VIXI, LVXI--I have lived, I have shone. Added together in -their values as Roman numerals the letters of these two words give his -age exactly at his death--eighty-three. - - -A PRIZE MOTTO - -On the return of the C.I.V. from the Boer War a prize was offered by -_Truth_ for the best motto appropriate to them. This was to consist of -three words of which the first must begin with C the second with I and -the third with V. - -The prize was taken by the following Latin motto which is singularly -happy both in construction and in meaning:-- - - CIVI IVI VICI - _I roused_ _I went_ _I won._ - -The sequence of events is perfect; no letters but C.I.V. are used and -the motto is a palindrome if read by syllables. - - -THE MUSICAL SCALE - -As in olden days some of the Psalms and other writings were constructed -in acrostic form, so in the Middle Ages even serious writers would -juggle with letters, as though they felt that such tricky methods were -an aid to memory. - -It was in this spirit that Guido Aretino, a Benedictine monk of Tuscany -in 1204, gave names to the notes used in the musical scale from the -first syllables of the lines of a Latin hymn. “Ut” is still used in -France, though we and the Italians have substituted “do.” - - UT queant laxis REsonare fibris, - MIra gestorum FAmuli tuorum, - SOLve polutis LAbii reatis - O Pater alme! - - -ALL THE ALPHABET! - -Many of us know that there is a long verse in the Book of Ezra in which -all the letters of the alphabet are used, taking “j” as “i” (_Ezra_ -vii., v. 21). - -This very curious coincidence also occurs in a comparatively short -sentence in “The Beth Book,” by Sarah Grand:--“It was an exquisitely -deep blue just then, with filmy white clouds drawn up over it like -gauze;” and here “j” is itself in evidence. - - -APT ALLITERATION - -Schopenhauer, the famous German philosopher, who was a confirmed -bachelor and misogynist, was compelled while living at Frankfort to -support an old lady who had been crippled by his violence. When her -death came as a welcome relief to him, he composed the following clever -epitaph:-- - - Obit anus, - Abit onus. - -which by the interchange of two letters pictured the position. It may be -freely rendered:-- - - Old lady dies, - My burden flies. - - -A DOUBLE SEQUENCE - -The following clever composition, which appeared in the pages of -_Truth_, contains a _double_ sequence of words, which increase a letter -at a time, the same letters appearing in varied order until at last “o” -culminates in _thornless_, and “a” in _restrainest_. It is quite a -remarkable _tour-de-force_. - - O lack-_a_-day! _at_ eve we _sat_, - One _star_ had lit its lamps _on_ high. - We did _not note_ the circling bat, - _Start_ from the _stone_ when flitting nigh. - For the _strait_ gate of _honest_ doubt - Shut off the _thrones_ of Love and Gain; - We dreamed not, as we mourned without, - That Time’s swift _transit shortens_ pain. - O Thou, Who _trainest_ souls to shine, - Though once we craved a _thornless_ lot, - This gracious truth we now divine: - The bruised reed Thou _strainest_ not; - But by _restraints_, that gently tame; - _Restrainest_ Passion’s kindling flame. - - -THE REIGN OF TERROR - -During the Reign of Terror, France and her people and position were thus -alphabetically described:-- - - Le peuple Français A B C. (abaissé). - La gloire nationale F A C. (effacée). - Les places fortes O Q P. (occupées). - Quarante trois députés C D. (cédés). - L’armée D P C. (dépaysée). - Les ministres A J. (agés). - La liberté O T. (ôtée). - La charte L U D. (éludée). - - -SEE-SAW - -This elaborate method of piling up no less than seven consecutive -“thats,” so that they make tolerable sense, was told to his boys during -school-time by Dr Moberly, then headmaster of Winchester, and afterwards -Bishop of Salisbury, just fifty years ago:-- - - I saw that C saw. - - C saw that that I saw. - - I saw that that that C saw was so. - - C saw that, that that that I saw was so. - - I saw that, that _that_ that that C saw was so. - - C saw _that_ that, that _that_ that that I saw was so. - - I saw _that_ that, that _that_ that that _that_ C saw was so. - - -FOR A ROMAN HOLIDAY - -If the Roman ladies and children, at their equivalent for Christmas, -amused themselves by acting verbal charades, an excellent word was at -their disposal, “sustineamus”--“let us endure,” which can be broken up -exactly into _sus_, _tinea_, _mus_--_a sow_, _a moth_, _a mouse_. - - -A WORD SQUARE - -1. Can you complete this word square, so that its four words read alike -from top to bottom and from left to right? - - * E * * - E * * * - * * * E - * * E * - - -ANOTHER WORD SQUARE - -2. Can you fill in this word square? - - C * * C * E - * N U * E S - * U * E S * - C * E * S * - * E S * * E - E * T E * * - - -DUPLICATE LETTERS - -3. In this sentence, when complete, - - So****AG****LATI****X****ITH - -each group of four missing letters contains two pairs of letters which -are alike. Can you on these lines complete the sentence? - -Here is a similar sentence by way of illustration: - - T****M****TERTAIN****MUND, - -which becomes when filled in-- - -T_wo_ _wo_m_en_ _en_tertain_ed_ _Ed_mund. - - -ANOTHER WORD SQUARE - -4. Can you complete this word square by substituting letters for the -dots? - - W * * * E - * * T * * - * T O N * - * * N * * - E * * * T - - -WORD BUILDING - -5. What word can be made with these? - -L S D U D O D U D. - - -6. A lovelorn youth consulted a married lady on his condition, and was -asked by her on a slip of paper:-- - - “Loruve?” - -When he had deciphered this, and had answered in the affirmative, she -handed to him another slip, on which this advice was written:-- - - L - “Prove A F and ensure success.” - D - -What did it all mean? - - -A DOUBLE ACROSTIC - - 7. _Saint of Spain, whose daily word - Twenty years hath London heard!_ - Sweet days, elastic metal, motion sharp. - My halls once echoed to an Irish harp. - The “son of sorrow,” honourable of yore. - Dread goddess, loosing the loud dogs of war. - Time’s atom--total of eternities. - This name an insect bears, a patriot bore. - “So do, yet hear me,” said Themistocles. - - -ANOTHER WORD SQUARE - -8. Can you complete this word square? - - * M * N * S - M * N * O * - * N * B * E - N * B * L * - * O * L * R - S * E * R * - - -A FRENCH ORACLE - -9. A spruce young Frenchman at a _fête_ consulted a modern oracle as to -how he could best please the ladies. This was the mystic response:-- - - MEC DO BIC. - -Can you interpret it? - - -A QUAINT EQUATION - -10. In our young days we have often wrestled with vulgar fractions, but -apart from Algebra we have had no serious concern with any in which -letters take the place of figures. A specimen of this sort, not known to -science, is the following curiosity:-- - - m - -- - ot - -- = mo. - y - - -11. The puzzle in _Truth_ was recently founded upon “ourang-outang,” -which had been cleverly buried. We will give a few of the best results. -This is one:-- - - Poor wretch! a moisture filled his eye, - “Do not rebuff a lonely boy,” - Said he, “If ere I sink and die - Your smile--O! pardon will be joy!” - -Another is:-- - - Though I jump, and row, and run, - Cap or cup I never won. - -What animals are buried in these lines? - - -LIKE A PEACOCK’S TAIL - - 12. Fourteen letters here we fix, - Vowels only two are spoken; - All together these we mix - Into what can not be broken. - - -A WEIRD WORD - -13. There is an English word of thirteen letters in which the same vowel -occurs four times, the same consonant six times, another consonant -twice, and another once. Can you hit upon it? - - -A CONDENSED PROVERB - -14. Though brevity is said to be the soul of wit, we are too often -flooded nowadays with a superabundance of words. - -Here is an attempt at modest condensation. A familiar English proverb is -quite clearly expressed to the solver’s seeing eyes in this brief -phrase:-- - - WE IS DO - -What is the proverb? - - -ANOTHER WORD SQUARE - -15. Can you complete this word square? - - W * * * * S - * R * * R * - * * O R * * - * * R M * * - * R * * N * - S * * * * M - - -CAN YOU DECIPHER IT? - -16. The following puzzle lines are attributed to Dr Whewell:-- - - O O N O O. - ----------- - U O A O O I O U - O N O O O O M E T O O. - U O A O I D O S O - I O N O O I O U T O O! - - -A BROKEN DIAMOND - -17. Can you fill in the vacancies in this diamond? - - P - F O * - C * R * * - F * * C * * * - P O R C E L A I N - R * * L * * * - S * A * * - S I * - N - -Its words must read alike from left to right and from top to bottom. - - -WHAT IS THIS? - - 18. Tan HE Edsa VEN in - It N Gja SmeTs AsgN - aD Az Rett De. - - -A PHONETIC JOURNEY - -19. I can travel first-class on the Great Eastern Railway from 2 2 2 2 2 -2 2 2 4 4 4 4 4 5 0 0. What is the cost of my journey, and its length in -time? - - -A CURIOUS OLD INSCRIPTION - - 20. Seogeh sreve ereh wcisume vahl - Lah sehs se otreh nos llebdnas - Regni freh nos gnires rohyer - Ganoed iryd ale nifae esots sorcy - Rub nabot es rohk co caed ir. - -Can you decipher it? - - -IRISH STEW AT SIMPSON’S - -21. I wrote the following note recently:-- - - Dear Jack,--Meet me at Simpson’s to-morrow at 1.30. We will sample - their excellent Irish stew. Here are some catchwords that will remind - you of the invitation:-- - - Join me at and - i - s - -Why should they remind him of it? - - -ENGLISH AS SHE IS SPELT! - -22. This was the exact text of a letter sent to the master of an English -village school by a labourer as an excuse for his boy’s absence:-- - - “Cepatomtogoatatrin” - -Can you decipher it? - - -A DOUBLE ACROSTIC - -23. This double Acrostic will afford an easy exercise in mental -gymnastics for those to whom such pastime appeals:-- - - Now we are fain - To rack your brain. - -1. More fit for babes and sucklings than for you. - -2. Robbed of externals this is very true. - -3. Diminutive in measure and in weight. - -4. Pen-name of one a true pen potentate. - -5. A palindrome quite plain is here in sight. - -6. Sans head and tail it also yields this light. - -7. Here is in short what anyone may write. - - -FIND THE PROVERB - - 24. c e f h i m n o r s t v y - 3 2 2 2 7 1 1 2 6 5 8 3 9 - 4 4 1 2 1 6 1 - 3 1 5 8 2 3 - 5 7 9 6 - 4 - -The letters with ones under them are the first letters of words, those -with twos under them are second letters of words, and so on. - - -A PUZZLE WILL - -25. Having occasion to make a few slight additions to my will, I called -in my lawyer to arrange the matter. How far forward did the instructions -contained in the following lines carry him in his work? - - Set down a hundred in my will, - Add nothing to the text; - Five hundred now a space may fill, - And one be added next. - - Another hundred write as well, - And yet another one; - Then fifty more, and try to tell - The deed that now is done. - - -ANOTHER WORD SQUARE - -26. Can you complete this word square? - - * D * * O * - D * * I * E - * S * A * D - T * A * A * - * R * A * E - R * D * E * - - -MUSICAL EPITAPHS - -27. Over the grave of a French musician, who was choked by a fish bone, -the following epitaph was inscribed in notes of music:--A. G. A. E. A. - -Over the porch of the house of Gustave Doré these musical notes were -placed on a tablet:--C. E. B. A. C. D. - -What do these inscriptions signify? - - -QUITE TOO TOO - -28. “Where can we meet to-morrow?” said Jack Spooner to his best girl. - -“We will go,” she replied, “at 222222222222 LEY STREET.” - -When and where did they meet? - - -A BROKEN WORD - -29. What does this spell? - - C - ------------------- - T T T T T T T T T T - - -CONTRADICTORY TERMS - -30. What English word is it which may be so treated as to affirm or -disallow the use of its own initial or final letter? - - -PRINTERS’ PIE - -31. Can you arrange these letters - - E I O O O U - B C N N R R S S - -so that they form the title of a book well-known to boys? - - -FILL IN THE GAPS - -32. Keeping these letters in their present order make a sensible -sentence by inserting among them as often as is necessary another -letter, which must be in every case the same. - - A DEN I I CAN DOCK. - - -DISTORTED SHAKESPEARE - -33. Here is a well-known quotation from Shakespeare, which seems to need -some straightening out:-- - - OXXU8 MAAULGIHCTE - NOR - - -A PHONETIC NIGHTMARE - -34. Here, as an awful warning to those who are ready to accept the -definition of English spelling given by a former headmaster of -Winchester--“Consonants are interchangeable, and vowels do not -count”--is a common English word of twelve letters, in “linked sweetness -long drawn out.” - - Iewkngheaurrhphthewempeighghtips. - -Can you decipher it? - - -ANOTHER WORD SQUARE - -35. Can you, by filling in letters, complete this word square so that it -shall read alike across and from top to bottom? - - * A * * - A * * A - * E * * - * A * E - - -A QUAINT INSCRIPTION - -36. The following curious inscription may be seen on a card hanging up -in the bar of an old riverside inn in Norfolk:-- - - THEM * ILL * ERSLEA * VET * HEMI - LLT * HEW * HER * RYMEN * LOW - ERTH * EIRS * AILTH * EMA - LTS * TER * SLE * AVET * HE * KI - LN * FORAD * ROPO * FTH - EWHI * TESW * AN * SALE. - -Can you decipher it? - - -A POET’S PI - - 37. TONDEBNIOTOCHUMFOARYHUR - OTDIRECTTHAWHOTERSOFKLSYA; - TIKATESTUBALIGHTSTILLETRUFLYR - OTBOWLALLNEFESLEAVARFWYAA. - -In this printer’s pie the words are in their proper sequence, but the -letters are tangled. - - -BURIED PLACES - -38. In the following short sentences five names of places are -buried--that is to say, the letters which spell them in proper order -form parts of more words than one. Thus, for example “Paris” might be -buried in the words “go u_p a ris_e:” - -“The men could ride all on donkeys, the skipper, though, came to a bad -end.” - -When you have discovered these places, try to find out what very -unexpected word of more than four letters is buried in the sentence, “On -Christmas Eve you rang out angel peals.” - - -TREASON CONDONED - -39. According to an old poet, Sir John Harrington (1561-1612):-- - - “Treason doth never flourish; what’s the reason? - For if it prosper none dare call it treason!” - -The classic lines may possibly have been the germ of the flippant modern -riddle, “Why is it no offence to conspire in the evening?” - - -A BIT OF BOTANY - - 40. Inscribe an _m_ above a line - And write an _e_ below, - This woodland flower is hung so fine - It bends when zephyrs flow. - - -A PIED PROVERB - -41. The following letters, if they are properly rearranged, will fall -into the words which form a popular proverb:-- - - AAEEGGHILLMNNNOOOORRSSSSTT - -Can you place them in position? - - -A DROP LETTER PUZZLE - -42. Can you fill in the gaps of this proverb? - - E**t* *e*s**s *a*e *h* *o** **i*e. - - -MULTUM IN PARVO - -43. There is an English word of five syllables which has only eight -letters, five of them vowels--an a, an e, twice i, and y. What are its -consonants? - - -DOUBLETS - -44. Can you turn TORMENT to RAPTURE, using four links, changing only one -letter each time, and varying the order of the letters? - - -A PIED PROVERB - -45. Can you arrange these letters so that they form a sentence of five -words? - - aaceeeffhhiiiiimnnoooprrssttttt. - -The result is a well-known English proverb. - - -WHAT CAN IT BE? - -46. Add one letter, and make this into a sensible English sentence:-- - - GDLDPRTFRRTHDXXFRDDNS - - -OUT OF PROPORTION - - 47. One vowel in an English word is found, - Which by eight consonants is hedged around. - - -48. Can you form an English word with these letters? - - AAAAABBNNIIRSSTT. - - -49. What is this? It is found in Shakespeare:-- - - K I N I. - - -ALPHA BETA - -50. There are two English words which contain each of them ten letters, -and six of these are a, b, c, d, e, f, the first six letters of the -alphabet. Can you build up either or both of them without looking at the -solution? - - -SHIFTING NUMBERS - - 51. Of a band of true kinsmen I stand at the head, - Who, to keep themselves warm, cluster three in a bed. - Put four into gaol and their number has risen, - So that six can be counted together in prison. - Take the six and recount them, they dwindle to three; - Count again, and a change into five you will see. - With no number from one to one hundred I mix, - Yet with five of my mates I am seen to make six. - - -AN IMPUDENT PRODIGAL - -52. The prodigal son of a wealthy colonial farmer received a letter from -his father, to suggest that a considerable part of his inheritance -should be safeguarded before he squandered it. His reply ran -thus:--“Dear dad, keep 1000050.” As such a sum, even in dollars, was out -of the question, the father was completely puzzled. - -What did the prodigal mean? - - -BURIED POETS - -53. The names of eight famous British poets are buried in these lines, -that is to say, the letters that spell the names form in their proper -order parts of different words:-- - - The sun is darting rays of gold - Upon the moor, enchanting spot, - Whose purpled heights, by Ronald loved, - Up open to his Shepherd cot. - - And sundry denizens of air - Are flying, aye, each to his nest; - And eager make at such an hour - All haste to reach the mansions-blest. - -Can you dig them up? - - -A FATEFUL LETTER - -54. When _A. B._ gave up the reins of government, and _C. B._ took -office in his place, it was found that their political positions could -be exactly described by two quite common English verbs, which differ -only in this, that the one is longer by one letter than the other, while -the rest of the letters are the same, and in the same order. What are -these two verbs? - - -A PRIZE REBUS - -55. The following is a prize Rebus:-- - - done | - mutt | a glutt - and | - i | T. c. d. - you make me - - -A LETTER TANGLE - - 56. First a _c_ and _a_ _t_, last _a_ _c_ and a _t_, - With a couple of letters between, - Form a sight that our eyes are delighted to see, - Unless in their sight it is seen. - - -A TRANSPOSITION - - 57. Cut off my tail and set it at my head, - What was an island is a little bear instead. - - -A REBUS - - T S. - -58. What English word do these two letters indicate? There are two -possible solutions of equal merit. - - -A PHONETIC PHRASE - -59. How can we read this? - - I N X I N X I N. - - -A GOOD END - -60. - -[Illustration: I F S] - - -SOLUTIONS - - -CHESS CAMEOS - - -No. XXVI - -Black has made the false move Kt from Q sq to Kt 3. When this is -replaced, and the king is moved as the proper penalty, White mates at -once with one or other of the Knights. - - -No. XXVII - -Replace the White Kt at B 7, and a Black Pawn at K 4; then P takes P _en -pas_. Mate. - -ANALYSIS AND PROOF - -It can be proved that Black’s last move _must have been_ P from K 2 to K -4, so that White may take the P _en pas_. - -The Black King cannot have moved from any _occupied_ square. - - (The White Kt now occupies B 7.) - -Nor from Kt 3 or 4, as both are now _doubly_ guarded, so that he cannot -have moved _out of a check_. - - (The White Kt now helps to guard Kt 5.) - -Nor can he have moved from K 2, as the White P on Q 6 cannot have moved -_to give check_. - -No other P can have moved. - -The K P cannot have moved from K 3, became of the position of the White -King. - -Therefore Black’s last move _must have been_ P from K 2 to K 4, which -White can take _en pas_ giving Mate. - - -No. XXVIII - - B--Q 2 B--R 5 P--Kt 4 - -------- ---------------- ------- White has no move. - P--R 7 P--R 7 becomes Q any - -The way in which the B runs to earth and is shut in is most ingenious. -Black with the new Q cannot anyhow give White a move. - - -No. XXIX - - R--Kt 7, ch. R--Kt 5 R--B 5, ch. - ------------ ----------- ----------------- - K moves P becomes Q Q × R, stalemate. - - -No. XXX - -B--Kt 8. - - -No. XXXI - -B--R 4. - - -No. XXXII - -B--R sq. - - -No. XXXIII - -B--Q 4. - - -No. XXXIV - -B--B sq. - - -No. XXXV - -K--R 4. - - -No. XXXVI - -Kt--Kt’s 6. - - -No. XXXVII - - R--Kt 5 Kt--B 6 Kt × Kt mate. - ------- ----------- ------------- - Kt × R Kt--B 6 ch. - - -No. XXXVIII - - Kt--R 7 Q--KB 8 Q--R 8 mate. - ------- --------- ------------ - B moves B returns - -Any other move of the Kt would impede the movements of the Q. - - -No. XXXIX - - R--R sq. Q--Kt sq. Q to Kt sq. mate. - -------- ---------- ----------------- - B moves. B returns. - - -No. XL - -This beautiful problem is solved by:-- - - Q--Kt 6 K--B 2 mates accordingly. - ------- ------ ------------------ - P × Q any - -or - - R--B 3 mates accordingly. - ------- ------ ------------------ - Kt--K 3 any - - -No. XLI - - R--R 2. Q--R sq. Q mates. - ------- -------- -------- - B × Kt any - -if - - Kt--QB 8, Q or Kt mates. - -------- --------- -------------- - B--Q sq. any - -if - - Kt--QB 6, Q or Kt mates. - ----------- --------- -------------- - B elsewhere any - - -No. XLII - - Kt--Kt 4, dis. ch. Q--KR 2, ch. Kt--B 2, mate. - ------------------ ------------ -------------- - K--R 8. P × Q. - -There are other variations. - - -No. XLIII - - B--Kt sq. Q--QR 7, Q mates. - --------- -------- -------- - P × Kt, K × Kt. - -If K × Kt, Q × P, and mates next move. - - -No. XLIV - - K--Q 7, R--Q 5, Q mates. - ------- ------- -------- - K moves K × R - - -No. XLV - - R--Q 8 Q × P, ch. B mates. - ------- ---------- -------- - K moves K × Q - -if - - Q--K 7 Q mates. - ------- ------ -------- - B moves any - - -No. XLVI - - B--B 6 Q--Q 7, ch. R mates. - ------ ----------- -------- - K × R K × Q - -if - - R--B 6, ch. Q mates. - ----- ----------- -------- - B × R K × P - -There are other variations. - - -No. XLVII - - Q--R 8 Kt--B 6 mates accordingly. - ------ ------- ------------------ - Kt × Q any - - -No. XLVIII - - B--Kt 8 Q × B, ch. Q--QR 7, mate. - --------- ---------- -------------- - B--K Kt 2 Kt--K 4 - -if - - Q--Q 2, ch. P mates. - ------ ----------- -------- - B--B 3 K moves - - -No. XLIX - - B-Kt 2 Q--K 3 ch. mates. - ------ ---------- ------ - K--K 4 any - -There are other variations. - - -No. L - - Q--KR 2 Q--Q 6, ch. Kt--K 5. double ch. mate. - ------------- ----------- ------------------------- - K--B 3 or B 4 Q × Q - -There are other variations. - - -No. LI - - R--QR sq. R--R 2 P mates. - --------- ------ -------- - P moves P × R - - -No. LII - - Q--B sq. Q × BP ch. Q mates. - -------- ---------- -------- - P--K 7 K--Q 3 - -if - - Q × BP ch. Q mates. - ------ ---------- -------- - K--Q 2 K--B 3 - -There are other variations. - - -No. LIII - - B--R 8 Q--QR sq. Q--QKt. 7, mate. - ------ --------- ---------------- - K--R 2 K moves - - -No. LIV - - Q--R 5 Kt--Kt 5 Kt mates. - --------------- -------- --------- - B × Q or B--B 2 any - - -No. LV - - K--Kt 7 Q--Q 5, ch. Kt. mates. - ------- ----------- ---------- - Kt--B 3 Kt × Q - -if - - Q--B 8, ch. Q mates. - ------- ------- -------- - P--K 3 K moves - - -No. LVI - - R--Kt 6 B--Kt 4 R × P mate. - ------- ------- ----------- - P moves P × B - - -No. LVII - - Kt from R 3--Kt 5 B--B 4 P--Q 4 ch. R--B 5 mate. - ----------------- ------ -------------- ------------ - P × Kt P × B P × P _en pas_ - -if - - R--Kt 5 ch. mates accordingly. - ----- ----------- ------------------ - R × B any - -and if - - Kt--Q 6 R--B 5 ch. Kt--B 7 mate. - ------ ------- ---------- ------------- - Q--K 6 Q--Kt 3 Q × R - - -SCIENCE AT PLAY - - -No. LVIII.--THE GEARED WHEELS - -The arrow head at the top of a small wheel with ten teeth, which is -geared into and revolved round a large fixed wheel with forty teeth, -will point directly upwards five times in its course round the large -wheel. Four of these turnings are due to the rotation of the small wheel -on its own axis, and one of them results from its revolution round the -large wheel. - - -No. LX.--THE FIFTEEN BRIDGES - -It is possible to pass over all the bridges which connect the islands -_A_ and _B_ and the banks of the surrounding river without going over -any of them twice. - -The course can be shown thus, using capital letters for the different -regions of land, and italics for the bridges:--E_a_ F_b_ B_c_ F_d_ A_e_ -F_f_ C_g_ A_h_ C_i_ D_k_ A_m_ E_n_ A_p_ B_q_ E_l_D. - -This order of the bridges can, of course, be reversed. - - -No. LXVI.--A DUCK HUNT - -In order that a spaniel starting from the middle of a circular pond, and -going at the same pace as a duck that is swimming round its edge, shall -be sure to catch it speedily, the dog must always keep in the straight -line between the duck and the centre of the pond. - -The duck can never gain an advantage by turning back, and if it swims on -continuously in a circle it will be overtaken when it has passed through -a quarter of the circumference, for the dog will in the same time have -described a semi-circle whose diameter is the radius of the pond, ending -at the point where the duck is caught. - - -No. LXIX.--THE TETHERED BIRD - -When a bird tethered by a cord 50 feet long to a post 6 inches in -diameter uncoils the full length of the cord, and recoils it in the -opposite direction, keeping it always taut, it flies 10,157 feet, or -very nearly 2 miles, in its double course. - -To avoid possible misunderstanding, we point out that, in order to pass -from the uncoiling to the recoiling position, the bird must fly through -a semicircle at the end of the fully extended cord. - - -No. LXX.--THE MOVING DISC AND THE FLY - -[Illustration] - -When a fly, starting from the point _A_, just outside the revolving -disc, and always making straight for its mate at the point _B_, crosses -the disc in four minutes, during which time the disc is turning twice, -the revolution of the disc has a most curious and interesting effect on -the path of the fly. - -The fly is a quarter of a minute in passing from the outside circle to -the next, during which the disc has made an eighth of a revolution, and -the fly has reached the point marked 1. The succeeding points up to 16 -show the position of the fly at each quarter of a minute, until, by a -prettily repeated curve, _B_ is reached. - - -No. LXXI.--A SHUNTING PUZZLE - -The following method enables the engine _R_ to interchange the positions -of the wagons, _P_ and _Q_, for either of which there is room on the -straight rails at _A_, while there is not room there for the engine, -which, if it runs up either siding, must return the same way:-- - -1. _R_ pushes _P_ into _A_. 2. _R_ returns, pushes _Q_ up to _P_ in _A_, -couples _Q_ to _P_, draws them both out to _F_, and then pushes them to -_E_. 3. _P_ is now uncoupled, _R_ takes _Q_ back to _A_, and leaves it -there. 4. _R_ returns to _P_, pulls _P_ back to _C_, and leaves it -there. 5. _R_, running successively through _F_, _D_, _B_, comes to _A_, -draws _Q_ out, and leaves it at _B._ - - -No. LXXV.--PHARAOH’S SEAL - -It is quite puzzling to decide how many similar triangles or pyramids -are expressed on the seal of Pharaoh. There are in fact 96. - - -No. LXXVI.--ROUND THE GARDEN - -The four persons who started at noon from the central fountain, and -walked round the four paths at the rates of two, three, four, and five -miles an hour would meet for the third time at their starting point at -one o’clock, if the distance on each track was one-third of a mile. - - -No. LXXVII.--A JOINER’S PUZZLE - -This diagram shows how to divide Fig. _A_ into two parts, and so -rearrange these that they form either Fig. _B_ or Fig. _C_, without -turning either of the pieces. - - +--------------+ - | | - +--------------+ | +--+ - | | | | - | +--+ +--------------+--+ | +--+ - | | | | | | | | | - | +--+ | | +--+ | | +--+ | - | | | | | | | | | - | +--+ | | +--+ | | +--+ | - | | | | | | | | | - | +--+ | | +--+ | +--+ | - | | | | | | | | - +--+ | | +--+ | +--+ | - | | | | | | | - +--------------+ +--+--------------+ +--------------+ - A B C - -Cut the five steps, and shift the two pieces as is shown. - - -No. LXXVIII.--THE BROKEN OCTAGON - -The Broken Octagon is repaired and made perfect if its pieces are put -together thus:-- - -[Illustration] - - -No. LXXIX.--AT A DUCK POND - -The pond was doubled in size without disturbing the duck-houses, thus:-- - - +-----------○-----------+ - | / \ | - | / \ | - | / \ | - | / \ | - | / \ | - ○ ○ - | \ / | - | \ / | - | \ / | - | \ / | - | \ / | - +-----------○-----------+ - - -No. LXXX.--ALL ON THE SQUARE - -This is a perfect arrangement:-- - -[Illustration] - - -No. LXXXI.--PINS AND DOTS - -The pins may be placed thus:-- - -On the third dot in the top line; on the sixth dot in the second line; -on the second dot in the third line; on the fifth dot in the fourth -line; on the first dot in the fifth line; on the fourth dot in the sixth -line. - - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - | \ / | \ / | \ / | \ / | \ / | - | \ / | \ / | \ / | \ / | \ / | - | * | * | * | * | * | - | / \ | / \ | / \ | / \ | / \ | - | / \ | / \ | / \ | / \ | / \ | - *-----------*-----------*-----------*-----------*-----------* - - -No. LXXXII.--A TRICKY COURSE - -To trace this course draw lines upon the diagram from square 46 to -squares 38, 52, 55, 23, 58, 64, 8, 57, 1, 7, 42, 10, 13, 27, and 19. -This gives fifteen lines which pass through every square only once. - - -No. LXXXIII.--FOR THE CHILDREN - -Make a square with three on every side, and place the remaining four one -on each of the corner men or buttons. - - -No. LXXXVII.--LOYD’S MITRE PROBLEM - -The figure given is thus divided into four equal and similar parts:-- - -[Illustration] - - -No. LXXXIX.--CUT OFF THE CORNERS - - A E F B - +------+--------+------+ - | / \ | - | / \ | - |/ \| - M+ +G - | | - | | - | | - L+ +H - |\ /| - | \ / | - | \ / | - +------+--------+------+ - C K I D - -A very simple rule of thumb method for striking the points in the sides -of a square, which will be at the angles of an octagon formed by -cutting off equal corners of the square, is to place another square of -equal size upon the original one, so that the centre is common to both, -and the diagonal of the new square lies upon a diameter of the other -parallel to its side. - - -No. XCIII.--MAKING MANY SQUARES - -The subjoined diagram shows how the two oblongs, applied to the two -concentric squares, produce 31 perfect squares, namely, 17 small ones, -one equal to 25 of these, 5 equal to 9, and 8 equal to 4. - - +------+ - | | - | | - +-------------+------+-------------+ - | | | | - | | | | - | +------+------+------+ | - | | | | | | - | | | | | | - +-----+------+------+------+------+------+------+ - | | | | | | | | - | | | | | | | | - +-----+------+------+------+------+------+------+ - | | | | | | - | | | | | | - | +------+------+------+ | - | | | | - | | | | - +-------------+------+-------------+ - | | - | | - +------+ - - -No. XCIV.--CUT ACROSS - -The Greek Cross can be divided by two straight cuts, so that the -resulting pieces will form a perfect square when re-set, as is shown in -these figures:-- - -[Illustration] - - -No. CV.--A TRANSFORMATION - -The diagram which is given below shows how the irregular Maltese Cross -can be divided by two straight cuts into four pieces, which form when -properly rearranged, a perfect square. - -[Illustration] - - -No. CVI.--SHIFTING THE CELLS - -The following diagram shows by its dark lines how the whole square can -be cut into four pieces, and these arranged as two perfect squares in -which every semicircle still occupies the upper half of its cell. - -One piece forms a square of nine cells, and it is easy to arrange the -other three pieces in a square of sixteen cells by lifting the three -cells and dropping the two. - - +-----------+-----------+-----------+-----------+-----------+ - | / \ | / \ | / \ | / \ ∥ / \ | - | / \ | / \ | / \ | / \ ∥ / \ | - |/ \|/ \|/ \|/ \∥/ \| - | | | | ∥ | - | | | | ∥ | - +-----------+-----------+-----------+-----------+-----------+ - | / \ | / \ | / \ | / \ ∥ / \ | - | / \ | / \ | / \ | / \ ∥ / \ | - |/ \|/ \|/ \|/ \∥/ \| - | | | | ∥ | - | | | | ∥ | - +-----------+-----------+===========+===========+===========+ - | / \ | / \ ∥ / \ | / \ | / \ | - | / \ | / \ ∥ / \ | / \ | / \ | - |/ \|/ \∥/ \|/ \|/ \| - | | ∥ | | | - | | ∥ | | | - +-----------+===========+-----------+-----------+-----------+ - | / \ ∥ / \ ∥ / \ | / \ | / \ | - | / \ ∥ / \ ∥ / \ | / \ | / \ | - |/ \∥/ \∥/ \|/ \|/ \| - | ∥ ∥ | | | - | ∥ ∥ | | | - +===========+-----------+-----------+-----------+-----------+ - | / \ | / \ ∥ / \ | / \ | / \ | - | / \ | / \ ∥ / \ | / \ | / \ | - |/ \|/ \∥/ \|/ \|/ \| - | | ∥ | | | - | | ∥ | | | - +-----------+-----------+-----------+-----------+-----------+ - - -No. CVII.--IN A TANGLE - -[Illustration] - -It will be seen, on the subjoined diagram, how twenty-one counters or -coins can be placed on the figure so that they fall into symmetrical -design, and form thirty rows, with three in each row. - - -No. CVIII.--STILL A SQUARE - - A - +------+------+------+ - | | | | - | | | | - +------+------+------+ C - | | | - | | | - +------+------+ - B - -In order that a square and an additional quarter may be divided by two -straight lines so that their parts, separated and then reunited, form a -perfect square, lines must be drawn from the point _A_ to the corners -_B_ and _C_. Draw the figure on paper, cut through these lines, and you -will find that the pieces can be so reunited that they form a perfect -square. - - -No. CIX.--A TRANSFORMATION - -The diagram below shows how the seven parts of the square can be -rearranged so that they form the figure 8. - -[Illustration] - - -No. CX.--TO MAKE AN OBLONG - -Here is an oblong formed by piecing together two of the smaller -triangles, and four of each of the other patterns-- - -[Illustration] - -Here is another:-- - -[Illustration] - - -No. CXI.--SQUARES ON THE CROSS - -This diagram shows how every indication of the seventeen squares is -broken up by the removal of seven of the asterisks which mark their -corners. - -[Illustration] - -Those surrounded by circles are to be removed. - - -No. CXII.--A CHINESE PUZZLE - - |\ - | \ - | \ - | \ - | \ - | \ - | +--\ - | | \ - | +--+--+ \ - | | | \ - | +--+ +--+\ - | | | \ - +--+ +--+\ - | | \ - +-----------------+--+ - -The dotted lines on the triangular figure show how a piece of cardboard -cut to the shape of Fig. 1 can be divided into three pieces, and -rearranged so that these form a star shaped as in Fig. 2. - - -No. CXIII.--FIRESIDE FUN - -To solve this puzzle slip the first coin or counter from _A_ to _D_, -then the others in turn from _F_ to _A_, from _C_ to _F_, from _H_ to -_C_, from _E_ to _H_, from _B_ to _E_, from _G_ to _B_, and place the -last on _G_. It can only be done by a sequence of this sort, in which -each starting point is the finish of the next move. - -[Illustration] - - -AMUSING PROBLEMS - - -1. THE CARPENTER’S PUZZLE - -The carpenter cleverly contrived to mend a hole 2 feet wide and 12 feet -long, by cutting the board which was 3 feet wide and 8 feet long, as is -shown in Fig. 1, and putting the two pieces together as is shown in Fig. -2. - - Fig. 1. - +----------------+ - | ________| - |________| | - | | - +----------------+ - - Fig. 2. - +------------------------+ - | ________¦ | - | ¦ | - +------------------------+ - - -2. GOLDEN PIPPINS - -Here is another solution:-- - - 1| 3| 5| 7| 9|11|13|15|17|19 - 39|37|35|33|31|29|27|25|23|21 - 2| 4| 6| 8|10|12|14|16|18|20 - 40|38|36|34|32|30|28|26|24|22 - --+--+--+--+--+--+--+--+--+-- - 82|82|82|82|82|82|82|82|82|82 - - -3. AN AWKWARD FIX - -I was able to find my way in a strange district, when the sign-post lay -uprooted in the ditch, without any difficulty. I simply replaced the -post in its hole, so that the proper arm, with its lettering, _pointed -the way that I had come_, and then, of necessity, the directions of the -other arms were correct. - - -4. LINKED SWEETNESS LONG DRAWN OUT - -The train was whistling for 5 minutes. Sound travels about a mile in 5 -seconds, so the first I heard of it was 5 seconds after it began. Its -last sound reached me 7¹⁄₂ seconds after it ceased, so I heard the -whistle for 5 minutes, 2¹⁄₂ seconds. - - -5. These quarters were not so elastic as they are made to appear. In -good truth, considering that the second man who was placed in _A_ was -afterwards removed to _I_, no real _second_ man was provided for at -all. - - -6. The first day of a new century can never be Sunday, Wednesday, or -Friday. The cycle of the Gregorian calendar is completed in 400 years, -after which all dates repeat themselves. - -As in this cycle there are only four first days of a century, it is -clear that three of the seven days of the week must be excluded. Any -perpetual calendar shows that the four which do occur are Monday, -Tuesday, Thursday, and Saturday, so that Sunday, Wednesday, and Friday -are shut out. - -A neat corollary to this proof is that Monday is the only day which may -be the first, or which may be the last, day of a century. - - -7. A cricket bat with spliced handle has such good driving power, -because the elasticity of the handle allows the ball to be in contact -with the blade of the bat for a longer time than would otherwise be -possible. - -With similar effect the “follow through” of the club head at golf -maintains contact with the ball, when it is already travelling fast. - - -8. When two volumes stand in proper order on my bookshelf, each 2 inches -thick over all, with covers ¹⁄₈ of an inch in thickness, a bookworm -would only have to bore ¹⁄₄ of an inch, to penetrate from the first page -of Vol. I, to the last page of Vol. II, for these pages would be in -actual contact if there was no binding. This very pretty and puzzling -question combines in its solution all the best qualities of a clever -catch with solid and simple facts. - - -9. A man would have to fall from a height of nearly 15 miles to reach -earth before the sound of his cry as he started. The velocity of sound -is constant, while that of a falling body is continually accelerated. At -first the cry far outstrips the falling man, but he _overtakes and -passes through his own scream_ in about 14¹⁄₂ miles, for his body falls -through the 15 miles in 70 seconds, and sound travels as far in 72 -seconds. Air resistance, and the fact that sound cannot pass from a rare -to a dense atmosphere, are disregarded in this curious calculation. - - -10. A man on a perfectly smooth table in a vacuum, and where there was -no friction, though no contortions of his body would avail to get away -from this position, could escape from the predicament by throwing from -him something which he could detach from his person, such as his watch -or coat. He would himself instantly slide off in the opposite direction! - - -11. The monkey clinging to one end of a rope that passes over a single -fixed pulley, while an equal weight hangs on the other end, cannot climb -up the rope, or rise any higher from the ground. - -If he continues to try to climb up, he will gradually pull the balancing -weight on the other end of the rope upwards, and the slack of the rope -will drop below him, while he remains in the same place. - -If, after some efforts, he rests, he will sink lower and lower, until -the weight reaches the pulley, because of the extra weight of rope on -his side, if friction is disregarded. - - -12. Though the tension on a pair of traces tends as much to pull the -horse backward as it does to pull the carriage forward, it is the -initial pull from slack to taut which sets the traces in motion; and -this, once started, must continue indefinitely until checked by a -counter pull. - - -13. Some say that a rubber tyre leaves a double rut in dust and a -single one in mud, because the air, rushing from each side into the wake -of the wheel, piles up the loose dust. Others hold that the central -ridge is caused by the continuous contraction of the tyre as it passes -its point of contact with the road. - -A correspondent, writing some years ago to “Knowledge,” said:--“It is -our old friend the sucker. The tyre being round, the weight on centre of -track only is great enough to enable the tyre to draw up a ridge of dust -after it.” - - -14. If two cats on a sloping roof are on the point of slipping off, one -might think that whichever had the longest paws (pause) would hold on -best. Todhunter, in playful mood, saw deeper into it than that, and -pronounced for the cat that had the _highest mew_, for to his -mathematical mind the Greek letter _mu_ was the coefficient of friction! - - -15. If a penny held between finger and thumb, and released by -withdrawing the finger, starts “heads” and makes half a turn in falling -through the first foot, it will be “heads” again on reaching the floor, -if it is held four feet above it at first. - - -16. HE DID IT! - -Funnyboy had secretly prepared himself for the occasion by rubbing the -chemical coating from the side of the box on to his boot. - - -17. THE CYCLE SURPRISE - -If a bicycle is stationary, with one pedal at its lowest point, and that -pedal is pulled backwards, while the bicycle is lightly supported, the -bicycle will move backwards, and the pedal relatively to the bicycle, -will move forwards. This would be quite unexpected by most people, and -it is well worth trying. - - -18. The rough stones, by which any number of pounds, from 1 to 364, can -be weighed, are respectively 1 ℔., 3 ℔s., 9 ℔s., 27 ℔s., 81 ℔s., and 243 -℔s. in weight. - - -19. If we disregard the resistance of the air, a small clot of mud -thrown from the hindermost part of a wheel would describe a parabola, -which would, in its descending limb, bring it back into kissing contact -with the wheel which had rejected it. - - -20. THE CARELESS CARPENTER - -When the carpenter cut the door _too little_, he did not in fact _cut it -enough_, and he had to cut it again, so that it might fit. - - -21. If from the North Pole you start sailing in a south-westerly -direction, and keep a straight course for twenty miles, you must steer -due north to get back as quickly as possible to the Pole, if, indeed, it -has been possible to start from it in any direction other than due -south. - - -22. DICK IN A SWING - -Dick’s feet will travel in round numbers nearly 16 feet further than his -head, or to be exact, 15·707,960 feet. - - -23. A POSER - -The initial letters of Turkey, Holland, England, France, Italy, Norway, -Austria, Lapland, and Spain spell, and in this sense are the same as, -“the finals.” - - -CURIOUS CALCULATIONS - - -1. The only sum of money which satisfies the condition that its pounds, -shillings, and pence written down as a continuous number, exactly give -the number of farthings which it represents, is £12, 12s., 8d., for this -sum contains 12,128 farthings. - - -2. If, when a train, on a level track, and running all the time at 30 -miles an hour, slips a carriage which is uniformly retarded by brakes, -and this comes to rest in 200 yards, the train itself will then have -travelled 400 yards. - -The slip carriage, uniformly retarded from 30 miles an hour to no miles -an hour, has an average speed of 15 miles an hour, while the train -itself, running on at 30 miles an hour all the time, has just double -that speed, and so covers just twice the distance. - - -3. The traveller had fivepence farthing when he said to the landlord, -“Give me as much as I have in my hand, and I will spend sixpence with -you.” After repeating this process twice he had no money left. - - -4. This is the way to obtain eleven by adding one-third of twelve to -four-fifths of seven-- - - TW(EL)VE + S(EVEN) = ELEVEN - - -5. Here is the completed sum:-- - - 215)*7*9*(1** 215)37195(173 - *** 215 - ---- ---- - *5*9 1569 - *5*5 1505 - ---- ---- - *4* 645 - *** 645 - === === - -The clue is that no figure but 3, when multiplied into 215, produces 4 -in the tens place. - - -6. If I attempt to buy as many heads of asparagus as can be encircled by -a string 2 feet long for double the price paid for as many as half that -length will encompass, I shall not succeed. A circle double of another -in circumference is also double in diameter, and its area is four times -that of the other. - - -7. If, when you reverse me, and my square, and my cube, and my fourth -power, you find that no changes have been made, I am 11, my square is -121, my cube 1331, and my fourth power 14641. - - -8. A thousand pounds can be stored in ten sealed bags, so that any sum -in pounds up to £1,000 can be paid without breaking any of the seals, by -placing in the bags 1, 2, 4, 8, 16, 32, 64, 128, 256, and 489 -sovereigns. - - -9. It is the fraction ⁶⁄₉ which is unchanged when turned over, and -which, when taken thrice, and then divided by two becomes 1. - - -10. When the three gamblers agreed that the loser should always double -the sum of money that the other two had before them, and they each lost -once, and fulfilled the conditions, remaining each with eight sovereigns -in hand, they had started with £13, £7, and £4 as the following table -shows:-- - - A B C - £ £ £ - At starts 13 7 4 - When A loses 2 14 8 - When B loses 4 4 16 - When C loses 8 8 8 - - -11. Tom’s sum, which his mischievous neighbour rubbed almost out, is -reconstructed thus:-- - - 345 345 - ** 37 - ----- ----- - **** 2415 - **** 1035 - ----- ----- - **76* 12765 - - -12. Here are two other arrangements of the nine digits which produce 45, -their sum; each is used once only:-- - - 5 × 8 × 9 × (7 + 2) - ------------------- = 45 - 1 × 3 × 4 × 6 - - 7² - 5 × 8 × 9 - -------------- + 1 = 45 - 3 × 4 × 6 - - -13. If, when the combined ages of Mary and Ann are 44, Mary is twice as -old as Ann was when Mary was half as old as Ann will be when Ann is -three times as old as Mary was when Mary was three times as old as Ann, -Mary is 27¹⁄₂ years old, and Ann is 16¹⁄₂. - -For, tracing the question backwards, when Ann was 5¹⁄₂ Mary was 16¹⁄₂. -When Ann is three times that age she will be 49¹⁄₂. The half of this is -24³⁄₄, and when Mary was at that age Ann was 13³⁄₄. Mary’s age, by the -question, was twice this, or 27¹⁄₂. - - -14. It is safer at backgammon to leave a blot in the tables which can be -taken by an ace than one which a three would hit. In either the case of -an actual ace or a three the chance is one in eleven; but there are two -chances of throwing deuce-ace, the equivalent of three. - - -15. If I start from a bay, where the needle points due north, 1200 miles -from the North Pole, and the course is perfectly clear, I can never -reach it if I steam continuously 20 miles an hour, steering always north -by the compass needle. After about 200 miles I come upon the Magnetic -Pole, which so affects the needle that it no longer leads me northward, -and I may have to steer south by it to reach the geographical Pole. - - -16. The 21 casks, 7 full, 7 half full, and 7 empty, were shared equally -by A, B, and C, as follows:-- - - Full cask. Half full. Empty. - A 2 3 2 - B 2 3 2 - C 3 1 3 - -or-- - - A 3 1 3 - B 3 1 3 - C 1 5 1 - -Thus each had 7 casks, and the equivalent of 3¹⁄₂ caskfuls of wine. - - -17. The foraging mouse, able to carry home three ears at a time from a -box full of ears of corn, could not add more than fourteen ears of corn -to its store in fourteen journeys, for it had each time to carry along -two ears of its own. - - -18. If, with equal quantities of butter and lard, a small piece of -butter is taken and mixed into all the lard, and if then a piece of this -blend of similar size is put back into the butter, there will be in the -end exactly as much lard in the butter as there is butter in the lard. - - -19. The fallacy of the equation-- - - 4 - 10 = 9 - 15 - - 4 - 10 + ²⁵⁄₄ = 9 - 15 + ²⁵⁄₄ - -and the square roots of these-- - - 2 - ⁵⁄₂ = 3 - ⁵⁄₂ - - therefore 2 = 3 - -is explained thus:--The fallacy lies in ignoring the fact that the -square roots are _plus or minus_. In the working we have taken both -roots as _plus_. If we take one root plus, and the other minus, and add -⁵⁄₂, we have either 2 = 2, or 3 = 3. - - -20. The largest possible parcel which can be sent through the post under -the official limits of 3 feet 6 inches in length, and 6 feet in length -and girth combined, is a cylinder 2 feet long and 4 feet in -circumference, the cubic contents of which are 2⁶⁄₁₁ cubic feet. - - -21. We can show, or seem to show, that either four, five, or six nines -amount to 100, thus:-- - - IX - IX - 99⁹⁄₉ = 100 IX 9 × 9 + 9 + 9⁹⁄₉ = 100 - IX - IX - --- - 100 - - -22. This is the magic square arrangement, so contrived that the -products of the rows, columns, and diagonals are all 1,000. - - +---+---+---+ - | 50| 1| 20| - +---+---+---+ - | 4| 10| 25| - +---+---+---+ - | 5|100| 2| - +---+---+---+ - - -23. If seven boys caught four crabs in the rock-pools at Beachy Head in -six days, the twenty-one boys who searched under the seaweed and only -caught one crab with the same rate of success were only at work for -_half a day_. - - -24. A watch could be set of a different trio from a company of fifteen -soldiers for 455 nights, and one of them, John Pipeclay, could be -included ninety-one times. - - -25. If Augustus Cæsar was born September 23, B.C. 63, he celebrated his -sixty-third birthday on September 23, B.C. 0; or, writing it otherwise, -September 23, A.D. 0; or again, if we wish to include both symbols, B.C. -0 A.D. It is clear that his sixty-second birthday fell on September 23, -B.C. 1, and his sixty-fourth on September 23, A.D. 1, so that the -intervening year may be written as above. - - -26. The difference of the ages of _A_ and _B_ who were born in 1847 and -1874, is 27, or 30 - 03. Hence, when _A_ was 30 _B_ was 03. And _A_ was -30 in 1877. Eleven years later _A_ was 41 and _B_ 14, and eleven years -after that _A_ was 52 and _B_ 25. Thus the same two digits served to -express the ages of both in 1877, 1888, and 1899. This can only happen -in the cases of those whose ages differ by some multiple of nine. - - - 27 A hundred and one by fifty divide, - To this let a cypher be duly applied; - And when the result you can rightly divine, - You find that its value is just one in nine-- - -is solved by CLIO, one of the nine Muses. - - -28. The man who paid a penny on Monday morning to cross the ferry, spent -half of what money he then had left in the town, and paid another penny -to recross the ferry, and who repeated this course on each succeeding -day, reaching home on Saturday evening with one penny in his pocket, -started on Monday with £1 1s. 1d. in hand. - - -29. When the three men agreed to share their mangoes equally after -giving one to the monkey, and when each helped himself to a third after -giving one to the monkey, without knowing that anyone had been before -him, and they finally met together, gave one to the monkey, and divided -what still remained, there must have been at least seventy-nine mangoes -for division at the first. - - -30. If, after having looked at my watch between 4 and 5, I look again -between 7 and 8, and find that the hour and minute-hands have then -exactly changed places, it was 36 12-13 minutes past 4 when I first -looked. At that time the hour-hand would be pointing to 23 1-13 minutes -on the dial, and at 23 1-13 minutes past 7 the hour hand would be -pointing to 36 12-13 minutes. - - -31. The number consisting of 22 figures, of which the last is 7, which -is increased exactly sevenfold if this 7 is moved to the first place, is -1,014,492,753,623,188,405,797. - - -32. The two sacks of wheat, each 4 feet long and 3 feet in -circumference, which the farmer sent to the miller in repayment for one -sack 4 feet long and 6 feet in circumference, far from being a -satisfactory equivalent, contained but half the quantity of the larger -sack, for the area of a circle the diameter of which is double that of -another is equal to four times the area of that other. - - -33. The five gamblers, who made the condition that each on losing should -pay to the others as much as they then had in hand, and who each lost in -turn, and had each £32 in hand at the finish, started with £81, £41, -£21, £11, and £6 respectively. - - -34. If we know the square of any number, we can rapidly determine the -square of the next number, without multiplication, by adding the two -numbers to the known square. Thus if we know that the square of 87 is -7569, - - then the square of 88 = 7569 + 87 + 88 = 7744; - so too the square of 89 = 7744 + 88 + 89 = 7921; - and the square of 90 = 7921 + 89 + 90 = 8100. - - -35. The two numbers which solve the problem-- - - Two numbers seek which make eleven, - Divide the larger by the less, - The quotient is exactly seven, - As all who find them will confess-- - -are 1³⁄₈ and 9⁵⁄₈, for 1³⁄₈ + 9⁵⁄₈ = 11, and ⁷⁷⁄₈ ÷ ¹¹⁄₈ = 7. - - -36. There must be nine things of each sort, in order that -^99999999999999999999^ different selections may be made from twenty -sorts of things. - - -37. The women who had respectively 33, 29, and 27 apples, and sold the -same number for a penny, receiving an equal amount of money, began by -selling at the rate of three a penny. The first sold ten pennyworth, the -second eight pennyworth, and the third seven pennyworth. - -The first had then left three apples, the second five, and the third -six. These they sold at one penny each, so that they received on the -whole-- - - The first 10d. + 3d. = 13d. - The second 8d. + 5d. = 13d. - The third 7d. + 6d. = 13d. - - -38. The puzzle-- - - Take five from five, oh, that is mean! - Take five from seven, and this is seen-- - -is solved by _fie_, _seen_. - - -39. If a bun and a half cost three halfpence, it is plain that each bun -costs a penny, but, by general custom, you buy seven for sixpence. - - -40. The hands of a watch would meet each other twenty-five times in a -day, if the minute-hand moved backwards and the hour-hand forwards. They -are, of course, together at starting. - - -41. The only way in which half-a-crown can be equally divided between -two fathers and two sons, so that a penny is the smallest coin made use -of, is to give tenpence each to a grandfather, his son, and his -grandson. - - -42. If the number of the revolutions of a bicycle wheel in six seconds -is equal to the number of miles an hour at which it is running, the -circumference of the wheel is 8⁴⁄₅ feet. - - -43. The hour that struck was twelve o’clock. - - -44. Sixty years. - - -45. If I jump off a table with a 20lb dumb-bell in my hand there is no -pressure upon me from its weight while I am in the air. - - -46. If at a bazaar I paid a shilling on entering each of four tents, and -another shilling on leaving it, and spent in each tent half of what was -in my pocket, and if my fourth payment on leaving took my last shilling, -I started with 45s., spending 22s. in tent 1, 10s. in tent 2, 4s. in -tent 3, and 1s. in tent 4, having also paid to the doorkeepers 8s. - - -47. When rain is falling vertically at 5 miles an hour, and I am walking -through it at 4 miles an hour, the rain drops will strike the top of my -umbrella at right angles if I hold it at an angle of nearly 39 degrees. - -As I walk along, meeting the rain, the effect is the same as it would be -if I was standing still, and the wind was blowing the rain towards me at -the rate of 4 miles an hour. - - -48. When one monkey descends from the top of a tree 100 cubits high, and -makes its way to a well 200 yards distant, while another monkey, leaping -upwards from the top, descends by the hypotenuse to the well, both -passing over an equal space, the second monkey springs 50 cubits into -the air. - - -49. The steamboat which springs a leak 105 miles east of Tynemouth -Lighthouse, and, putting back, goes at the rate of 10 miles an hour the -first hour, but loses ground to the extent in each succeeding hour of -one-tenth of her speed in the previous hour, never reaches the -lighthouse, but goes down 5 miles short of it. - - -50. Twenty-one hens will lay ninety-eight eggs in a week, if a hen and -a-half lays an egg and a-half in a day and a-half. Evidently one egg is -laid in a day by a hen and a-half, that is to say three hens lay two -eggs in a day. Therefore, twenty-one hens lay fourteen eggs, in a day, -or ninety-eight in a week. - - Q. E. D. (Quite easily done!) - - -51. If the population of Bristol exceeds by 237 the number of hairs on -the head of anyone of its inhabitants that are not bald, at least 474 of -them must have the same number of hairs on their heads. - - -52. In tipping his nephew from seven different coins, the uncle may give -or retain each, thus disposing of it in two ways, or of all in 2 × 2 × 2 -× 2 × 2 × 2 × 2 ways. But as one of these ways would be to retain them -all, there are not 128, but only 127 possible variations of the tip. - - -53. The prime number which fulfils the various conditions of the -question is 127. Increased by one-third, excluding fractions, it becomes -169, the square of 13. If its first two figures are transposed, and it -is increased by one-third, it becomes 289, the square of 17. If its -first figure is put last, and it is increased by one-third, it becomes -361, the square of 19. If, finally, its three figures are transposed, -and then increased by one-third, it becomes 961, the square of 31. - - -54. Six things can be divided between two boys in 62 ways. They could be -_carried_ by two boys in 64 ways (2 × 2 × 2 × 2 × 2 × 2), but they are -not _divided_ between two boys if all are given to one, so that two of -the 64 ways must be rejected. - - -55. The highest possible score that the dealer can make at six cribbage, -if he is allowed to select the cards, and to determine the order of -play, is 78. The dealer and his opponent must each hold 3, 3, 4, 4, the -turn-up must be a 5, and crib must have the knave of the suit turned up, -and 5, 5, 5. It will amuse many of our readers to test this with the -cards. - - -56. The picture frame must be 3 inches in width all round, if it is -exactly to equal in area the picture it contains, which measures 18 -inches by 12 inches. - - -57. If my mother was 20 when I was born, my sister is two years my -junior, and my brother is four years younger still, our ages are 56, 36, -34, and 30. - - -58. The spider in the dockyard, whose thread was drawn from her by a -revolving capstan 1 foot in diameter, until 73 feet of it were paid out, -after walking for a mile round and round the capstan at the end of the -stretched thread in an effort to unwind it all, had, when she stopped in -her spiral course, 49 more feet to walk to complete her task. - - -59. The mountebank at a fair, who offered to return any stake a -hundredfold to anyone who could turn up all the sequence in twenty -throws of dice marked each on one face only with 1, 2, 3, 4, 5, or 6, -should in fairness have engaged to return 2332 times the money; for of -the 46,656 possible combinations of the faces of the dice, only one can -give the six marked faces uppermost. Thus the chance of throwing them -all at one throw is expressed by ¹⁄₄₆₆₅₆, and in twenty throws by about -¹⁄₂₃₃₂. - - -60. If 90 groats (each = 4d.) feed twenty cats for three weeks, and five -cats consume as much as three dogs, seventy-two hounds can be fed for -£39 in a period of ninety-one days. - - -61. When equal wine-glasses, a half and a third full of wine, are filled -up with water, and their contents are mixed, and one wine-glass is -filled with the mixture, it contains ⁵⁄₁₂ wine and ⁷⁄₁₂ water. - - -62. The arrangement by which St Peter is said to have secured safety for -the fifteen Christians, when half of the vessel’s passengers were thrown -overboard in a storm, is as follows:-- - - XXXXIIIIIXXIXXXIXIIXXIIIXIIXXI - -Each Christian is represented by an X, and if every ninth man is taken -until fifteen have been selected, no X becomes a victim. - - -63. If Farmer Southdown’s cow had a fine calf every year, and each of -these, and their calves in their turn, at two years old followed this -example, the result would be no less than 2584 head in sixteen years. - - -64. The number of the flock was 301. This is found by first taking the -least common multiple of 2, 3, 4, 5, 6, which is 60, and then finding -the lowest multiple of this, which with 1 added is divisible by 7. This -301 is exactly divisible by 7, but by the smaller numbers there is 1 as -remainder. - - -65. The rule for determining easily the number of round bullets in a -flat pyramid, with a base line of any length, is this:-- - -Add a half to half the number on the base line, and multiply the result -by the number on that line. Thus, if there are twelve bullets as a -foundation-- - - 12 + ¹⁄₂ = ¹³⁄₂; and ¹³⁄₂ × ¹²⁄₁ = 78. - -The same result is reached by multiplying the number on the base line by -a number larger by one, and then halving the result. Thus-- - - 12 × 13 = 156, 156 ÷ 2 = 78. - - -66. We can gather from the lines-- - - Old General Host - A battle lost, - And reckoned on a hissing, - When he saw plain - What men were slain, - And prisoners, and missing. - - To his dismay - He learned next day - What havoc war had wrought; - He had, at most, - But half his host - Plus ten times three, six, ought. - - One-eighth were lain - On beds of pain, - With hundreds six beside; - One-fifth were dead, - Captives, or fled, - Lost in grim warfare’s tide. - - Now, if you can, - Tell me, my man, - What troops the general numbered, - When on that night - Before the fight - The deadly cannon slumbered? - -that old General Host had an army 24,000 strong. - - -67. When the farmer sent five pieces of chain of 3 links each, to be -made into one continuous length, agreeing to pay a penny for each link -cut, and a penny for each link joined, the blacksmith, if he worked in -the best interest of the farmer, could only charge sixpence: for he -could cut asunder one set of 3 links, and use these three single links -between the other four sets. - - -68. If, in a parcel of old silver and copper coins, each silver piece is -worth as many pence as there are copper coins, and each copper coin is -worth as many pence as there are silver coins, there are eighteen silver -and six copper coins, when the whole parcel is worth eighteen shillings. - - -69. These are five groups that can be arranged with the numbers 1 to 11 -inclusive, so that they are all equal:-- - - (8² - 5² + 1) = (11² - 9²) = (7² - 3²) = (6² + 2²) = 4(10). - - -70. John Bull, under the conditions given, lived to the age of -eighty-four years. - - -71. The two numbers to each of which, or to the halves of which, unity -is added, forming in every case a square number, are 48 and 1680. - - -72. The true weight of a cheese that seemed to weigh 16 ℔s. in one scale -of a balance with arms of unequal length, and only 9℔s. in the other, is -12℔. This is found by multiplying the 16 by the 9, and finding the -square root of the result. - - -73. The two parts into which 100 can be divided, so that if one of them -is divided by the other the quotient is again exactly 100 are 99¹⁄₁₀₁ -and ¹⁰⁰⁄₁₀₁. - - -74. If, with marbles in two pockets, I add one to those in that on the -right, and then multiply its contents by the number it held at first, -and after dealing in a similar way with those on the left, find the -difference between the two results to be 90; while if I multiply the sum -of the two original quantities by the square of their difference the -result is 176, I started with twenty-three in the right-hand pocket and -twenty-one in the other. - - -75. The circle of twenty-one friends who arranged to meet each week five -at a time for Bridge so long as exactly the same party did not meet more -than once, and who wished to hire a central room for this purpose, would -need it for no less than 20,349 weeks, or more than 390 years, to carry -out their plan. - - -76. If a herring and a half costs (not cost) a penny and a half, the -price of a dozen such quantities is eighteenpence. - - -77. The sum of money which in a sense appears to be the double of itself -is 1s. 10d., for we may write it _one_ and _ten_ pence or _two_ and -_twenty_ pence. - - -78. The “comic arithmetic” question set by Dr Bulbous Roots-- - -Divide my fifth by my first, and you have my fourth; subtract my first -from my fifth, and you have my second; multiply my first by my fourth -followed by my second, and you have my third; place my second after my -first, and you have my third multiplied by my fourth--is solved by -COMIC. - - -79. If the earth could stand still, and a straight tunnel could be bored -through it, a cannon ball dropped into it, if there is no air or other -source of friction, would oscillate continually from end to end. - -Taking air into account, the ball would fall short of the opposite end -at its first lap, and in succeeding laps its path would become shorter -and shorter, until its initial energy was exhausted, when it would come -to rest at the centre. - - -80. He sent 163. She sent 157. - - -81. When twins were born the estate was properly divided thus:-- - - Taking the daughter’s share as 1 - The widow’s share would be 2 - And the son’s share 4 - - - Total 7 shares. - -So the son takes four-sevenths, the widow two-sevenths, and the daughter -one-seventh of the estate. - - -82. If each of my strides forwards or backwards across a 22 feet carpet -is 2 feet, and I make a stride every second; and if I take three strides -forwards and two backwards until I cross the carpet, I reach the end of -it in forty-three seconds. In three steps I advance 6 feet. Then in two -steps I retrace 4 feet, thus gaining only 2 feet in five steps, _i.e._, -in five seconds. I therefore advance 16 feet in forty seconds, and three -more strides cover the remaining 6 feet. - - -83. If the captain of a vessel chartered to sail from Lisbon to New -York, which appear on a map of the world to be on the same parallel of -latitude, and which are, along the parallel, about 3600 miles apart, -takes his ship along this parallel, he will not be doing his best for -the impatient merchant who has had an urgent business call to New York. - -The shortest course between the two points is traced by a segment of a -“great circle,” having its centre at the centre of the earth, and -touching the two points. This segment lies wholly north of the parallel, -and is the shortest possible course. - - -84. When John and Harry, starting from the right angle of a triangular -field, run along its sides, and meet first in the middle of the opposite -side, and again 32 yards from their starting point, if John’s speed is -to Harry’s as 13 to 11, the sides of the field measure 384 yards. - - -85. If two sorts of wine when mixed in a flagon in equal parts cost -15d., but when mixed so that there are two parts of _A_ to three of _B_ -cost 14d., a flagon of _A_ would cost 20d., and a flagon of _B_ 10d. - - -86. If, when a man met a beggar, he gave him half of his loose cash and -a shilling, and meeting another gave him half what was left and two -shillings, and to a third half the remainder and three shillings, he had -two guineas at first. - - -87. The clerk who has two offers of work from January 1, one from _A_ of -£100 a year, with an annual rise of £20, and the other from _B_ of £100 -a year, with a half-yearly rise of £5, should accept _B_’s offer. - -The half-yearly payments from _A_ (allowing for the rise), would be 50, -50, 60, 60, 70, 70, etc., etc.; and from _B_ they would be 50, 55, 60, -65, 70, 75, etc., etc., so that _B_’s offer is worth £5 a year more than -_A_’s always. - - -88. If I have a number of florins and half-crowns, but no other coins, I -can pay my tailor £11, 10s. in 224 different ways. - -This can be found thus by rule of thumb: Start with 0 half-crowns and -115 florins. Then 4 half-crowns and 110 florins. Add 4 half-crowns and -deduct 5 florins each time till 92 half-crowns and 0 florins is reached. - - -89. The monkey climbing a greased pole, 60 feet high, who ascended 3 -feet, and slipped back 2 feet in alternate seconds, reached the top in 1 -minute, 55 seconds, for he did not slip back from the top. - - -90. When Adze, the carpenter, secured his tool-chest with a puzzle lock -of six revolving rings, each engraved with twelve different letters, the -chances against any one discovering the secret word formed by a letter -on each ring was 2,985,983 to 1; for the seventy-two letters may be -placed in 2,985,984 different arrangements, only one of which is the -key. - - -91. The five married couples who arranged to dine together in -Switzerland at a round table, with the ladies always in the same places, -so long as the men could seat themselves each between two ladies, but -never next to his own wife, were able under these conditions to enjoy -thirteen of these nights at the round table. - - -92. If in a calm the tip of a rush is 9 inches above the surface of a -lake, and as the wind rises it is gradually blown aslant, until at the -distance of a yard it is submerged, it is growing in water that is 5 -feet 7¹⁄₂ inches deep. - - -93. Aminta was eighteen. - - -94. When Dick took a quarter of the bag of nuts, and gave the one over -to the parrot, and Tom and Jack and Harry dealt in the same way with the -remainders in their turns, each finding a nut over from the reduced -shares for the bird, and one was again over when they divided the final -remainder equally, there were, at the lowest estimate, 1021 nuts in the -bag. - - -95. Eight and a quarter is the answer to the nonsense question-- - - If five times four are thirty-three, - What will the fourth of twenty be? - - -96. The similar fraction of a pound, a shilling, and a penny which make -up exactly a pound are as follows:-- - - s. d. - ²⁴⁰⁄₂₅₃ of £1 = 18 11¹⁶⁹⁄₂₅₃ - ²⁴⁰⁄₂₅₃ of 1s. = 11⁹⁷⁄₂₅₃ - ²⁴⁰⁄₂₅₃ of 1d. = ²⁴⁰⁄₂₅₃ - --------------- - £1 0 0 - ======== - - -97. When Dr Tripos thought of a number, added 3, divided by 2, added 8, -multiplied by 2, subtracted 2, and thus arrived at double the number, he -started with 17. - - -98. When _A_ and _B_ deposited equal stakes with _C_, and agreed that -the one who should first win three games of billiards should take all, -but consented to a division in proper shares when _A_ had won two games -and _B_ one, it was evident that if _A_ won the next game all would go -to him, while if he lost he would be entitled to one half. One case was -as probable as the other, therefore he was entitled to _half of these -sums taken together_; that is, to three quarters of the stakes, and _B_ -to a quarter only. - - -99. The average speed of a motor which runs over any course at 10 miles -an hour, and returns over the same course at 15 miles an hour, is 12 -miles an hour, and not 12¹⁄₂, as might be imagined. Thus a run of 60 -miles out takes, under the conditions, six hours, and the return takes -four hours; so that the double journey of 120 miles is done in ten -hours, at an average speed of 12 miles an hour. - - -100. Farmer Hodge, who proposed to divide his sheep into two unequal -parts, so that the larger part added to the square of the smaller part -should equal the smaller part added to the square of the larger part, -had but one sheep. - -Faithful to his word, he divided this sheep into two unequal parts, ²⁄₃ -and ¹⁄₃, and was able to show that ²⁄₃ + ¹⁄₉ = ⁷⁄₉, and that ¹⁄₃ + ⁴⁄₉ = -⁷⁄₉. He was heard to declare further, and he was absolutely right, that -_no number larger than_ 1 can be so divided as to satisfy the conditions -which he had laid down. - -The fact that _sheep_ is both singular and plural, adds much to the -perplexing points of this attractive problem. - -Here is a very simple proof that the number _must be_ 1:-- - - Let a + b = no. of sheep - - then a² + b = b² + a - - a² - b² = a - b - - or (a + b)(a - b) = a - b - - therefore a + b = 1. - - -101. A horse that carries a load can draw a greater weight _up the shaft -of a mine_ than a horse that bears no burden. The load holds him more -firmly to the ground, and thus gives him greater power over the weight -he is raising from below. - - -102. In the six chests, of which two contained pence, two shillings, and -two pounds, there must have been at least the value of 506 pence. This -can be divided into 22 (or 19 + 3) shares of 23d. each, or 23 (19 + 4) -shares of 22d. each. Evidently then the treasure can be divided so that -19 men have equal shares, while their captain has either 3 shares or 4 -shares. - - -103. If I bought a parcel of nuts at 49 for 2d., and divided it into two -equal parts, one of which I sold at 24, the other at 25 a penny; and if -I spent and received an integral number of pence, but bought the least -possible number of nuts, I bought 58,800 nuts, at a cost of £10, and I -gained a penny. - - -104. When, with a purse containing sovereigns and shillings, after -spending half of its contents, I found as many pounds left as I had -shillings at first, I started with £13, 6s. - - -105. When the lady replied to a question as to her age-- - - If first my age is multiplied by three, - And then of that two-sevenths tripled be, - The square root of two-ninths of this is four; - Now tell my age, or never see me more-- - -she was 28 years old. - - -106. If cars run, at uniform speed, from Shepherd’s Bush to the Bank, at -intervals of two minutes, and I am travelling at the same rate in the -opposite direction, I shall meet 30 in half-an-hour, for there are -already 15 on the track approaching me, and 15 are started from the -other end during my half hour’s course. - - -107. If it was possible to carry out my offer of a farthing for every -different group of apples which my greengrocer could select from a -basket of 100 apples, he would be entitled to the stupendous sum of -£18,031,572,350 19s. 2d. - - -108. If the minute-hand of a clock moves round between 3 and 4 in the -opposite direction to the hour-hand, the hands will be exactly together -when it is really 41⁷⁄₁₃ minutes past 3. - - -109. If the walnut monkey had stopped to help the other, and they had -eaten filberts at equal rates, they would have escaped in 2¹⁄₄ minutes. - - -110. The value of the cheque, for which the cashier paid by mistake -pounds for shillings, was £5, 11s. 6d. The receiver to whom £11, 5s. 6d. -was handed, spent half-a-crown, and then found that he had left £11, -3s., just twice the amount of the original cheque. - - -111. The number 14 can be made up by adding together five uneven figures -thus:--11 + 1 + 1 + 1. It will be seen that although only four _numbers_ -are used, 11 is made up of _two figures_. - -Here is another, and quite a curious solution, 1 + 1 + 1 + 1 = 4, and -with another 1 we can make up 14! - - -112. A business manager can fill up three vacant posts of varying value -from seven applicants in 210 different ways. For the first post there -would be a choice among 7, for the second among 6, and for the third -among 5, so that the possible variations would amount to 7 × 6 × 5 = -210. - - -113. If the fasting man, who began his task at noon, said it is now ⁵⁄₁₁ -of the time to midnight, he spoke at 3.45 p.m., meaning that ⁵⁄₁₁ of the -remaining time till midnight had elapsed since noon. - - -114. If a clock takes six seconds to strike 6, it will take 12 seconds -to strike 11, for there must be ten intervals of 1¹⁄₁₅ seconds each. - - -115. Twenty horses can be arranged in three stalls, so that there is an -odd number in each, by placing one in the first stall, three in the -second, and sixteen (an odd number to put into any stall!) in the third. - - -116. The little problem, “Given _a_, _b_, _c_, to find _q_,” is solved, -without recourse to algebra, thus: _a_, _b_, _c_, = _c_, _a_, _b_; take -a cab and go over Kew Bridge, and you find a phonetic _Q_! - - -117. Tom Evergreen was 75 years old when he was asked his age by some -men at his club in 1875, and said--“The number of months that I have -lived are exactly half as many as the number which denotes the year in -which I was born.” - - -118. Eight different circles can be drawn. A circle can have one of the -three inside and two outside in three ways, or one outside and three -inside in three ways (each of the three being inside or outside in -turn), or all three may be inside, or all three may be outside, the -touching circle. - - -119. The way to arrange 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, so that used once -each they form a sum which is equal to 1 is this:-- - - 35 148 - -- + --- = 1. - 70 296 - - -120. The sum of the first fifty numbers may be found without any -addition thus:--The first fifty numbers form twenty-five pairs of -fifty-one each (1 + 50, 2 + 49, etc., etc.), and 51 × 25 is practically -51 × 100 ÷ 4 = 1275. - - -121. The tramcar _A_, which started at the same time as _B_, but ran -into a “lie by” in four minutes, and waited there five minutes till _B_ -came along, when they completed their courses at the same moment in -opposite directions, could have run the whole distance in ten minutes. - - -122. What remains will be 8 if we take 10 and double it by writing one -10 over another so as to form 18, and then deduct 10. - - -123. If the average weight of the Oxford crew is increased by 2℔s., when -one of them who weighs 12 stone, is replaced by a fresh man, the weight -of that substitute is 13 stone 2℔s. - - -124. If a motor-car is twice as old as its tyres were when it was old as -its tyres are, and if, when these tyres are as old as the car itself is -now, their united ages will be 2¹⁄₄ years, the car is now 12 months old, -and the tyres have had 9 months’ wear. - - -125. _A_ and _B_, who could each carry provisions for himself for twelve -days, started to penetrate as far as possible into a desert, on the -understanding that neither of them should miss a day’s food. After an -advance of four days, each had provisions still for eight days. One gave -four portions of his store to his companion, which did not overload him, -and returned with the other four. His comrade was then able to advance -another four days’ journey, and still have rations for the eight days’ -return. Thus the furthest possible penetration into the desert under the -conditions was an eight days’ march. - - -126. If, when a bottle of medicine and its cork cost half-a-crown, the -bottle and the medicine cost two and a penny more than the cork, the -cork cost twopence half-penny. - - -127. A boat’s crew far from land, with no sail or oars, and with no -assistance from wind or stream, or outside help of any kind, can regain -the shore by means of a coil of rope. Motion is given to the boat by -tying one end of the rope to the after thwart, and giving the other end -a series of violent jerks in a direction parallel to the keel. This -curious illustration of mechanical principles is from “Ball’s Mechanical -Recreations.” (_Macmillan._) - - -128. It will be found that after a crown and as many four-shilling -pieces as possible have been crammed into our pockets, there would still -be room for one sixpence and one threepenny-piece in some corner or -cranny. We can, therefore, have one crown, one sixpence, one -threepenny-piece, and as many four-shilling pieces as our pockets will -hold, and yet be unable to give change for a half-sovereign. - - -129. There were fifteen apples in the basket. Half of these and half an -apple, _i.e._, eight were first given, then half the remainder and half -an apple, _i.e._, four, then on similar lines two, leaving one in the -basket. - - -130. The Queer Division-- - - A third of twelve divide - By just a fifth of seven; - And you will soon decide - That this must give eleven-- - -is solved by LV ÷ V, or 55 ÷ 5 = 11. - - -131. A motor that goes 9 miles an hour uphill, 18 miles an hour -downhill, and 12 miles an hour on the level, will take 8 hours and 20 -minutes to run 50 miles out and return at once over the same course. - - -132. The number of shots fired at a mark was 420 each by _A_, _B_, and -_C_. _A_ made 280 hits, _B_ 315, and _C_ 336. - - -133. If a dog and a cat, evenly matched in speed, run a race out and -back over a course of 75 yards in all, and the dog always takes 5 feet -at a bound, and the cat 3 feet, the cat will win, because at the turning -point the dog overleaps the half distance more than the cat does, and so -has a longer run in. - - -134. When a man caught up a wagon going at 3 miles an hour, which was -just visible to him in a fog at a distance of 55 yards, and which he saw -for five minutes before reaching it, he was walking at the rate of 3³⁄₈ -miles an hour. - - -135. Three horses, _A B C_, can be placed after a race in thirteen -different ways, thus:--_A B C_, _A C B_, _B A C_, _B C A_, _C A B_, _C B -A_, or _A B C_ as a dead heat; or _A B_, _A C_, or _B C_ equal for the -first place; or _A_ first with _B C_ equal seconds; or _B_ first with _A -C_ equal seconds; or _C_ first with _A B_ equal seconds. - - -136. The 34 points scored against Oxbridge by the New Zealanders can be -made up in two ways, either by 8 tries and 2 converted tries, or by 3 -tries and 5 converted tries. - -The highest possible score on these lines is 10 tries converted, -equalling 50 points, and as the New Zealanders’ score, if all tries are -converted, becomes four-fifths of this, their actual score was 3 tries -and 5 converted into goals. - - -137. The smallest number, of which the alternate figures are cyphers, -which is divisible by 9 and by 11 is 909090909090909090909! - - -138. Our problem in which it is stated that _A_ with 8d. met _B_ and _C_ -with five and three loaves, and asked how the cash should be divided -between _B_ and _C_, if all agreed to share the loaves. Now each eats -two loaves and two-thirds of a loaf, and _B_ gives seven-thirds of a -loaf to _A_, while _C_ gives him one-third of a loaf. So _B_ receives -7d. and _C_ 1d. - - -139. When, on opening four money-boxes containing pennies only, it was -found that those in the first with half of all the rest, those in the -second with a third of the others, those in the third with a fourth, and -those in the fourth with a fifth of all the rest, amounted in each case -to 740, the four boxes held £6. 1s. 8d., and the numbers of pennies were -20, 380, 500, and 560. - - -140. If two steamers, _A_ and _B_, start together for a trip to a -distant buoy and back, and _A_ steams all the time at ten knots an hour, -while _B_ goes outward at eight knots and returns at twelve knots an -hour, _B_ will regain port later than _A_, because its loss on the -outward course will not have been recovered on the run home. - - -141. If in London a new head to a golf club costs four times as much as -a new leather face, while at St Andrews it costs five times as much, and -if the leather face costs twice as much in London as in St Andrews, and -if, including a shilling paid for a ball, the charges in London were -twice as much as they would have been at St Andrews, the London cost of -a new head is four shillings, and of a leather face a shilling. - - -142. When two children were asked to give the total number of sheep and -cattle in a pasture, from the number of each sort, and one by -subtraction answered 10, while the other arrived at 11,900 by -multiplication, the true numbers were 170 sheep, 70 cattle, 240 in all. - - -143. If a man picks up one by one fifty-two stones, placed at such -intervals on a straight road that the second is a yard from the first, -the third 3 yards from the second, and so on with intervals increasing -each time by 2 yards, and bring them all to a basket placed at the first -stone, he has to travel about 52 miles, or, to be quite exact, 51 miles, -1292 yards. - - -144. When, in the House of Commons, if the Ayes had been increased by 50 -from the Noes, the motion would have been carried by 5 to 3; and if the -Noes had taken 60 votes from the Ayes it would have been lost by 4 to 3, -the motion succeeded; 300 voted “Aye,” and 260 “No.” - - -145. There are 143 positions on the face of a watch in which the places -of the hour and minute-hands can be interchanged, and still indicate a -possible time. There would be 144 such positions but for the fact that -at twelve o’clock the hands occupy the same place. - - -146. If in a cricket match the scores in each successive innings are a -quarter less than in the preceding innings, and the side which goes in -first wins by 50 runs, the complete scores of the winners are 128 and -72, and of the losers 96 and 54. - - -147. When a ball is thrown vertically upwards, and caught five seconds -later, it has risen 100 feet. It takes the same time to rise as to fall, -and when a body falls from rest, it travels a number of feet represented -by sixteen times the square of the time in seconds. - -Hence comes the rule that the height in feet of a vertical throw is -found by squaring the time in seconds of its flight, and multiplying by -four. - - -148. The carpet which, had it been 5 feet broader and 4 feet longer, -would have contained 116 more feet, and if 4 feet broader and 5 longer -113 more, was 12 feet long and 9 feet broad. - - -149. When, in estimating the cost of a hundred similar articles, -shillings were read as pounds, and pence as shillings, and the estimated -cost was in consequence £212, 18s. 4d. in excess of the real cost, the -true cost of each article was 2s. 5d. - - -150. If the square of the number of my house is equal to the difference -of the squares of the numbers of my next door neighbours’ houses, and if -my brother in the next street can say the same of his house, though its -number is not the same as that of mine, our houses are numbered 8 and 4. -In my street the even numbers are all on one side, in my brother’s -street they, run odd and even consecutively, and so 8² = 10² - 6², and -4² = 5² - 3². - - -151. When two men of unequal strength have to move a block which weighs -270 ℔s., on a light plank 6 feet long, if the stronger man can carry 180 -℔s., the block must be placed 2 feet from him, so that he may have that -share of the load. - - -152. If a man who had twenty coins, some shillings, and the rest -half-crowns, were to change the half-crowns for sixpences, and the -shillings for pence, and then found that he had 156 coins, he must have -had eight shillings at first. - - -153. If, when coins are placed on a table at equal distances apart, so -as to form sides of an equilateral triangle, and when as many are taken -from the middle of each side as equal the square root of the number on -that side, and placed on the opposite corner, the number on each side is -then to the original number as five is to four, there are forty-five -coins in all. - - -154. When the gardener found that he would have 150 too few if he set -his posts a foot apart, and seventy to spare if he set them at every -yard, he had 180 posts. - - -155. In order to buy with £100 a hundred animals, cows at £5, sheep at -£1, and geese at 1s. each, the purchaser must secure nineteen cows, one -sheep, and eighty geese. - - -156. If John, who is 21, is twice as old as Mary was when he was as old -as Mary is, Mary’s age now is 15³⁄₄ years. - - -157. If in a cricket match _A_ makes 35 runs, and _C_ and _D_ make -respectively half and a third of _B_’s score, and if _B_ scores as many -less than _A_ as _C_ scores more than _D_, _B_ made 30, _C_ 15, and _D_ -10 runs. - - -158. The least number which, divided by 2, 3, 4, 5, 6, 7, 8, 9, or 10, -leaves remainders 1, 2, 3, 4, 5, 6, 7, 8, 9, is 2519, their least common -multiple less 1. - - -159. A square table standing on four legs, which are set at the middle -points of its sides, can at most uphold its own weight upon one of its -corners. - - -160. The division of ninety-nine pennies, so that share 1 exceeds share -2 by 3, is less than share 3 by 10, exceeds share 4 by 9, and is less -than share 5 by 16, is 17, 14, 27, 8, and 33. - - -161. If Indians carried off a third of a flock and a third of a sheep, -and others took a fourth of the remainder and a fourth of a sheep, and -others a fifth of the rest and three-fifths of a sheep, and there were -then 409 left, the full flock was 1025 sheep. - - -162. When a cistern which held fifty-three gallons was filled by three -boys, _A_ bringing a pint every three minutes, _B_ a quart every five -minutes, and _C_ a gallon every seven minutes, it took 230 minutes to -fill it, and _B_ poured in the final quart, _A_ and _C_ _coming up one -minute too late_ to contribute at the last. - - -163. A man who said, late in the last century, that his age then was the -square root of the year in which he was born, was speaking in the year -1892. - - -164. If when a dealer in curios sold a vase for £119, his profit per -cent., and the cost price of the vase, were expressed by the same -number, it had cost him £70. - - -165. The chance of throwing at least one ace in a single throw with a -pair of dice is ¹¹⁄₃₆, for there are five ways in which each dice can be -thrown so as not to give an ace, so that twenty-five possible throws -exclude aces. Hence the chance of _not_ throwing an ace is ²⁵⁄₃₆, which -leaves ¹¹⁄₃₆ in favour of it. - - -166. The policeman who ran after a thief starting four minutes later, -and running one-third faster, if they both ran straight along the road, -caught him in twelve minutes. - - -167. At a bazaar stall, where twenty-seven articles are exposed for -sale, a purchaser may buy one thing or more, and the number of choices -open to him is one less than the continued product of twenty-seven twos, -or 134217727. - - -VERY PERSONAL - -168. When Nellie’s father said:-- - - I was twice as old as you are - The day that you were born. - You will be just what I was then - When fourteen years are gone-- - -he was 42, and she was 14. - - -WORD AND LETTER PUZZLES - - -1. The word square is completed thus:-- - - MEAD - EDGE - AGUE - DEED - - -2. The word square filled in is:-- - - CIRCLE - INURES - RUDEST - CREASE - LESSEE - ESTEEM - -_Notice the curious diagonal of E’s._ - - -3. In the incomplete sentence, - - SO****AG****LATI****X****ITH - -the duplicate letters are filled in thus:-- - - SOME MEAGRE RELATIVE VEXED EDITH - -The two last letters of each word are repeated as the two first of the -word that follows. - - -4. The word square is completed thus:-- - - WASTE - ACTOR - STONE - TONIC - ERECT - - -5. By twice building up two Ds into a B we make BULBOUS. - - -6. The question put on paper to the love-lorn youth, “Loruve?” is, when -interpreted, “Are you in love?” and the advice given to him on another -slip, “Prove - - L - A F - D - -and ensure success,” reads into, “Prove a fond lover, and ensure -success” (a f _on_ d l _over_). - - -7. DOUBLE ACROSTIC ST. JAMES’ GAZETTE - - S . . . prin . . . G - T . . . ar . . . A - J . . . abe . . . Z - A . . . t . . . E - M . . . omen . . . T - E . . . mme . . . T - S . . . trik . . . E - - -8. The completed word square is-- - - AMENDS - MINION - ENABLE - NIBBLE - DOLLAR - SNEERS - - -9. The oracular response to a young Frenchman at a _fête_, who inquired -how he could best please the ladies-- - - MEC DO BIC - -conceals this sage advice-- - - Aimez, cédez, obéissez! - Love, yield, obey! - - -10. The solution to our Letter Fraction Problem is of a verbal -character. The original statement -15844 - - m - -- - ot = mo - -- - y - -is dealt with thus:-- - -m _on_ ot _on_ y = mo _not on_ y, and so the word monotony solves the -equation. - - -11. The buried beasts are _chamois_, _buffalo_, _heifer_, and _leopard_; -and when the Oxford athlete cries-- - - “Though I jump and row and run, - Cap or cup I never won” - -he introduces us to a _porcupine_. - - -12. The lines-- - - Fourteen letters here we fix, - Vowels only two are spoken; - All together these we mix - Into what can not be broken-- - -is solved by _indivisibility_, which has many an _i_, like a peacock’s -tail. - - -13. The English word of thirteen letters in which the same vowel occurs -four times, the same consonant six times, another twice, and another -once, is _Senselessness_. - - -14. The condensed proverb “WE IS DO” reads at its full length as “Well -begun is half done.” - - -15. This is the completed word square:-- - - WASHES - ARTERY - STORMS - HERMIT - ERMINE - SYSTEM - - -16. Dr Whewell’s puzzle lines-- - - O O N O O. - ---------- - U O A O O I O U, - O N O O O O M E T O O. - U O A O I D O S O - I O N O O I O U T O O! - -read thus:-- - - OH SIGH FOR NO CIPHER - - You sigh for a cipher, O, I sigh for you, - Sigh for no cipher, O sigh for me too. - You sigh for a cipher, I decipher so, - I sigh for no cipher, I sigh for you too! - - -17. This is the completed diamond:-- - - P - POR - CORES - FORCEPS - PORCELAIN - REFLECT - SPACE - SIT - N - - -18. The medley-- - - Tan HE Edsa VEN in - It N Gja SmeTs AsgN - aD Az Rett De - -is read by taking first the capitals in their order, and then the small -type. It comes put out as “The Evening Standard and Saint James’s -Gazette.” - - -19. The statement, I can travel first-class on the G.E.R. from -2222222244444500, reads into--from 22 to 2 to 22 to 4 for 44 4d; or, in -plain terms, from 1.38 to 3.38 for 14s. 8d. This works out at about 3d. -a mile, the usual allowance for first-class, for two hours, at about 29 -miles an hour. - - -20. A CURIOUS OLD INSCRIPTION - -Read the inscription backwards, and it resolves itself into the lines -familiar to us in our childhood:-- - - Ride a cock horse to Banbury Cross - To see a fine lady ride on a grey horse. - Rings on her fingers and bells on her toes, - She shall have music wherever she goes! - - -21. The reason why the invitation to Jack to sample the Irish stew at -Simpson’s was to be kept in mind by the catch words-- - - Join me at and - i - s, - -is because if you join _me_ and _at_, and note that _and_ is _on i_, -which is _on s_, you arrive at the suggestive sentence--_meat and -onions_. - - -22. The labourer’s quaint letter, which ran “Cepatomtogoatatrin,” was, -in plainer English, “Kept at home to go a tatering.” - - -23. Our double acrostic comes out thus:-- - - PROBLEM--PUZZLES - - P ........a....... P - (T) R ................ U (E) - O ................ Z - B ........o....... Z - L .......eve...... L - E ........v....... E - M ................ S - - -24. The Hidden Proverb is-- - - “Necessity is the mother of invention.” - - -25. The “deed done” in our Will puzzle is the making in Roman numerals -of “Codicil.” The lawyer was to set down, a hundred, to add nothing, to -set down five hundred, then one, then another hundred, and then one -more, and, finally, fifty, and accordingly he wrote upon the parchment -the one word CODICIL. - - -26. The word square is-- - - EDITOR - DESIRE - ISLAND - TIARAS - ORNATE - REDSEA - - -27. The notes of music A. G. A. E. A. over the grave of a French -musician, who was choked by a fish bone, are in the French notation, “La -sol la mi la,” which reads into “La sole l’a mis 1à.” - -Similarly the inscription over the porch of Gustave Doré’s house C. E. -B. A. C. D. is equivalent to “Do, mi, si, la, do, re,” which may be -taken to represent “Domicile à Doré.” - - -28. When his best girl said to Jack Spooner, “We can go to-morrow at -222222222222 LEY STREET,” he understood her to mean, “We can go -to-morrow, at two minutes to two, to two twenty-two, to 222 Tooley -Street.” - - -29 - - C - ---------- spells _contents_ (c on ten ts!). - TTTTTTTTTT - - -30. We can treat the word _disused_ so as to affirm or to disallow the -use of its initial or final d, for we can write it _d is used_, or -_disuse d_! - - -31. The title of the book shaken up into - - EIOOOU - BCNNRRSS - -is “Robinson Crusoe.” - - -32. If the letter M only is inserted in the proper places in the line-- - - A DEN I I CAN DOCK - -it will read: _Madmen mimic and mock_. - - -33. The quotation from Shakespeare-- - - OXXU8 MAAULGIHCTE - NOR - -is by interpretation:--“Nothing extenuate, nor set down aught in -malice.” - - -34. The phonetic nightmare-- - - Ieukngheaurrhphthewempeighghteaps-- - -is merely the word _unfortunates_. It can be justified thus by English -spelling of similar sound taken letter by letter:-- - -u--iew in view; n--kn in know; f--gh in tough; o--eau in beau; r--rrh in -myrrh; t--phth in phthisis; u--ewe; n--mp in comptroller; a--eigh in -neigh; t--ght in light; e--ea in tea; and s--ps in psalm. - - -35. The word square is completed thus:-- - - FARM - AREA - RENT - MATE - - -36. A QUAINT INSCRIPTION - - The millers leave the mill, - The wherrymen lower their sail; - The maltsters leave the kiln, - For a drop of the White Swan’s ale. - - -37. A POET’S PI - - TONDEBNIOTOCHUMFOARYHUR - OTDIRECTTHAWHOTERSOFKLSYA; - TIKATESTUBALIGHTSTILLETRUFLYR - OTBOWLALLNFESLEAVARFWYAA - -is disentangled thus:-- - - Don’t be in too much of a hurry - To credit what other folks say; - It takes but a slight little flurry - To blow fallen leaves far away. - - -38. BURIED PLACES - -The five buried places are Deal, London, Esk, Perth, and Baden. The word -is Ourangoutang. - - -39. It is no offence to conspire in the evening, because what is -treasonable is _reasonable after t_! - - -40. The bit of botany-- - - Inscribe an _m_ above a line, - And write an _e_ below, - This woodland flower is hung so fine - It bends when zephyrs blow-- - -is solved by, - - m - -, - e - -_an em on e_, the delicately hung wind-flower. - - -41. A PIED PROVERB - -The pied proverb, is “A rolling stone gathers no moss.” - - -42. The Drop Letter Proverb-- - -E..t. .e.s..s .a.e .h. .o.. ..i.e, is--_Empty vessels make the most -noise_. - - -43. The English word of five syllables, which has eight letters, five of -them vowels--namely an a, an e, twice i, and y--is _Ideality_. - - -44. TORMENT may be turned into RAPTURE, using four links, changing only -one letter each time, and varying the order of the letters, thus: -TORMENT, _portent_, _protest_, _pratest_, _praters_, RAPTURE. - - -45. The pied sentence-- - - a a c e e e f f h h i i i i i m n n o o o p r r s s t t t t t - -can be cast into the proverb-- - -“Procrastination is the thief of time.” - - -46. The English sentence, when the letter _o_ is added, reads:-- - - “Good old port for orthodox Oxford dons.” - - -47 - - One vowel in an English word is found, - Which by eight consonants is hedged around-- - -is solved by _Strengths_. - - -48. The letters AAAAABBNNIIRSSTT form the word _Antisabbatarians_. - - -49. The quotation from Shakespeare, - - KINI - -stands for “A little more than kin, and less than kind.” - - -50. The two English words which have the first six letters of the -alphabet among their ten letters are _fabricated_ and _bifurcated_. - - -51. SHIFTING NUMBERS - -The letter _A_ stands at the head of the letters of the alphabet. For -_bed_ 3 of these are used; for _goal_, 4; for _prison_, 6; for _six_, 3; -for _three_, 5. The letter _A_ is not used in the spelling of the name -of any number from 1 to 100, but it makes up, with the other vowels, the -number 6. - - -52. The prodigal’s letter to his father, “Dear Dad, keep 1000050,” in -reply to a suggestion for safeguarding some of his prospects, was -written in playful impudence; and its interpretation is, “Dear Dad, keep -cool!” for the figures in Roman numerals are COOL. - - -53. BURIED POETS - -The poets’ names buried in the lines-- - - The sun is darting rays of gold - Upon the moor, enchanting spot; - Whose purpled heights, by Ronald loved, - Up open to his Shepherd cot. - - And sundry denizens of air - Are flying, aye, each to his nest; - And eager make at such an hour - All haste to reach the mansions blest. - -are Gray, Moore, Byron, Pope, Dryden, Gay, Keats, and Hemans. - - -54. When _A. B._ gave up the reins of government, and _C.B._ took office -in his place, the two verbs, similar in all respects, except that the -one is longer by one letter than the other, which expressed the change, -were _resigns_--_reigns_. - - -55 - - Underdone mutton and onion make between you and me, - A glutton a little seedy after a capital tea. - - -56 - - First a _c_ and _a t_, last _a c_ and a _t_, - With a couple of letters between, - Form a sight that our eyes are delighted to see, - Unless in their sight it is seen-- - -is solved by _Cataract_. The first line reads, First a _c_ and _a t_, -last _a c_ and a _t_, that is _cat_ and _act_. - - -57. Cuba. - - -58. The Rebus T S is solved by the words _tones_ and _tans_, _t_ before -_one s_, or _t_ before _an s_. - - -59. The phonetic phrase-- - - INXINXIN-- - -is, _Ink sinks in_! - - - A GOOD END - - -60. Finis (F IN IS). - - - - -=PART III.= - - -CONTENTS - - PAGE - - WORD PUZZLES, MISSING WORDS, LETTER PUZZLES III-1 - - ANAGRAMS, PICTURE PUZZLES III-48 - - PALINDROMES III-108 - - SOLUTIONS III-111 - - -WORD PUZZLES - - -No. I--AN EARLY CRYPTOGRAM - -The use of some sort of grille was not uncommon in olden days among the -many methods then employed for secret correspondence. Here is an early -and interesting specimen:-- - -[Illustration: VENITE PAUPERES] - -An important despatch would appear to be a mere confusion of letters, -until it fell into the right hands, and this perforated key was laid -over it, when the intended instructions were at once revealed, and read -in the openings of the tracery. - - -No. II.--A MANIFOLD MONOGRAM - -Here, by seven straight lines and one circle, a manifold monogram is -formed. - -[Illustration] - -Within its borders we find a circle, a square, a parallelogram, a -triangle, the vowels a, e, i, o, u; the consonants, C, D, H, K, L, M, T, -W; and other forms and figures. - - -MISSING WORDS - - -1. PICKING AND STEALING - - What tempting ...... beguiled the boy to sample - Fruit that hung ...... on the parson’s trees? - ...... upon ...... shall make him an example - When the stern ...... has brought him to his knees. - -The missing words are spelt with the same six letters. - - -No. III.--A BOOK AND ITS AUTHOR - -What well-known book and its author may be represented thus:-- - -[Illustration] - - -2. A SWARM OF MISSING WORDS - -No less than eight different words, spelt with the same six letters, are -available to fill the gaps in the following lines:-- - - Man of the dark room, ...... none I find - Upon these ...... of likeness to my features. - ...... then nought, O man of evil mind, - Who ...... thus to libel fellow-creatures? - - Evil thus done ...... upon the doer, - The ...... in thy conduct, Sir, are many; - ...... thy life, and let thy crimes be fewer, - Or all thy ...... of good won’t fetch a penny! - - -No. IV.--ON THE SHUTTERS - -Upon the shutters of a barber’s shop the following legend was painted in -bold letters:-- - - NO. I - JOHN MARSHALL - IN ATTENDANCE - FROM 8 A.M. DAILY - BARBER AND - HAIR CUTTER - THE BALD CRY ALOUD - FOR HIS CREAMS - AS DISPLAYED IN THIS WINDOW - WHICH MAKE HAIR GLISTEN - CLOSES AFTER 8 P.M. - -One evening about 8.30, when it was blowing great guns, quite a crowd -gathered round the window, and seemed to be enjoying some excellent -joke. What was amusing them when one shutter blew open? - - -3. NO HEART! - - False Kate! ... .... . ......’s nest, - .. ..... the Upas tree, - I will not budge, ... .... to rest, - .. .... . coward be. - - No, not .... ... enough their sting - To drive me back to thee; - None swifter meet thy beckoning - .... ... the hills I flee. - - ... .... frosts less my love would quell. - Rather than seek thy side, - Of ... .... horse I love so well - I’ll ... .... hoofs and hide! - -The number of letters in each word of the missing phrases is indicated -by dots, and the seven letters in each case are those that spell also -“no heart,” which we give as a title and clue. - - -No. V.--A PHONETIC MAXIMUM - -How far phonetic spelling may be pushed, is illustrated by the following -swarm of variations given in a book published at Enfield in 1829:-- - - Scissars -- ers -- irs -- ors -- urs -- yrs - Scisars -- „ -- „ -- „ -- „ -- „ - Sciszars -- „ -- „ -- „ -- „ -- „ - Scizars -- „ -- „ -- „ -- „ -- „ - Scizscars -- „ -- „ -- „ -- „ -- „ - Scizzars -- „ -- „ -- „ -- „ -- „ - -Or the word may start with Sis, Siss, Siz, Sys, Syss, Syzz, Syzs, Syz, -Cis, Ciss, Ciz, Cisz, Cysz, Cyz, Cyzz. By substituting “z” for the final -“s” we may double the number, and reach a total of 1224. - - -4. UNNATURAL HISTORY - - ’Neath ...... Indian seas fierce battles spread - ’Twixt ...... hermit-crabs and other shellfish! - With horrid ...... when their foes are dead, - These crabs declare their shells ......, so selfish! - -Each missing word has the same six letters. - - -No. VI.--SOLVITUR AMBULANDO - -On this chequered floor, paved with slabs each a foot square, the -palindrome word ROTATOR can be traced in various ways. - - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - |=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=| - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O |=R=| O | T | A | T | O | T | A | T | O |=R=| O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | O |=R=| O | T | A | T | A | T | O |=R=| O | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | A | T | O |=R=| O | T | A | T | O |=R=| O | T | A | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | A | T | O |=R=| O | T | O |=R=| O | T | A | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O | T | A | T | O |=R=| O |=R=| O | T | A | T | O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - |=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=| - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O | T | A | T | O |=R=| O |=R=| O | T | A | T | O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | A | T | O |=R=| O | T | O |=R=| O | T | A | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | A | T | O |=R=| O | T | A | T | O |=R=| O | T | A | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | O |=R=| O | T | A | T | A | T | O |=R=| O | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O |=R=| O | T | A | T | O | T | A | T | O |=R=| O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - |=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=| - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - -If a man walks over it, taking one slab at every step, and never -lengthening his strides, how many steps will he take in tracing every -possible variation of the word, and how many such variations are there? - - -No. VII.--A CURIOUS CHRONOGRAPH - -A bachelor clergyman, whose initials were I.E.V., had built a fernery -with the profits of his tracts on the deceased wife’s sister question. -He dated it on a mural tablet thus:-- - - | | - -+------------------------------------+- - |My LateVVIfe’ssIsterbVILtthIs VVaLL;| - | bVt I In trVth | - | neVer VVeD any VVIfe at aLL, | - | nor VVont forsooth, | - | saIth I. e. V. | - -+------------------------------------+- - | | - -If the Roman numerals are extracted from this inscription, and added -together, they amount to 1884, the desired date. - - -5 - - Though ------ secure and ------ in his cage, - Our Polly, when ------, will fly into a rage. - -Each missing word has the same six letters. - - -6 - - All courtly honours are but light - As grains that from a ------ fly; - And he who wears the ------ bright - May haply in a ------ die. - -The missing words are spelt with the same six letters. - - -7 - - I’d rather from a ------ eat, - I give my sacred word, - Than dine in slums where ------ meet, - And ------ pedlars herd. - -Each missing word has the same six letters. - - -No. VIII.--AN OLD SAMPLER - -In the drawer of a cabinet that had belonged to my grandmother I came -upon an old sampler, beautifully worked in scarlet cross-stitch. Its -very curious legend runs as follows:-- - - | | - -+-----------------------------+- - | AL. IT. | - |T.L EW. O. MA! | - |N.T. Ho! UGH. AVE. Ryli. | - |T.T. Let. Hi! N.G.I. | - |S.S. We. Et. Erf. Art. Ha!| - |N.S. Ug. Ara. N.D.F. Lo! | - |W.E. R.S.T. Ha! TB. | - |L.O. O! Mins. Pri. | - | N. G. | - -+-----------------------------+- - | | - - -8 - - A much married ....... of Cadiz - Once ....... some riotous ladies. - To ....... him they chucked - A ......., but he ducked, - Which ....... these rude ladies of Cadiz. - -The five missing words are spelt with the same seven letters. - - -9. THE LASS AND HER LOVER - - A lass and her lover were ------ by the sky - Not to ------ too far where no shelter was nigh. - She lingered behind, and ----- -- old church, - St. ------ by name, and was left in the lurch. - She tried a short cut through a park on the grass, - But sternly the ------- forbade her to pass; - Then helplessly stood the disconsolate maid, - When the lad she was soon to --- --- to her aid. - -The missing words are spelt with the same six letters. - - -No. IX.--THE LANDLORD’S PUZZLE - -The following curious Missing Words Puzzle is to be seen on a card which -hangs in the bar of an inn in the Isle of Man:-- - - I had both-- |by both I set great store |and a-- - I lent my-- |and took his word therefor;|to my-- - I asked my-- |and nought but words I got.|from my-- - I lost my-- |for sue him I would not. |and my-- - - At length with--|which pleased me very well,|came my-- - I had my-- |away quite from me fell: |but my-- - If I’d both-- |as I have had before, |and a-- - I’d keep my-- |and play the fool no more. |and my-- - -It is to be read thus:-- - - I had both _money_ and a _friend_, by both I set great store, - I lent my _money_ to my _friend_, and took his word therefor, - -_and so on to the end_. - - -10 - - When ------- smiles, and sunbeams play - On flowers that ------- and deck the green, - ------- can match the scene so gay - ------ they crown the May-day queen? - -The missing words are spelt with the same seven letters. - - -11 - - ’Tis said of William, while his forces rested - On Albion’s ------, when Harold had been bested, - He made the ------ of his ------ fuse - Saxon spear-heads, to fashion into shoes. - -Each missing word has the same six letters. - - -No. X.--DECAPITATED WORDS - -The decapitated words are in italics:-- - - The ship rode in an _eastern_ bay, - Asleep _astern_ the master lay, - A _stern_ and rugged man was he, - And, like a _tern_, at home at sea. - Like swooping _ern_ he caught his prey - Whene’er an _R.N._ came his way; - But while due _N._ the needle kept - He in his cabin lay and slept. - -The ern, or erne, is the sea-eagle. - - -12 - - Happiness, brighter than ------, is dead; - Life’s battle, sterner and ------ now, - Heals the sore ------ that love left as it fled, - ------ remembrance of long broken vow! - -The missing words are spelt with the same six letters. - - -13. AN AUTHOR’S EPIGRAM - - Press critics fall on me like sharks; - “A shameless ....... of odds and ends, - No ....... original,” and more remarks - In adverse mood. But stay, my friends, - He ....... best who hath his record clean; - My faults are published, yours are yet unseen! - -The missing words have the same seven letters. - - -14 - - ...... are his ......, fashion-forms of grace - In ...... deftly hinted. - ...... soft as ......, crowned by Beauty’s face, - In ...... hues are tinted. - -The six missing words are spelt with the same six letters. - - -No. XI.--AN ANCIENT ANAGRAM - -On the front of a church, in the Largo Remedios, at Braga, in Portugal, -there is an inscription which, with its letter-perfect Anagram, runs as -follows:-- - - | | - -+----------------------------+- - | BEATUS IOANNES MARCUS | - | CHRISTI DOMINI DISCIPULUS | - | ---- | - | ANAGRAM | - | -------------- | - |IS IN MUNDO PIUS EST MEDICUS| - | TUIS INCOLIS, BRACHARA | - | -----*----- | - -+----------------------------+- - | | - -which may be rendered--“Blessed John Mark, disciple of Christ the Lord.” -_He in this world is the holy healer of thy people Braga!_ - - -15 - - When Kate --- -------- ----- -------- displayed - ----- ----- --- hide a tear; - “All love is dead --- --------,” he said. - “------- I’ll ----- --------!” - -The missing word and groups of words are spelt with the same seven -letters. - - -16 - - Some grinding at the ------ must toil, - Down-trodden ------ of to-day; - While other children of the soil - In vast ------ their wealth display. - -The missing words are spelt with the same six letters. - - -No. XII.--STRIKE A BALANCE - -This diagram shows that the odd numbers of the 9 digits add up to 25, -and the even numbers to 20. - - +----------------------+ - /| |\ - +-+----------------------+-+ - | | 1 | | - | | 3 2 | | - | | 5 4 | | - | | 7 6 | | - | | 9 8 | | - | | -- -- | | - | | 25 20 | | - | | ======== | | - +-+----------------------+-+ - \| |/ - +----------------------+ - -Can you arrange the 9 digits in two groups in which the odd numbers and -the even will add up to exactly the same sum? - - -17 - - Betrayed by faithless friends, in ------ mood - Man ------ his fellows as the ------ brood. - -The missing words are spelt with the same six letters. - - -18. HONEST INDIAN - - With divers ---- his ---- is scarred, - He hangs a bangle in his nose; - Such marks secure his ---- regard, - Exalt his fame, and ---- his foes. - -Each missing word is spelt with the same four letters. - - -No. XIII.--HKISTA! - - MRS LR’S SR - MR LR KRS. - “BLR MR LR!” - MRS LR HRS. - -How do you read these lines and their title? - - -19. ON THE OCEAN WAVE - - ------- who, as we ------- roll, - ------- for me the foaming bowl, - And ------- off unfriendly spray - With oilskin cape, thou shalt not say - “In vain I’ve ------- my favours here.” - I’ll think of thee when port is near! - -The four missing words are spelt with the same seven letters. - - -20. THE ZENANA MISSION - - With high ------ for hearts and hands, - These ------ ------ for distant lands. - -The three missing words are spelt with the same six letters. - - -21 - - The ------- of his speech did not - ------- his audience a jot. - They greeted all he said thereafter - With -------, smiles, and open laughter. - -The missing words have the same seven letters. - - -22 - - To convent shrine at break of day - With ----- together nuns repair; - Mid gleaming ----- they kneel and pray, - And chanted ----- allays each care. - -Spelt with the same five letters. - - -No. XIV.--IN MEMORIAM - -The following puzzle-epitaph was engraved on a tombstone in Durham -Cathedral:-- - - | | - -+-------------------------+- - |WEON . CEW . ERET . WO| - |WET . WOM . ADEO . NE| - |NON . EFIN . DUST . WO| - |NO . WLI . FEB . EGO . NE| - | WILLIAM and MARGARET | - | TAYLOR | - | Anno Domini 1665. | - -+-------------------------+- - | | - - -23 - - Here once, as a hag is bedizened with paint, - A ----- ----- ----’- in the garb of a saint. - -The three missing words are spelt with the same five letters. - - -24. IN PRAISE OF SUSSEX - - Sussex! No ----- of a bygone age - Ride through thy ----- to-day with shield and -----, - And ----- no horseflesh so they may engage - To save some damozel from harm or fear. - - Who now would give a thought to ----- or peaches? - He truly farms who ----- a golden store; - And, though he cannot ----- the simplest speeches, - ----- down expense, and savings has galore! - -Each missing word is spelt with the same five letters. - - -No. XV.--A FRENCH WORD SQUARE - -Here is an excellent French Word Square of seven letters:-- - - +-+-+-+-+-+-+-+ - |R|E|N|E|G|A|T| - +-+-+-+-+-+-+-+ - |E|T|A|L|A|G|E| - +-+-+-+-+-+-+-+ - |N|A|V|I|R|E|S| - +-+-+-+-+-+-+-+ - |E|L|I|D|A|N|T| - +-+-+-+-+-+-+-+ - |G|A|R|A|N|C|E| - +-+-+-+-+-+-+-+ - |A|G|E|N|C|E|R| - +-+-+-+-+-+-+-+ - |T|E|S|T|E|R|A| - +-+-+-+-+-+-+-+ - -This is a worthy companion to the English seven-letter squares on -“Problem” and “Palated,” which are given on other pages. - - -25 - - ----- in the ----- far away, - Remote alike from heaven and hell, - The silent -----, so poets say, - Who shape the ends of mortals dwell. - -Each missing word has the same five letters. - - -26 - - In all our ------ the mechanician’s skill - Now compasses the rogue with artful wile. - The patent ------ and the “tell tale” till - Beset his way who ------ the path of guile, - Besotted youth, who ------ to defy - The rule of right, beware his awful fate - Who, sitting down to eat a stolen pie, - ------ the eighth commandment on the plate! - -Spelt with the same six letters. - - -No. XVI.--A QUAINT EPITAPH - -This epitaph, most of it in some sort of dog Latin, tells its own -pathetic tale on its tablet. - - | | - -+------------------------------+- - |IT - OBIT - MORTI - MERA | - |PUBLI - CANO - FACTO - NAM | - |AT - RES - T - M - ANNO - XXX | - |ALETHA - TE - VERITAS | - |TE - DE - QUA - LV - VASTO | - |MI - NE - A - JOVI - ALTO | - |PERAGO - O - DO - NE - AT | - |STO - UT - IN - A - POTOR - AC| - |AN - IV - VAS - NE - VER - A | - | =R - I - P= | - -+------------------------------+- - | | - - -27 - - The .... with .... importunate - To rule his .... may try; - His .... is so unfortunate - That .... they may reply! - -The missing words are spelt with the same four letters. - - -28. “TURN AGAIN WHITTINGTON!” - - In all the pomp of ---- and chains - He lords it o’er the town; - The ---- of his hopes he gains - Who ---- with half-a-crown. - -Each missing word has the same four letters. - - -No. XVII.--A TRAGIC CALENDAR - - | | - -+--------------------------------------+- - |Jan-et was quite ill one day; | - |Feb-rile troubles came her way. | - |Mar-tyr like, she lay in bed, | - |Apr-oned nurses softly sped. | - |May-be, said the leech judicial, | - |Jun-ket would be beneficial. | - |Jul-eps, too, though freely tried, | - |Aug-ured ill, for Janet died. | - |Sep-ulchre was sadly made, | - |Oct-aves pealed and prayers were said.| - |Nov-ices with many a tear | - |Dec-orated Janet’s bier. | - -+--------------------------------------+- - | | - - -29. A SAUCY JADE - - A writer quite devoid of tact, - She valued ------ more than fact. - A wayward ------ she made her muse - On ------ and noble heaped abuse. - Dealt ----- on ------ to prince or peer, - Her ----- wit a paltry jeer. - -Each missing word is spelt with the same six letters. - - -30. MISSING WORDS - - Of all destructive country pests - The farmer ..... ..... least; - He cannot yet the puzzle ..... - How to suppress the beast! - -The missing words have the same five letters. - - -No. XVIII.--A DIAMOND PALINDROME - -Within the four corners of this Mystic Diamond the Palindrome, NAME NO -ONE MAN, can be traced in 16,376 different directions, in straight -lines, or at right angles, starting from the centre or from the borders. - - N - NaN - NamaN - NamemaN - NamenemaN - NamenonemaN - NamenooonemaN - NamenoonoonemaN - NamenoonenoonemaN - NamenoonemenoonemaN - NamenoonemamenoonemaN - NamenoonemaNamenoonemaN - NamenoonemamenoonemaN - NamenoonemenoonemaN - NamenoonenoonemaN - NamenoonoonemaN - NamenooonemaN - NamenonemaN - NamenemaN - NamemaN - NamaN - NaN - N - - - 31. TO THE FRESH AIR FUND - OH THE ------ OF THE ------. - - The ------ of darkest London are radiant with ------, - You can ----- it in their ----- little faces. - So wherever you ------ let it be your heart’s ------ - To ease the ----- and sorrows of all -----. - -The missing words in the title and those in the first and third lines -each contain six letters. Those in the second four, and in the fourth -five. - - -No. XIX.--SHAKESPEARE RECAST - -If you start with the right letter in this combination, and then take -every third letter, a well-known quotation from Shakespeare will be -formed. - - +----------------------+ - |HOUSE.CANOE.AFTER. | - |HOUR.PRINT.CAVE.CHILD | - |SASH.SLEVE.ACORN. | - |AMPLE.SAD.TATTA.HENA | - |MAT.ACHE.CAKE.TACHES. | - |HELIAC.SACQUE.USUAL. | - |ARBOR.SEE.MULCH.JACUR.| - |USE.STOP. | - +----------------------+ - - -32. THE FLIRT THAT FAILED - - She ...... in vain, “Men are ......, and as shy - As ...... in October,” she says with a sigh. - -The missing words are spelt with the same six letters. - - -33 - - When good men lapse the ....... grins, - When one ....... he swears, - And strives to set his former sins - Against his ....... prayers. - -Each missing word is spelt with the same seven letters. - - -No. XX.--A DOUBLE ACROSTIC - - An old Italian bird we know - Whose heart is ever touched by snow. - - 1. None can press me without pain - Pressure is against the grain. - 2. I am a king without my head. - 3. Here is another king instead. - -It is fair to our readers to say that some knowledge of Latin and French -is needed for dealing with this very excellent Acrostic, of which a full -explanation is given with the solution. - - -34. THE GIPSY LAD - - His hands and face were -----, and sad - Upon the ----- a gipsy lad - Lay; as the breeze his temples fanned - He counted ----- on either hand. - -Each missing word has the same five letters. - - -35. THE OLD DIVINE - - In yon grey ----- an old divine - Taught me my ----- to decline, - And verbs with ----- of mood and tense; - But while I plodded on apace - I had to keep the ----- of grace, - And close his prayers with loud -----. - -Each missing word is spelt with the same five letters. - - -36. BANZAI! - - No reckless ------ of the sword, - He ------ his fatherland to save. - Fighting for freedom, not ------, - Now ------ of the eastern seas. - -The four missing words contain six letters. - - -No. XXI.--HIDDEN PROVERBS - -Five familiar proverbs are hidden in this square of 169 letters. - - R E N O W N E D T H A N W - S Y O U R C A K E A N D A - S T E T O B E F E A R H R - E A R K S S P O I L E A F - L E O O H E R S N T D V O - O T M O T L I N O H T E U - N O S C A L A G M E H I R - S N I Y G O R S O B A T S - E N G N E N O T S R N P A - I A O A M O O T S O A E W - R C D E V I L A H T D A S - O U O Y N O I L D A E C A - T C I V R E H H T A H E Z - -The proverbs are arranged in a regular sequence. - - -37. OF DOUBTFUL WORTH - - A fair ------, though ------ and frayed, - The critic ------ to own, - And it might interest the trade - If ------ by some one known. - -The missing words are spelt with the same six letters. - - -38 - - In his ------ days, as when he was young, - The ------ indulges in ------ of tongue. - -Each missing word is spelt with the same six letters. - - -No. XXII.--AN ALPHABETICAL TOAST - -Lord Duff, who evidently had a turn for puzzles, proposed this -alphabetical toast, which became popular among the Jacobites. - - A.B.C. A blessed change. - D.E.F. Down every foreigner. - G.H.J. God help James. - K.L.M. Keep Lord Mar. - N.O.P. Noble Ormond preserve. - Q.R.S. Quickly resolve Stuart. - T.U.V.W. Truss up vile Whigs. - X.Y.Z. Exert your zeal. - -Another quaint and ingenious use of separate letters is recorded of the -well-known preacher, Henry Ward Beecher. - -Years ago, before his reputation had become world-wide, he was asked to -give a lecture without charge, and assured that it would increase his -fame. His reply was characteristic and very much to the point: “I will -lecture for F.A.M.E.--fifty and my expenses!” - - -39. MISSING WORDS - - (1) A cylindrical lock - Where no key can be found, - (2) An instrument treble - And ringing in sound. - (3) In story-land ranging, - (4) Now chopping and changing; - (5) Broken up, reunited, - Quite whole I am found. - -Words, spelt with the same eight letters are indicated in these lines. -There are two words in (1). - - -No. XXIII.--A MORAL PRECEPT - -The following obscure legend was worked on an old sampler, in the red -cross-stitch that found favour when our grandmothers were girls:-- - - +----------------+ - | Elizabeth out | - |Rue Constantine | - |Very thin gloves| - | Way Susan dart.| - +----------------+ - -This was evidently some excellent moral precept, but it hung on its -frame, a mere puzzle on the school-room wall, until an expert word -juggler came that way, and solved the mystery by reading it off thus:-- - -“Eliza be thou true, constant in everything. Love sways us, and art.” - - -40 - -In the following lines the first missing word has two letters, and the -letters are carried on, with one more added each time, and in varied -order, throughout the verses, either in single words or in groups of -words:-- - - A lover of .. unkind fair - Were less than ... did he not .... - “Mine is no ..... life, I swear, - It dwells in this ...... alone. - Grant me thy love, like ....... chaste - .. ...... lest thou live unwooed, - ..... .. . lowly life to waste - The treasures of sweet ..........” - - -No. XXIV.--SHAKESPEARE’S MANTLE - -Ingenious cryptic efforts have been made to prove that Bacon was the -author of Shakespeare’s plays, but it has been reserved for us to -reveal, by a convincing cryptogram, the modern wearer of his mantle. - -The secret is disclosed by a line of capital letters shown below:-- - - Mac B eth. - Oth E llo. - Comedy of Er R ors. - Merchant of Ve N ice. - Coriol A nus. - Midsummer Night’s D R eam. - Merry Wives of Win D sor. - - Measure for Mea S ure. - Much Ado about Not H ing. - Antony and Cleop A tra. - All’s Well that ends W ell. - - -41. MISSING WORDS - - Till a man is as ----- of a ----- as his palm is, - We ----- him from earning his ----- in our armies. - -The missing words are spelt with the same five letters. - - -42. THE PAUPER’S PLAINT - - Pale penury that ------ social bands, - And any link that ------ worth to fame, - Take ye the blame for my inactive hands, - I ------ in vain to build upon the sands, - Without a ------ who can make a name? - -The missing words are spelt with the same six letters. - - -No. XXV.--CAPITAL SHORT CUTS - -The following example of the use of phonetic capitals and figures is -fresh and original. It contains more than eighty such symbols in its -twenty-four lines:-- - -A MAID OF ARCADY - - A rosy maid of R K D - Is L N in her bower; - Brisk as U C A honey B, - And sweet as N E flower. - - Does she S A herself 2 please - (XQQ the saucy miss), - She sings an L E G 2 TT, - Or blows an M T kiss. - - “B mine, I say, U bonny J, - B 4 I CC mine L; - When you are gay my hopes D K, - In T sing U X L.” - - Without ado she takes the Q, - Her II B 9 and B D, - “O, sir, I do not N V U - I C that U R C D. - - “X S of spirits--O D V-- - Begins 2 U U U up; - The cure must B a dish of T - With K N in the cup!” - - “O L N U I C R true, - Y need I C Q less? - I’ll never D V 8 from U, - But end my cares with S.” - (_caress_). - - -43. MISSING WORDS - - Mr Backslide, afflicted with weakness of mind, - -------- over to Lushington’s inn, where he dined. - He -------- the pledge he had taken as handy, - And emptied forthwith a -------- of brandy. - -Each missing word has eight letters. - - -44 - - A ------ sat in his ------ grey, - Watching the moonbeams ------ play - On a keg that in the bushes lay, - And these were the words of his song:-- - “Thou ------ the weak, thou ------ the strong, - To thee the ------ of bad deeds doth belong.” - And the leaves with a ------ took up the sad song. - -Each of these missing words is spelt with the same six letters. - - -No. XXVI.--SIMPLE SCHOLARSHIP - -Three hungry scholars came to a wayside inn, and saw this sign over the -door: - - +-----------+ - |PLACET ORE | - |STAT ORDINE| - |ORE STABIT | - |ORE AT ABIT| - +-----------+ - -One of them eager to show his ready wit, translated these Latin words of -welcome roughly into English verse:-- - - “Good cheer we provide, - Our service is sure; - Their savours abide - Though meats don’t endure!” - -The complacent smile faded from his face as a village schoolboy, who had -overheard him, broke in with the real rendering of the words:--“Place to -rest at or dine; O rest a bit, or eat a bit!” - - -45 - -In these lines, where the dots occur, insert words, each of which is -longer by one letter than the one before, and so complete the poem. The -same letters are carried on each time in varied arrangement:-- - - Nature . love .. every land, - On burning plain, by wooded rill; - Where ... is girt by coral strand, - Or .... rears her castled hill. - - Then ..... from me the tale to hear, - How, true to one ......, the bee - Once ....... out keeps, year by year, - The ........ by her instinct given, - Which teach her, wheresoe’er she roam, - In every clime beneath the heaven, - To build the same ......... home. - - -No. XXVII.--WAS IT VOLAPÜK? - - | | - -+---------------+- - |FFAH CHTI WT | - |HGU ACT ONE| - |RASD RIB DLO| - -+---------------+- - | | - -A schoolmaster in the Midlands, who was a bit of a wag, wrote this on -the blackboard, as a novel exercise for the boys of Standard VI. Can you -decipher it? - - -46 - -Here is another ingenious specimen of missing words, spelt each of them -with the same five letters:-- - - That Samson did a thousand ----- - Is not so wondrous strange. - In days like these at ----- such feats - Assume a wider range. - The Press ----- news ----- now, - Enough to scare a sinner, - And any fool who chooses may, - In Samson’s way, his thousands slay - Who chews his ----- at dinner. - - -No. XXVIII.--ANOTHER EPITAPH - -(_On an Old Pie Woman_) - - BENE AT hint HEDU S.T.T.H. emo Uldy O - L.D.C. RUSTO F.N.E. L.L.B. - AC. hel orl AT Ely - W ASS hove N.W. how ASS Kill’d - Int heart SOF pi escu Star - D. sand Tart Sand K N ewe, - Ver yus E oft he ove N.W. Hens he - ’Dliv’ Dlon geno - UG H.S. hem Ade he R la STP uffap - UF FBY HE RHU - S. B an D. M. - Uchp R.A. is ’D no Wheres He dot - H.L. i.e. TOM a Kead I.R.T.P. Iein hop est - Hat he R.C. Rust W I - L.L.B. ERA IS ’D----! - - -47. IN A FARM-YARD - - All his flock from ------ rough, - To the ------ ran apace, - Where their ------, old and tough, - ------, the guardian of his race. - -In these lines each missing word is spelt with the same six letters. - -48 - -This is a bright little specimen of a missing words puzzle:-- - - Come, landlord, fill the flowing ---- - Until their ---- run over; - For in this ---- to-night I’ll ----, - To-morrow ---- to Dover! - -Each missing word has the same four letters. - - -No. XXIX.--DOG LATIN - -An old worn stone, with the inscription given below just legible, was -found near to some ancient Roman remains, and was the valued possession -of a local antiquarian, who was convinced that it dated back to the days -of the Emperor Claudius:-- - - BENE - AT . HTH . IS . ST - ONERE . POS . ET - H . CLAUD . COS. TERT - R . I . P - ES . ELLE . RO - F . IMP - IN . G . TONAS . DO - TH . HISCO - N . SORTJ - A . N . E - -His pride of possession was, however, shattered when a rival collector -read it off into excellent English:--“Beneath this stone reposeth Claud -Coster, tripe seller, of Impington, as doth his consort Jane.” - - -49 - -Here, as quite a novelty, is a double-barrelled missing words puzzle. As -a puzzle, Part I. should stand alone, but the second part forms a -thinly-veiled solution, which throws light upon the missing words. These -are four in number and are spelt differently with the same six letters. - -Part I - - I tell of voices hushed and still, - I bid men prick their ears, - I help an army’s ranks to fill, - My gleam like gold appears. - -Part II - - Hushed is the still and ------ voice, - Pricked ears are keen to ------, - Men who ------ make noble choice. - ------ like gold will glisten. - - -No. XXX.--THE PROBLEM SQUARED - - P R O B L E M - R E C E I V E - O C T A V E S - B E A C O N S - L I V O N I A - E V E N I N G - M E S S A G E - -This is a singularly perfect specimen of a seven-letter Word Square. - - -50. MISSING WORDS - - Some men their -------- escorted on their way, - When “-------- look here!” I heard a driver say: - “It -------- our pluck to toil like -------- all day, - When wanting -------- we starve on wretched pay.” - -Each missing word is spelt with the same five letters. - - -No. XXXI.--BY LEAPS AND BOUNDS - -Can you disentangle the eight-line verse which is scattered over these -64 squares? You must leap always from square to square, as a knight -moves on the chess-board. - - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | tle | to | a |cat- |life | and |live | In | - | | | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | By | tle | ow- |bro | of | non |tle |fall | - | | | |wse | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | ter |tur- | gain| like|land |one’s|quiet| And | - | | | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | of | ar | Bet-| me | and |Than | a- |bat- | - | | m | | ad- | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - |bask | Be | lau-| or | tle |ness |done |wan- | - | | t- | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | rel | let |Than |die |With | der | of | smo | - | | | | | | | | ke | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | ter | in |brain|myr- | on | and |har- | un- | - | | | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | Ch | or |to |sun |with |work | In |heat | - | ap- | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - -The verses begin with “Better to die,” and end with “tle” in the top -left-hand corner. - - -51. WISDOM WHILE YOU WAIT - - As a -------- -------- of facts you’ll find - Our Encyclopedia -------- the mind. - -The three missing words are spelt with the same seven letters. - - -52. MISSING WORDS - - You drink that --------, -------- wine, too lavishly at night, - And say a -------- or a swim next morning puts you right, - When night brings you a sudden --------, and morning devils blue, - Then you’ll ------ your careless boast, and own my warning true. - -Each missing word is spelt with the same six letters. - - -No. XXXII.--A BROKEN SQUARE - -Can you complete this broken Word Square? - - +---------+ - | |O| |E| | - +-+-+-+-+-+ - |O| | | |E| - +-+-+-+-+-+ - | |I| |O| | - +-+-+-+-+-+ - |E| | | |E| - +-+-+-+-+-+ - | |E| |E|-| - +-+-+-+-+-+ - - -53 - -The missing words in these lines are all spelt with the same six -letters:-- - - --- -------- but for rebel act - Without --- -------- should be; - But this --- --- --- end, in fact - None find --- -------- in me. - - -54. MISSING WORDS - - “Oh for a ----- in this vast solitude, - This endless rise and fall of ----- and moor!” - Soliloquised a ----- in sad mood, - As through the lonely hills the staff of life he bore. - -Spelt with the same five letters. - - -No. XXXIII.--A KNIGHT’S TOUR PROVERB - -If the letters on these squares are taken in proper sequence they will -form the words of a well-known proverb:-- - - +-+-+-+-+-+-+-+-+ - | | | | | | | | | - +-+-+-+-+-+-+-+-+ - | | | | |E| | | | - +-+-+-+-+-+-+-+-+ - | | |E| | | |T| | - +-+-+-+-+-+-+-+-+ - | | | |L|H| | | | - +-+-+-+-+-+-+-+-+ - | |E| |R| |S| | | - +-+-+-+-+-+-+-+-+ - | | |E|A|S| | | | - +-+-+-+-+-+-+-+-+ - |D| |E| |O| |S| | - +-+-+-+-+-+-+-+-+ - | | | |S|P| |M| | - +-+-+-+-+-+-+-+-+ - -When a starting point has been chosen for trial of this puzzle, the -successive letters must occupy the squares which in every case are -reached by a knight’s move at chess, until a popular proverb is formed. - - -55. “MONSTRUM HORRENDUM INFORME INGENS” - - ’Twas in ........ that we saw him play - Like a ........ in his sports, and they - Amuse us as a good ........ may. - -Each missing word has the same eight letters. - - -No. XXXIV.--GUARINI’S PROBLEM - -The following curiosity, which is known as _Guarini’s Problem_, dates -back to the year 1512. On a board of 9 squares two white Knights are -placed in the top corners, and two black Knights in the bottom corners, -thus:-- - - +---+---+---+ - | N |...| N | - +---+---+---+ - |...| |...| - +---+---+---+ - | n |...| n | - +---+---+---+ - -The problem is to interchange, in as few moves as possible, the -positions of the white and black knights. - - -56 - -We call particular attention to the construction of this very curious -couplet, in which the spaces are filled by the same seven letters. In -every case four of the letters of the missing words or phrases are the -same, and keep the same order, and in all but the first the order of the -letters is unchanged throughout, though the meaning always alters, as it -does in that most perfect old Latin motto, “Persevera, per severa, per -se vera,” “persevere through trials, true to thyself.” - - Soup is --- ------- for a ------- divine, - Who with --- -------- is ----- -------- to sit down and dine. - - -No. XXXV.--AN ANAGRAM SQUARE - -Can you break up and recast the five words in this square, so that the -fresh words form a perfect Word Square? The initials are A, M, E, N, D, -S. - - +-+-+-+-+-+-+ - |S|E|N|D|E|R| - +-+-+-+-+-+-+ - |O|N|I|O|N|S| - +-+-+-+-+-+-+ - |B|A|B|B|L|E| - +-+-+-+-+-+-+ - |M|A|N|N|E|R| - +-+-+-+-+-+-+ - |S|M|I|L|E|D| - +-+-+-+-+-+-+ - |L|I|N|E|A|L| - +-+-+-+-+-+-+ - - -57. MISSING WORDS - - Sweet as the ------ and cruel as its thorn, - ------ thy power is great, thy pity scorn. - Swift as the ------ that through the forest fly, - Deep as the ------ that deepest hidden lie, - Is thine own ------ to hapless mortals given, - Semblance of darkest hell or brightest heaven. - -These missing words are spelt with the same four letters. - - -58. MISSING WORDS - -(_Dedicated to the Fresh Air Fund_) - -Good ----- for City ----- - - My pipe ----- for -- ---- charms, that yield - Pictures and ----- of a children’s day. - Lest conscience ----- I ----- -- down to say - My ----- shall send some city ----- afield. - -Each word or group is spelt with the same five letters. - - -No. XXXVI.--SHAKESPEARE’S PSALM - -Quite as cryptic and convincing as any of the curious Shakespeare-Bacon -cyphers is the evidence which connects our great English poet with the -forty-sixth Psalm of the authorised Bible version. - -Shakespear, spelt thus, as it often was, contains four vowels and six -consonants. This is the key to the position. If, guided by these -figures, we turn to the _forty-sixth_ Psalm and count from the -beginning, we find the _forty-sixth_ word is “Shake.” - -Then, counting from the end, disregarding the “Selah,” which is no part -of the text, we find that the _forty-sixth_ word is “spear.” - -Thus, by a startling and perfect succession of affinities, the poet’s -name-number is linked again and again with this Psalm, until it reveals -his name. - -If any sceptic asks why the Book of Psalms should thus be turned to, the -answer comes in the curious fact that the actual letters of the name -William Shakespere, another of its different spellings, form this -sentence as their anagram, and thus afford the necessary clue:-- - - “We are like his Psalm.” - -A final point of interest is made when we notice that Shakespeare -himself must have been just _forty-six_ years old when the Psalms were -re-translated. - - -59. MISSING WORDS - - He said “You ------” when one lied, - He said “Don’t ------” when one hied, - His glass held ------ at his side, - He can ------ what he denied. - -Each missing word is spelt with the same six letters. - - -No. XXXVII.--A KNIGHT’S TOUR - -The letters on this board, if read aright in the order of a Knight’s -moves at chess, will give a popular proverb. - - +-+-+-+-+-+-+-+-+ - |R|L|T|E|Y|L|R|O| - +-+-+-+-+-+-+-+-+ - |Y|H|L|T|O|B|T|A| - +-+-+-+-+-+-+-+-+ - |T|A|A|A| |H|T|I| - +-+-+-+-+-+-+-+-+ - |E|L| |E|I|N|E|O| - +-+-+-+-+-+-+-+-+ - |D|H|W| |Y|E|S|Y| - +-+-+-+-+-+-+-+-+ - |R|T|E|S|D| |B|W| - +-+-+-+-+-+-+-+-+ - |Y|N|E|S|N|D|A|E| - +-+-+-+-+-+-+-+-+ - |H|A|A|A|W|I|D|E| - +-+-+-+-+-+-+-+-+ - -Start from the most central E, and you will be able to trace the -proverb. - - -60. MISSING WORDS - - Mr Snip, the --------, was -------- a hill, - With a bag of new -------- for stock; - When a runaway motor-car gave him a spill - Which scattered his doubts with the shock. - -Each missing word is spelt with the same eight letters. - - -No. XXXVIII.--A WORD SQUARE - -The pupils of Dr Puzzlewitz found one morning these vowels printed -boldly on the blackboard:-- - - E * A * E - - * A * E * - - A * E * * - - * E * * E - - E * * E * - -Under it the doctor had written “Fill in the consonants, so that the -words read alike from top to bottom, and from side to side.” How is this -to be done? - - -61. MISSING WORDS - - ----- her fair cheek, and back o’er all - The ----- of years ----- memory. - Those wedding ----- to her recall - The ----- he urged so tenderly. - -Each of these missing words has five letters. - - -62. MISSING WORDS - - Two burglars attempted to ----- a house, - The ----- was heard, though as still as a mouse. - When challenged at once he a ----- became, - But caught as a ----- he finished his game. - -Each word has the same five letters. - - -No. XXXIX.--THE SQUAREST WORD - -The squarest word in any language is the Latin _time_, which, in -connection with the three other Latin words, _item_, _meti_, _emit_, can -be read, when written as a square, in every possible direction. Thus:-- - - T I M E - I T E M - M E T I - E M I T - -As it seems impossible to go one better, we have been seeking, as a new -nut for our store, some English word which may be a good second. Can you -complete the square which is built up on these lines? - - D E L F - * * * * - * * * * - * * * * - -Delf is the key word, but it so far falls short of the perfection aimed -at, that other letters are used in four of the vacant places. Still, it -is so constructed that words which begin with D, E, L, or F appear each -of them in four different directions, and is thus quite a notable -example. - - -No. XL.--A PUZZLE DIAMOND - -Can you fill in this diamond with four words that read alike from left -to right, and from top to bottom? - - D - . I . - . . A . . - D I A M O N D - . . O . . - . N . - D - - -63. MISSING WORDS - - The -------- fool in olden days - Gave kings advice in jesting phrase; - He’s -------- now; the modern throne - -------- all follies but its own. - -Each missing word is spelt with the same eight letters. - - -64. MISSING WORDS - - Days of ------ and times of evil, - Starving girls with ------ do toil, - No man ------ feast or revel, - Hushed is ------ and turmoil. - -Each missing word contains the same six letters. - - -65. MISSING WORDS - - Who ------- in his pride and rage, - To ------- vice a prey, - May hope to reach a green old age, - And find ------- his stay. - -Each word has the same seven letters. - - -No. XLI.--A DEFECTIVE DIAMOND - - S - . . M - P . . . L - . . N . . A L - S . . . N . . . R - M . . . C . E - L A . . E - L . E - R - -The places now occupied by dots are to be filled in with letters so that -a complete diamond is formed, of words that read alike from left to -right, and from top to bottom. - - -66. A POET’S POLITICS - - When Limerick once, in idle whim, - Moore as her member gaily courted, - The boys, for fun’s sake, asked of him - To state what party he supported. - When thus to them the answer ran, - “I’m of no party as a man, - But as a poet ------” - -What is the missing word? - - -67. MISSING WORDS - - Is England ------? That this is so - A solemn ------ aspires to show. - By most ignored, the theme -- ---- to some - Who gravely to the same conclusion come. - Like ------ o’er obstacles they soar, - And if an ---- -- ’vert they rave the more. - -There are six letters in the missing words and phrases. - - -No. XLII.--A SPECIMEN MAGIC SQUARE - -The following clever word square of the unusual number of seven letters, -in which there is no undue straining of words or inflexions, is by a -master hand, and would be difficult to match:-- - - P A L A T E D - A N E M O N E - L E V A N T S - A M A S S E S - T O N S U R E - E N T E R E R - D E S S E R T - - -68. MISSING WORDS - - Off to the links is now their cry, - For golf is man’s --------: - Be not -------- or slow, - -------- hit the ball will go. - -Each missing word is spelt with the same eight letters. - - -69. MISSING WORDS - - No maid e’er ------- North, South, East, or West, - More ------- than she who ------- Love’s request. - -Each missing word is spelt with the same seven letters. - - -70. OUT IN THE COLD - - Though in ......... I be, - It is, alas! ... ...... - No ...... ... comes nigh to me. - -Each word or phrase has the same nine letters. - - -No. XLIII.--A LETTER PUZZLE - -Can you fill in the places of these 21 asterisks with only 3 different -letters, so arranged that they spell a common English word of 5 letters -in 12 different directions? - - * * * * * - * * * * - * * * - * * * * - * * * * * - -Two of the five letters are vowels. - - -71 - - --------- his pride the Royal James - Came down upon the --------- Thames; - Like --------- his court repair - To breathe -- -------’s freer air. - -Each space has the same nine letters. - - -72. DROP LETTER LINES - - With lily leaves his oars are ........, - Her eager hands their treasures ......., - To the fair winds all cares . ....., - And echo faintly answers .....! - -The first letter is dropped in each case, so that while the word which -ends line 1 has eight letters, the last word of line 4 has but five. - - -73. ENIGMA WITH MISSING LETTERS - -There was no good ... in the d...y, so the klim. - - -No. XLIV.--A CANINE CHRONOGRAPH - -Some years ago a country parson had the following inscription engraved -upon the tombstone of a favourite dog that died in 1885:-- - - CarLo - Dear DoggIe - LoVIng faIthfVL anD trVe - she Lost her sIght - bVt not her LoVe - for - I. e. V. - -If the large capital letters are treated as Roman numerals, they add up -to the year of the dog’s death, 1885. - - -74 - -If the missing letters, indicated by dots, are supplied, and the words -are separated, this will be found to form a line in a well-known poem:-- - - .u.u.m.r.i.u.d.s.s.e..o.l.w.d.a.t.n.f.l.o.e.f.s.e. - - -75 - -Complete this sentence by filling in five words in the gaps, each spelt -with the same five letters: - -If you write ----- ----- at ----- do not ----- the -----. - - -76. SIX MISSING WORDS - - A ..... ..... on ....’. strands - Caught Pat’s heart in her meshes; - He left the ..... in Cupid’s hands, - And watched her ..... her tresses; - Tresses of ..... coloured gold, - That did her fairy form enfold. - -Each missing word has the same five letters. - - -No. XLV.--A HIDDEN NAME - -“Yes,” said the village wit, as a merry party sat round the tap-room -fire at Stratford-on-Avon, “some wiseacres have tried to prove that -Bacon wrote Shakespeare’s plays, because his name can be found hidden in -some of the lines. Let me show you how easily this sort of thing can be -arranged to suit our fancy.” - -Taking a piece of chalk he wrote upon the door-- - - “Titus Andronicus” - “All’s Well that Ends Well” - “The Merchant of Venice” - “Coriolanus” - “Cymbeline” - “A Midsummer Night’s Dream” - “Much Ado about Nothing” - -“Look down the letters under _d_ of these titles of some of -Shakespeare’s plays,” he said, “and you will find the well-known name of -one who certainly did not write them.” What name did he mean? What but -that of the prince of jokers, Dan Leno! - - -77. MISSING WORDS - -Can you supply the missing words in these lines? Each is spelt with the -same five letters:-- - - A man of ----- had caught a -----, - And it was windy weather; - “Give me my -----,” he cried, “to fix - My fish and ----- together.” - - -No. XLVI.--A CRYPTIC INSCRIPTION - -The following cryptic inscription was engraved, in his own language, -upon a tablet in honour of the great French astronomer and scientist, -Arago:-- - - +-------------+ - | URE | - |AR ERIL| - +-------------+ - -It has this interpretation:-- - - AR à gauche, - ERIL à droit, - URE sur tout. - - Arago chérit la droiture sur tout. - - Arago cherished integrity above all. - - -78. ON THE LOOSE - - When ....., our puppy, sets out for a run, - Over ..... he ....., all frolic and fun. - For no whistle he ..... in his desperate hurry - The cattle to ....., and the slow sheep to worry. - -Each word has the same five letters. - - -79. MISSING WORDS - - Buy my ripe ------, my ------ who’ll buy? - Don’t look so ------, but take some and try! - -The missing words are spelt with the same six letters. What are they? - - -No. XLVII.--SQUARE THE CIRCLE - -Here is a circle which it is quite possible to square:-- - - C I R C L E - I . . . E . - R . . E . . - C . E . . E - L E . . E . - E . . E . . - -Can you fill it in with English words, that read alike from top to -bottom, and from left to right? Try it before you turn to the solution. -Every E must be worked in as it stands. - - -80. MISSING WORDS ILLUSTRATED - - He who .... may .... at last, - How to .... we show; - Take a sixpence, hold it fast, - Press the .... and blow! - -Each missing word has the same four letters. - -[Illustration] - - -No. XLVIII.--A BROKEN SQUARE - -We give as clues the complete border, and a diagonal in which the same -letter persists. Can you construct the whole square? - - +---+---+---+---+---+---+---+ - |_B_|_O_|_A_|_S_|_T_|_E_|_R_| - +---+---+---+---+---+---+---+ - |_O_| | | |_E_| |_E_| - +---+---+---+---+---+---+---+ - |_A_| | |_E_| | |_S_| - +---+---+---+---+---+---+---+ - |_S_| |_E_| | | |_E_| - +---+---+---+---+---+---+---+ - |_T_|_E_| | | | |_N_| - +---+---+---+---+---+---+---+ - |_E_| | | | | |_T_| - +---+---+---+---+---+---+---+ - |_R_|_E_|_S_|_E_|_N_|_T_|_S_| - +---+---+---+---+---+---+---+ - - -ANAGRAMS - -Anagrams, as a method of divining and illustrating personal destiny and -character, were quite a craze in the sixteenth and seventeenth -centuries. No specimens of this word juggling have ever been more apt -than the perfect pair of political anagrams evolved from the names of -two of our greatest statesmen. - -When the reins of power changed hands, it was found that the letters -which form Gladstone also spell out exactly, “G. leads not,” while the -name of his great rival and successor Disraeli itself announces, when -recast, “I lead, sir!” - - -No. XLIX.--A CARD PROBLEM - -Here is a pretty card problem, akin in its character and arrangement to -a Magic Square. - -Take from a pack of cards the four aces, kings, queens, and knaves, and -arrange them so that in each horizontal, vertical, and diagonal row, -each of the four suits and each of the four denominations shall be -represented once, and only once. - - -IDEAL ANAGRAMS - - | | - -+--------------------------------------------------------+- - |Ave Maria, gratiâ plena, Dominus tecum! | - |Virgo serena, pia, munda et immaculata. | - |Regia nata, evadens luctum amari pomi. | - |Eva secunda, Agni immolati pura mater. | - | | - |Hail, Mary, full of grace, the Lord is with thee! | - |A virgin calm, holy, pure and spotless. | - |Of royal kin, free from the penalty of the bitter apple.| - |A second Eve, pure mother of the slain Lamb. | - -+--------------------------------------------------------+- - | | - -These wonderful anagrams need no word of praise. Constructed each of -them with the same letters, the lines express with startling emphasis -the character and special attributes of her whom they describe. - - -No. L.--TURF-CUTTING - -I cut eight narrow strips of turf from my lawn, to form a double -rose-border, with sides of the relative lengths shown in the diagram:-- - -[Illustration] - -How can I relay these eight pieces, without turning or breaking them, on -a piece of level soil, so that they enclose three flower-beds of similar -size? - - -AN ANAGRAM EPITAPH - -This was engraved on a slate monument in memory of Marya Arundell, in -Duloe, Cornwall, June 8, 1629:-- - - | | - -+------------------------------------------------+ - | MARYA ARUNDELL--MAN A DRY LAUREL | - | | - |Man to the marigold compared may be, | - |Man may be likened to the laurel tree. | - |Both feede the eye, both please the optic sense,| - |Both soon decay, both suddenly fleete hence. | - |What then infer you from her name but this, | - |Man fades away, _man a dry laurel_ is! | - -+------------------------------------------------+- - | | - - -No. LI.--A READY RECKONER - -Two schoolboys, looking into a small water-butt after a heavy rain, -could not agree as to whether it was quite half full. - -[Illustration] - -They appealed to the gardener, as there were no means of measurement at -hand, and he, being a shrewd, practical man, was able to decide the -point. How did he do this? - - -TWIN ANAGRAMS - - Paradise lost. - _Reap sad toils._ - - Paradise regained. - _Dead respire again!_ - - -No. LII.--A TRANSFORMATION - -Can you turn this flat-headed 3 into a 5 by one continuous line, without -scratching out any portion of the 3? - -[Illustration] - - -ADVANCE AUSTRALIA - -What were “The Australian Cricketers?” - -ANSWERED BY ANAGRAM - -_Clinkers! Each a true artist._ - - -BUNYAN’S ANAGRAM - -John Bunyan, in the conclusion of the advertisement of his “Holy War,” -has these quaint lines (using i for j):-- - - “Witness my hand, if Anagrammed to thee - The letters make ‘Nu hony in a B.’” - - -OLD POLITICAL ANAGRAMS - - “The Earl of Beaconsfield.” - _Chief one of all debaters._ - - “William Ewart Gladstone.” - _Wit so great will lead man._ - - -No. LIII.--A CLEAR COURSE - -These diagrams show two of the many ways in which eight pieces of -chessmen or draughtsmen can be so placed upon the board that each of -them has a clear course in every direction, along straight or diagonal -lines. - - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - | |.X.| |...| |...| |...| | |...| |...| |.X.| |...| - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - |...| |...| |...| X |...| | |...| |...| X |...| |...| | - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - | X |...| |...| |...| |...| | |.X.| |...| |...| |...| - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - |...| |...| |...| |.X.| | |...| |...| |...| |...| X | - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - | |...| |.X.| |...| |...| | |...| |...| X |...| |...| - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - |...| |...| |...| |...| X | |...| |...| |...| |.X.| | - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - | |...| X |...| |...| |...| | X |...| |...| |...| |...| - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - |...| |...| |.X.| |...| | |...| |.X.| |...| |...| | - +---+---+---+---+---+---+---+---+ +---+---+---+---+---+---+---+---+ - -We will give a table in the solutions which shows a large number of -similar possible positions. Meantime our solvers may like to trace some -for themselves. - - -APPOSITE AND OPPOSITE - -Three most excellent anagrams are formed with the letters of the great -name Thomas Carlyle. Two of them seem to point to the rugged sage of -Chelsea in life, and one to his repose in death. They are:-- - - Mercy! lash a lot. - - Cry shame to all! - - A calm holy rest. - - -A ROYAL ANAGRAM - - (Adsit omen!) - “Albert Edward and Alexandra.” - _All dear bread and war tax end!_ - - -No. LIV.--QUARRELSOME NEIGHBOURS - -Three families, who were not on speaking terms, lived in three houses -within the same enclosing fence. Determined to avoid each other, they -built covered ways from the doors of their houses to their gates, so -that they might never cross each other’s paths. The family in A had -their gate at A, those in B at B, and those in C at C. How were these -covered ways arranged so as to secure their complete separation? - -[Illustration] - - -HIS HOBBY - - William Ewart Gladstone. - _A man will go wild at trees._ - - -A SOLDIER’S ANAGRAM - - Lord Kitchener of Khartoum. - _Oh firm rod! the knack to rule!_ - - -No. LV.--A PRETTY TRICK - -Ask some one to place five cards (not court cards) in a row, to add up -their pips, and to place two cards representing that number below, for -subtraction, as is shown in the diagram. - - /-------\ /-------\ /-------\ /-------\ /-------\ - | ♠ | | ♦ | | ♣ ♣ | | ♥ ♥ | | ♦ ♦ | - | | | | | | | ♥ | | ♦ ♦ | - | | | ♦ | | ♣ ♣ | | ♥ ♥ | | ♦ | = 28. - | | | | | | | ♥ | | ♦ ♦ | - | ♠ | | ♦ | | ♣ ♣ | | ♥ ♥ | | ♦ ♦ | - \-------/ \-------/ \-------/ \-------/ \-------/ - - /-------\ /-------\ - | ♣ | | ♠ ♠ | - | | | ♠ | - | | | ♠ ♠ | - | | | ♠ | - | ♣ | | ♠ ♠ | - \-------/ \-------/ - - /-------\ /-------\ /-------\ /-------\ /-------\ - | ♥ | | ♣ | | ♠ ♠ | | ♦ ♦ | | | - | | | | | | | | | | - | | | ♣ | | ♠ ♠ | | ♦ ♦ | | ♥ | - | | | | | | | | | | - | ♥ | | ♣ | | ♠ ♠ | | ♦ ♦ | | | - \-------/ \-------/ \-------/ \-------/ \-------/ - -Let him then place cards to represent the result of subtraction, remove -which one he pleases of these, and tell you the sum of the remaining -pips. - -You can at once tell him the value of the card removed by deducting the -number of pips in that remainder from the next highest multiple of 9. -Thus, in the instance shown above, if one of the sixes is removed, the -sum of the remaining pips is 12, and 18 - 12 = 6. A space must be left -for any 0. - - -BOAT-RACE ANAGRAMS - -Here is a batch of anagrams, all letters perfect, which show how, by a -little ingenuity, words may be twisted into opposite and appropriate -meanings. - - “The Oxford and Cambridge annual boat-race.” - - ANAGRAMS - - Hard race, but Cantab gained lead from Oxon. - - Ah! bad rudder line for Cantab cox to manage. - - Cantab blue had raced in an extra good form. - - -No. LVI.--THE CROSS-KEYS - -This pretty puzzle can be made at home by anyone who is handy with a -fret-saw. - -[Illustration] - -Cut three pieces of hard wood according to the patterns given in this -diagram, and try to fit the three sections together so that they form a -firm symmetrical figure with six projecting ends. - - -ANGLO-JAPANESE ANAGRAMS - - “The Anglo-Japanese treaty of Alliance.” - - Yea, Fate enjoins to help a gallant race - - or - - Hail, gallant East! Fear not, enjoy peace - - or - - A peace angel, then joy to all in far East. - - -A WONDERFUL ANAGRAM - -If the letters which spell the names of the twelve months are shaken up -and recast, these appropriate lines and their title are formed-- - -POEM - - Just a jury by number, each a scrap of year, - A number recording every jumble, tumble, tear! - - -No. LVII.--THE NABOB’S DIAMONDS - -An Indian Nabob left a casket of valuable diamonds to his children under -the following conditions:--The first was to take a diamond and -one-seventh of the remainder; the second was to take two and a seventh -of the then remainder; the third three and a seventh of the rest, and so -on, on similar lines, till all the diamonds were taken. Each of the -children had then exactly an equal share. How many diamonds were there, -and how many children? - - -A PRIZE ANAGRAM - -It would be difficult to find a more ingenious and appropriate anagram -than this, which took a prize in _Truth_ in 1902, and connects the -King’s recovery with the Coronation. - -The sentence was-- - - “God save our newly crowned King and Queen! - Long life to Edward and Alexandra!” - -The letters of this were recast thus-- - - Can we wonder an anxious devoted England followed drear danger - quakingly? - - -A GOOD ANAGRAM - - Sir Francis Bacon, the Lord Keeper. - _Is born and elect for rich speaker._ - - -THE DREAMER’S ANAGRAM - -“Imagination”--_I’m on it again!_ - - -A SEASONABLE ANAGRAM - - “Spring, Summer, Autumn, Winter.” - _We murmur--“Time’s running past!”_ - - -No. LVIII.--A CARD CHAIN - -The cardboard chain in this diagram is formed of unbroken links cut from -one card. - -[Illustration] - -There are no joinings in these links, no paste or gum is used, and the -chain is fairly cut from a single card. - - -APPROPRIATE - -Very apt indeed, in these days of books and papers without end, is the -descriptive anagram which we find involved in - - “The Alphabet,” _That be a help_. - - -A TOUR DE FORCE - -Made with the letters which form the names of the twelve months, each -being used once, and only once:-- - - Merry durable just grace - My every future month embrace, - No jars remain, joy bubble up apace! - - -No. LIX.--STRAY DOTS - -These represent the four quarters of a torn design, on which large black -dots had been so drawn that no two of them stood on the same row, -column, or diagonal. - - +--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+ - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+ +--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--●-----+-----+-----+--+ +--+-----●-----+-----+--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--+-----+-----●-----+--+ +--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+ +--+-----+-----●-----+--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - +--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+ - - +--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+ - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+ +--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--●-----+-----+-----+--+ +--●-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+ +--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /| |\ | / \ | / \ | / \ | /| - +--+-----+-----+-----●--+ +--+-----+-----+-----●--+ - |/ | \ / | \ / | \ / | \| |/ | \ / | \ / | \ / | \| - +--+--+--+--+--+--+--+--+ +--+--+--+--+--+--+--+--+ - -Can you copy out these four pieces, and place them in close contact, so -that the proper edges come together to reproduce the original effect? - - -AN OLD POLITICAL ANAGRAM - - The initials of Brougham, Russell, Allthorp, and Grey, - If rightly disposed the word “brag” will display; - Transpose them and “grab” will appear to the view, - Which hints at what many assert to be true, - That they, like some others, still follow the plan - To _brag_ what they’ll do, and then _grab_ what they can! - - -No. LX.--THE OPEN DOOR - -A prisoner placed in the cell marked _A_ is promised his release on the -condition that he finds his way out of the door at _X_ by passing -through all the cells, entering each of them once only. - - +---+---+---+---+---+---+---+---+ - | A | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | _x_| - +---+---+---+---+---+---+---+ + - -How can he do this? - - -A ROYAL ANAGRAM - -The following remarkable anagram is recast from the name and title of -the daughter of George IV., who was direct heir to the throne:-- - - “Princess Charlotte Augusta of Wales.” - - -ANAGRAM - - _P. C. her august race is lost, O fatal news!_ - - -No. LXI.--THE SHEPHERD’S PUZZLE - -When a farmer told his shepherd to put 21 sheep into 4 pens at the fair, -and added, “I wish you could put an odd number into each pen, as there -is luck in odd numbers, but that is impossible,” he did not take into -account the shrewdness of the shepherd, who very cleverly folded them -thus:-- - - +---------------------------------+ - | * * * | - | +-------------------------+ | - | | * * | | - | | +-----------------+ | | - | | | * * | | | - | | | +---------+ | | | - | | | | * * | | | | - | * | | | * | | | * | - | | | | * * | | | | - | | | +---------+ | | | - | | | * * | | | - | | +-----------------+ | | - | | * * | | - | +-------------------------+ | - | * * * | - +---------------------------------+ - -Each fold or pen has by this arrangement an odd number of sheep within -the hurdles that form its outer boundaries, and in this sense the -farmer’s wish was satisfied. - - -We are familiar, most of us, with what is called Macaronic verse or -prose, in which the letters and syllables of Latin words can be read so -as to form English sentences. - -It would seem to be too much to expect that there could be any -connection in meaning between these Latin and English words, but there -is one striking exception to this general rule. “Non est” means exactly -“it is not,” and “No nest” conveys precisely the same idea, when a bird -finds that its home has been destroyed. - - -No. LXII.--LEAP-FROG - -Here is an interesting puzzle which can be worked out with coins or -counters on a corner of a chess or a draughtboard. - -[Illustration] - -At starting only the central point is vacant. A piece that is moved to a -vacant spot must leap over two other pieces if it goes along the solid -black lines, and can only move over one of the dotted diagonals at a -time to an adjoining point. Try, on these lines, to enable the frog, now -in the second hole of the lowest row, to reach the centre in the fewest -possible moves, leaving its own original point vacant, and at the last -surrounded by the words “leap-frog” as they now stand. - -Moves can only be made to vacant places. - - -LXIII.--MUSIC HATH CHARMS - -[Illustration] - - Transpose two letters, and the lad - Who grinds his organ in the Strand, - Can sing “my music is not bad, - I wake it with a master hand!” - -How did he justify this ambitious claim? - - -No. LXIV.--GRIST FOR THE MILL - -If the letters P E A R S O N S are printed on small wafers or buttons, -and set at hap-hazard and out of order on the points which they now -occupy, a very pretty game of patience will result from the attempt to -restore them to their places. - -[Illustration] - -Any letter can be pushed along one of the lines to a vacant place, and -those on the mill sails can be moved to or from the central spot. There -is no fixed limit to the number of moves, but the puzzle is to restore, -in as few moves as possible, the broken and disordered word to its -proper reading round the mill. - - -No. LXV.--YOUR WATCH A COMPASS - -We are indebted to Sam Loyd, the famous American problem composer and -puzzle king, for the following very practical curiosity, which is so -closely akin to a puzzle that it is well worth giving for the benefit of -our readers when they are out on holiday. If you are uncertain as to -your bearings, lay your watch flat on the palm of your hand so that the -hour-hand points in the direction of the sun. The point exactly midway -between the hour-hand and the figure 12 will be due south at any time -between 6 in the morning and 6 in the afternoon. During any other hours -our rule will give the _north_ point, and in the southern hemisphere the -rules will be reversed. - -[Illustration] - - -In the days of Pope Pio Nono someone extracted from the Papal title -“Supremus Pontifex Romanus” an anagram, which cut at the very foundation -of the faith. It ran thus: “O non sum super petram fixus”--“O I am not -founded on the rock.” - -This held its place as a clever topical anagram, until in a moment of -happy inspiration a son of the Church discovered that if the first words -are recast and rearranged, a splendidly appropriate motto for the then -reigning pontiff leaps to sight, “Sum Nono, super petram fixus,” “I am -Nono, founded on the rock!” - - -No. LXVI.--A MYSTIC SQUARE - -This is an arrangement of numbers in 9 cells, so that no cell contains -the same figure as appear in any other, and the two upper rows, the two -side columns, the two long diagonals, and the four short diagonals all -add up to 18:-- - - +-------------+-------------+-------------+ - | | | | - | | 5 + 5| 2 | - | 1 + 1 + 1 |5 + 5 + -----| 2 + - | - | | 5 | 2 | - | | | | - +-------------+-------------+-------------+ - | | | | - | | | 4 + 4 | - | 3 + 3 | 6 | 4 + ----- | - | | | 4 | - | | | | - +-------------+-------------+-------------+ - | | | | - | 7 + 7 | 9 + 9 + 9| 8 | - | 7 + ----- |9 + ---------| 8 + - | - | 7 | 9 | 8 | - | | | | - +-------------+-------------+-------------+ - -Though not, strictly speaking, a Magic Square, this is a most ingenious -fulfilment of the conditions of the puzzle. - - -UP-TO-DATE ANAGRAMS - -Good up-to-date anagrams are:--Chamberlain, “Rich able man,” and -Pierpont Morgan, “Man prone to grip.” - - -No. LXVII.--A SWARM OF WORDS - -In each of the five crosses of this mystic figure the same letters are -to be inserted where there are asterisks, so that seven different -English words are formed, which can be read altogether in 64 different -ways and directions. - - * - * - * * D * * - * - * - * +---/*\---+ * - * | * | * - * * D * *|* * D * *|* * D * * - * | * | * - * +---\*/---+ * - * - * - * * D * * - * - * - -There will then be in all the five crosses 320 readings of these seven -words, three of them having 80 variations and four of them having 20, -and only three different letters are used. - - -SEASONABLE ANAGRAMS - - | | - -+---------------------------------------+- - | “_A Merry Christmas and a Happy | - | New Year._” | - |My prayer and wishes reach many a part.| - | _or_ | - |Many a sad heart can whisper my prayer.| - -+---------------------------------------+- - | | - - -No. LXVIII.--AFTER SOME SAD REVERSE - -We admit this most miserable picture of a discontented outcast into our -bright pages, to “point a moral,” if it does not “adorn a tale.” - -[Illustration] - -Can our readers gather from it the lesson, that when things seem to be -at the worst, a turn of fortune’s wheel may set them on their legs -again, and change the merest melancholy to the merriest mirth? A reverse -of another sort will set things right. Turn the page round! - - -A lady, to whom the momentous question had been put with some -diffidence, handed to her lover a slip of paper, telling him that it -embodied her reply. Nothing was written but the word “stripes,” which -seemed at first to be of sinister omen; but to his relief and joy the -fateful letters presently resolved themselves into a message of direct -encouragement, and never was an anagram more welcome than this which -bade him “persist.” - - -No. LXIX.--THE EXPLOSIVE RAFT - -With eight large wooden matches form a miniature raft, as is shown in -the diagram:-- - -[Illustration] - -Place the little raft on a wine-glass, and apply a lighted match to one -of its corners. The tension on its parts will cause the whole -construction to fly asunder as soon as the pressure on any point is -removed. - - -A NOTABLE HISTORIC ANAGRAM - -It is very remarkable that the letters which form the sentence-- - -“The Jubilee Day of Victoria, Queen and Empress,” also exactly spell-- - -_Joys are never quite complete if a husband die._ - - -No. LXX.--A PICTURE PUZZLE - - Much is bad, and much is sad, - And life has many woes. - -[Illustration] - - May we keep clear from year to year - Of what this picture shows! - -Can you interpret it? - - -CONTRADICTION BY ANAGRAM - -Logica, Latin for logic, can be resolved into the strangely -contradictory anagram, _caligo, darkness_; and, in seeming support of -this perversion, our word logic can be turned into _I clog_! - -Here are two good anagrams connected with the land of the Pharaohs:-- - - David Livingstone, - “Go and visit Nile, D.V.” - - Cleopatra’s Needle on the Thames Embankment, - “An Eastern emblem; then take me to Cheops’ land.” - -Danes should be _dark men_, according to the anagram of “Denmark.” - - -No. LXXI.--PATCHWORK PICTURES - -This is good fun for old and young as a round game. Each player draws on -the upper part of a slip of paper some fancy head and folds it back, -leaving just enough in sight to guide his left-hand neighbour, who takes -it and adds a body. Again the slips are handed on for the final addition -of legs of any sort, some continuation being always indicated. - -[Illustration] - -Then these completed patchwork pictures are thrown into a central bowl, -shaken up, drawn out, and passed round for inspection and merry comment. -The folds are the dotted lines. - - -A HOUSEHOLD WORD - -The wounded and sick soldiers whom Florence Nightingale nursed so -tenderly in the Crimea would have acclaimed her beautiful anagram--“Flit -on, cheering angel!” - - -No. LXXII.--A WINTER NIGHT’S DREAM - -Mr Jolliboy, chubby and active, had been dancing until the small hours -at a house in the suburbs, which was the home of sweet Lucy, the lady of -his love. - -The full moon shone down upon him as he walked happily to his own modest -quarters, and the “man in the moon” seemed to smile and wink at him most -knowingly. - -[Illustration] - -Letting himself in presently with his latch-key, Mr Jolliboy was soon in -bed and fast asleep, when in his dreams the full moon shone again, -showing at one moment a likeness of his own round face, at another two -smiling profile views of his Lucy, and at times all the three mixed. - -Here, changed by a few touches, are the three moon-faces to be seen in -one moon! - - -When the great Tichborne trial was still dragging its slow length along, -a barrister with a turn for anagrams amused himself and his learned -friends by constructing the following really remarkable specimen:--Sir -Roger Charles Doughty Tichborne, Baronet, “Yon horrid butcher Orton, -biggest rascal here.” - - -No. LXXIII.--POINTS AND PICTURES - -Among the many openings for pleasant fun in the home circle, there is -none which appeals more easily to young and old than the good old puzzle -of drawing off-hand some fanciful figure, based on five dots placed at -random, which must fall on the face, hands, and feet of the subject -chosen. - -[Illustration] - -This spirited specimen shows how well it may be done, and similar -efforts, more or less successful, will provoke much amusement. Try it -with pencil or pen and ink. - - -ANOTHER BOAT-RACE ANAGRAM - -Among the many points which have to be taken into account by those who -in successive years are responsible for the selection of the Oxford -eight, there is one which is thus neatly expressed by an anagram:-- - - “The Oxford and Cambridge annual boat-race.” - - _Much extra load on board can bring a defeat._ - - -No. LXXIV.--A NERVOUS SHOCK - -This is the astounding portrait of himself, which presented itself to -our scientific professor in his dreams. What very poor justice it does -to the real lines of his benevolent and shrewd old countenance will be -seen in a moment if this weird picture is reversed. - -[Illustration] - - -HOLIDAY HAUNTS - -_Divination by Name_ - -Whenever we are making our plans, some of us for a holiday abroad, some -for a few weeks at the seaside, there is a special interest in these -descriptive anagrams:-- - - Davos Platz, Engadine. - “Stop, gaze, and live!” - - Weston-super-Mare, Somerset. - “A sweet open summer’s resort.” - -A very appropriate anagram that exactly describes its subject is -this:--Cleopatra’s Needle, London--“An old lone stone replaced.” Very -suggestive, too, are these short ones, which assure us that skeletons -are “not sleek,” and that editors are “so tired!” - - -No. LXXV.--HOGARTH’S PUZZLE - -A soldier, a dog, and a door can be thus drawn by only three strokes of -a pen:-- - -[Illustration] - -It is said that this originated with Hogarth, who made a bet with his -boon companions that he would draw a soldier, a dog, and a door in three -strokes. For the bayonet he drew a pike. - - -No. LXXVI.--A REBUS - -Why is this “Joker” like a poor joke? - -[Illustration] - -Because he is _in an E_ (inane). - - -Here are three ingenious instances of what may be called answers by -anagram:-- - -What is the protector of “wealth?” - - _The law._ - -Where would a “cart-horse” be unhandy? - - In an _orchestra_. - -What is the “Daily Express?” - - _Pressa die lux._ - Concise daily light. - (u is used for y.) - - -It is curious that Mary, a name so sweet and simple, has as its anagram -“army.” The conflicting thoughts suggested by these two words are very -happily harmonised by George Herbert in his quaint style:-- - - “How well her name an army doth present, - In whom the Lord of Hosts doth pitch His tent!” - - -No. LXXVII.--THREE SQUARES - -Here is quite a simple method of arranging nine matches so that they -represent three squares. - -[Illustration] - -The figure also includes at its sides two equilateral triangles. - - -A ROYAL ANAGRAM - -Victoria the First, Queen of Great Britain and Ireland, and Empress of -India. These letters also spell exactly:-- - - Fit for a bard I claim inspiréd strain:-- - The sad and even tenor of a quiet reign. - - -POLITICAL ANAGRAMS - -Here are two very perfect specimens:-- - - Earl Beaconsfield. - An able force is led_, - -or, - - _A free lance is bold_. - - -No. LXXVIII.--A TRANSPARENCY - -When the plebiscite was taken in France to decide whether Napoleon III. -should be Emperor, the number of votes cast in his favour was 7,119,791. -Against him there were 1,119,000 votes. - -[Illustration: 7119791/1119] - -If these numbers are written down quite plainly, as is shown above, with -a dividing line, and without the three cyphers, and the paper or card on -which they are strongly marked is reversed and held up against the -light, the very word with which they were concerned, “empereur,” stands -out with startling distinctness. - -It can be drawn on thin cardboard with good effect. - - -AN IMPERIAL ANAGRAM - - A sa Majesté impériale le Tsar Nicolas, souverain et autocrat de - toutes les Russies. - -The same letters exactly spell-- - - O, ta vanité sera ta perte. O, elle isole la Russie; tes successeurs - te maudiront à jamais! - -This most remarkable anagram was published in the early days of the -Crimean war. - - -This curiously apposite anagram was formed letter by letter from the -surnames of the Oxford and Cambridge crews:-- - -April first nineteen hundred and five. How all warm, as arms, strong as -light or dark blue crew’s, all ply oars on very smooth Thames! Oh! shall -Cam’s boat lose? - - -No. LXXIX.--FOR THE CHILDREN - -Here is an excellent and amusing pastime for the winter evenings. Cover -a square of stout cardboard with glazed black paper, and divide it as is -shown in this diagram:-- - -[Illustration] - -With a little ingenuity and some sense of fun, any number of grotesque -figures can be constructed with the pieces, such as those which we give -here as samples. Try it. - - -The truth that there is often much in common between puzzles and -politics is borne out by the following up-to-date anagram:--This Eastern -question--“Is quite a hornet’s nest.” - - -Quite a good anagram, appropriate to the name of a great author, and one -of his works runs thus:-- - - Charles Dickens: Oliver Twist. - “Now C. D. strikes till vice hears.” - - -Confessions of an Opium-Eater - -The same letters recast spell-- - - _If so man, refuse poison at once!_ - - -No. LXXX.--JUDGING DISTANCE - -(For the Children) - -Can you, without measuring, say which two of these posts are farthest -apart? - -[Illustration] - - -A JAPANESE ANAGRAM - - “Oyama is Field-Marshal.” - _Fame aid his loyal arms!_ - - -A TOPICAL ANAGRAM - - “North Sea outrage.” - _A ghost near route!_ - - -APPROPRIATE ANAGRAMS - - Madame Rachel. - _Deal me a charm._ - - A. Tennyson. - _Any sonnet._ - - -A FOURFOLD ANAGRAM - - “Notes and Queries” - _A question sender._ - _Enquires on dates._ - _Reasoned inquest._ - _I send on a request._ - - -No. LXXXI.--HIT IT HARD - -Place the two parts of a common wooden match-box, empty, and in good -condition, in the position shown below. - -[Illustration] - -Now challenge any one to break them with a smart downward blow of the -edge of the hand. What will happen? Try it. - -It is well to take care that no people are sitting, or children -standing, near the box, as it might fly into their faces. - - -An amusing sequence and a note of warning run through these three -anagrams:--Sweetheart, “There we sat;” Matrimony, “Into my arm;” One -hug, “Enough.” - - -No. LXXXII.--A RE-“BUS” - -The driver of a London ’bus the other day broke out into florid language -as he nearly collided with a brand new motor omnibus. - -[Illustration] - -One of the travesties of “motor-’bus” which he hurled at his rival is -depicted in this diagram. What was it? - - -A PRIZE ANAGRAM - -This letter-perfect anagram could not be more apposite if the words had -been chosen from a dictionary:--“Abdul Hamid Khan, Sultan of the Ottoman -Empire.”--“Inhuman despot, that maketh Armenia bloodful.” - - -The words in italics in-- - - One lovely _May morn it_ chanced that I set - My all on a new speculation; - But the venturesome step I can never regret, - For my prize has surpassed expectation, - -find in _Matrimony_ their anagram, which is also the solution of the -lines. - - -No. LXXXIII.--ROUSING DEAD DOGS - -A GOOD OLD PUZZLE - - These dogs are dead, we all should say; - Give them four strokes, they run away! - -[Illustration] - - -A MEAL OF ANAGRAMS - - Mute hen. - Your posset. - Try our steak. - One solid lamb. - Steamed or tossed. - Mince sole. - -This is solved thus:-- - - The Menu. - Oyster soup. - Roast turkey. - Boiled salmon. - Dressed tomatoes. - Lemon ices. - -Each corresponding sentence is a perfect anagram. - - -_Earl of Beaconsfield_ is spelt with the same letters as the sentence “O -able dealer in scoff!” - - -If a lion with an ear for music were to hear the sound of an “oratorio,” -he might say, as an answer by anagram, _I roar too_! - - -No. LXXXIV.--LIKE A BLACK SWAN - -(_Nigroque simillima cygno._) - -Here is quite a good “shadowgraph.” - -[Illustration] - -With a strong light and a little practice, any one may easily produce -this effect with the shadow thrown by arms and hands. - - -ANSWERS BY ANAGRAM - -What is Russia?--Russia _is ursa_ (a bear). - -What did a Prime Minister say of the _Saturday Review_? - - That _it was a very rude_ periodical. - - -BEANS AND BACON - -What appropriate advice might be given by anagram to those who support -the “Shakespeare-Bacon” controversy? - - _Soak cheaper beans._ - - -No. LXXXV.--CHEQUERS AND STRIPES - -Here is a particularly charming domino puzzle:-- - - +---+ +---+ +---+ +---+ +---+ - | 2 | | | | 3 | | | | 3 | - | | | | | | | | | | - | 2 | | | | 1 | | | | 3 | - +---+ +---+ +---+ +---+ +---+ - - +---+ +---+ +---+ +---+ +---+ - | | | 1 | | | | 3 | | | - | | | | | | | | | | - | | | 4 | | | | 4 | | | - +---+ +---+ +---+ +---+ +---+ - - +---+ +---+ +---+ +---+ +---+ - | 1 | | | | 3 | | | | 5 | - | | | | | | | | | | - | 5 | | | | 5 | | | | 5 | - +---+ +---+ +---+ +---+ +---+ - - +---+ +---+ +---+ +---+ +---+ - | | | 3 | | | | 5 | | | - | | | | | | | | | | - | | | 6 | | | | 6 | | | - +---+ +---+ +---+ +---+ +---+ - -Place any twenty stones, as is shown in the diagram, so that in every -row their fronts and backs alternate. How can you change the picture by -only two movements, so that, retaining its present form, you alter its -chequers into stripes? - - -The answer by anagram to--What helps to make “bakers fat?” is -_Breakfast_. - - -No. LXXXVI.--HANG THE MATCHES! - -Here is an amusing method of turning wax matches to quaint account:-- - -[Illustration] - -If the wax is slightly melted, and perhaps shredded for some effects, -all sorts of fanciful figures can be thus contrived. - - -ANSWER BY ANAGRAM - -What does an editor say to each “ream of paper?” _Appear for me._ - - -LEWIS CARROLL’S WILL PUZZLE - -Here is a most ingenious will puzzle, by Lewis Carroll, which will be -new to most of our readers. Each of the following five questions has to -be answered by a different sentence, nine letters long, and each -sentence is spelt with the same letters used in varied order:-- - - When are you going to make your will? - Shall I write it for you in pencil? - When may a man leave all his money to charities? - What did the uncle say when he heard this? - What did the nephew say when the uncle made him his heir? - -The anagram answers to the five questions in Lewis Carroll’s will puzzle -are as follows:-- - - When are you going to make your will? - _Now I think._ - Shall I write it for you in pencil? - _No, with ink._ - When may a man leave all his money to charities? - _With no kin._ - What did the uncle say when he heard this? - _Hint, I know._ - What did the nephew say when the uncle made him his heir? - _Think I won!_ - - -No. LXXXVII.--A PARROT CRY - -The good old Rebus-- - -[Illustration] - -may stand for the proverb-- - -“Honesty is the best policy.” (On ST is the best poll I see!) - - -No. LXXXVIII.--A PICTURE PUZZLE - -Can you find eight animals that are concealed in this wood? - -[Illustration] - - -If we may go by its anagram the _gardenia_ needs careful “drainage.” - - -DEFINITIONS BY ANAGRAM - - What is the “soldiers’” anagram? - _Lo I dress._ - - What motto befits “Christianity?” - _I cry that I sin._ - - -No. LXXXIX.--A SHADOWGRAPH - -Here is a good old sample of an effect produced by supple fingers in a -strong light on the wall:-- - -[Illustration] - -Adjust the fingers as is shown, so as to secure the bright spot for the -eye, and then life-like movements can easily be made with legs and ears. - - -The characteristic for the moment of the gaol-bird who began to tear his -clothing, crying out, “I mean to rend it!” was _determination_, which -contains exactly the same letters. - - -Those who, according to their anagram, are best equipped for a “sea -trip” are _Pirates_. - - -AN ANSWER BY ANAGRAM - -What is most unlike a festival?--_Evil fast_. - - -The three words in italics in the verse below form also a long single -word, of which the lines themselves give a vivid description:-- - - While many greet the friends they meet, - I know no face, I press no hand. - Though busy feet may throng the street, - I _sit alone, sirs_, in the land. - - “Solitariness.” - - -No. XC.--A REBUS - -Can you interpret this word-picture? - -[Illustration] - -It represents the name of a famous man. - - -ANSWER BY ANAGRAM - - Should you wish to go by rail, - Hasten to the station; - “Train on time” can never fail - To reach its destination. - If you need a further clue - Keep your journey’s end in view. - - _Termination._ - - -We may expect to find “Anarchists” involved _in rash acts_ according to -their anagram. - - -When his patient has recovered, a “surgeon,” can say by anagram _go -nurse_! - - -ANSWER BY ANAGRAM - -What momentous event of the last century forms in two words an anagram -of the three words appropriate to it, “violence run forth?” - - _French Revolution._ - - -No. XCI.--ON THE WALL - -Here is a picturesque head, which in a strong light can be thrown upon -the wall by anyone who is handy with his fingers. - -[Illustration] - -The peaked cap seems to suggest a French soldier. - - -ANSWERS BY ANAGRAM - -What manner of men has “Eton” produced? - - Men of _tone_ and _note_. - -What worries the “postman?” - - _No stamp._ - -What are to be seen at “Epsom Races?” - - _Some pacers._ - - -No. XCII.--ILLUSTRATED EGGS - -As an excellent illustration of how much expression can be given by -quite a few simple lines, if the pen or pencil is in artistic hands, we -give the outlines of half a dozen eggs, on which by a few deft touches -varied emotions of the human face are cleverly depicted. - -[Illustration] - -Here is a hint for fun in the home circle, with a basket of eggs, a -sheaf of pencils, and a prize for the best rapid design. There is room -for two contrasting faces on each egg. - - -ANSWERS BY ANAGRAM - -What did “Henry Wadsworth Longfellow” do for America? - - He _Won half the New World’s glory_. - -What was the happy result of patriotic “sentiment” in our colonies -during the Boer war? - - _It sent men._ - - -No. XCIII.--THE FIVE STRAWS - -Take five straws, each about four inches long, and a shilling, and -arrange them so that by holding an end of one of the straws you can lift -them all. - -[Illustration] - -The diagram given above shows how, by properly interlacing the five -straws, the shilling may be so inserted as to form a wedge which locks -them all together. - - -ANSWERS BY ANAGRAM - -What can you say when using a “fire-escape?” - - _I creep safe._ - - -What is the extreme of “slow reading?” - - _A single word._ - - -How might a “Poorhouse” in olden days have been described by its own -letters?--_O sour hope!_ - - -What is “Old England” to her sons and daughters?--_Golden land._ - - -The battle of “Inkermann” tells by its anagram of _men in rank_. - - -No. XCIV.--EQUIVALENT REDISTRIBUTION - -In the problem known as “The Flighty Nuns,” the Abbess in the central -cell was satisfied so long as she could count nine of her charges in the -cells on each of the four sides. Here are diagrams which show how the -thirty-six inmates could on these terms absent themselves without -discovery, 2, 4, 8, 10, 12, 16, and even 18 at a time by re-arrangement -of their numbers in the cells. - - +-+-+-+ +-+-+-+ +-+-+-+ - |0|9|0| |1|8|0| |2|5|2| - +-+-+-+ +-+-+-+ +-+-+-+ - |9|A|9| |8|A|8| |5|A|5| - +-+-+-+ +-+-+-+ +-+-+-+ - |0|9|0| |0|8|1| |2|5|2| - +-+-+-+ +-+-+-+ +-+-+-+ - - +-+-+-+ +-+-+-+ +-+-+-+ - |2|5|2| |2|4|3| |3|3|3| - +-+-+-+ +-+-+-+ +-+-+-+ - |5|A|5| |4|A|4| |3|A|3| - +-+-+-+ +-+-+-+ +-+-+-+ - |2|5|2| |3|4|2| |3|3|3| - +-+-+-+ +-+-+-+ +-+-+-+ - - +-+-+-+ +-+-+-+ +-+-+-+ - |2|2|5| |4|1|4| |5|0|4| - +-+-+-+ +-+-+-+ +-+-+-+ - |2|A|2| |1|A|1| |0|A|0| - +-+-+-+ +-+-+-+ +-+-+-+ - |5|2|2| |4|1|4| |4|0|5| - +-+-+-+ +-+-+-+ +-+-+-+ - - -The clue by anagram to those in search of “hidden treasure” who sought -to discover a dish-cover is _dish under a tree_. - - -No. XCV.--THE PUZZLED CARPENTER - -To stop a serious leak a carpenter sought for a board a foot square. The -only piece he could find was two feet square, but it was pierced with -sixteen holes, as in the diagram below:-- - -[Illustration] - -How did he contrive to cut a square from this of the necessary size? - - -The answer by anagram to “What should we all welcome, if the Chancellor -of the Exchequer could ‘introduce’ it into his Budget?” is _reduction_. - - -Things that we know to be “transient” must be looked at, according to -their anagram, _instanter_. - - -A MUSICAL ANAGRAM - -Sweet Mary, the Maid of the Mill, arranged an ingenious signal by song, -by which, in olden days, she could assure her father that all was well -when mischief was abroad. If he heard her singing, “Do, re, mi, fa, sol, -la, si,” he was sure that nothing was amiss. When these syllables are -shaken up, and recast as an anagram, what reassuring sentence do they -form? - -The musical syllables, sung as a reassuring signal to her father, by -Mary, the Maid of the Mill, “Do, re, mi, fa, sol, la, si,” when shaken -up and recast as an anagram form the sentence “A mill door is safe.” - - -No. XCVI.--NOT EASY WHEN YOU KNOW - -Of the many “match puzzles” the following seems to be the most confusing -to the ordinary solver, and any variation of its original position is -enough to create fresh confusion. - - +-----+-----+-----+ - | | | | - | | | | - +-----+-----+-----+ - | | | | - | | | | - +-----+ +-----+ - -Re-arrange three of these matches and form four squares. - - -The enigma anagram-- - - They were orthodox as beadles, - But in business tricks and wheedles - They were “sharp I see” as needles-- - -is solved by _Pharisees_. - - -The question--Where did we buy “our fancy mat?”--is answered by anagram -at the _manufactory_. - - -No. XCVII.--SIMPLICITY - -Construct this figure with five matches:-- - - /\ - / \ - / \ - ---- - \ / - \ / - \/ - -Remove three of the matches, and then replace two of them so as to form -a similar figure. - - -A common and much-appreciated “dose at meat shop” is, according to its -anagram, _mashed potatoes_. - - -Tiglath-Pileser was the name of the king which can be resolved into the -anagram, “I till the grapes.” - - -“Art? I begin art!” is an anagram for _Great Britain_. - - -If heartily administered, _nine thumps_, the anagram of “punishment,” -would fall deservedly upon the shoulders of a wife-beater. - - -ANSWER BY ANAGRAM - -Our strongest “armaments” are _men-at-arms_. - - -No. XCVIII.--OVER THE WINE AND WALNUTS - -Can you build a bridge with three wooden matches, which shall connect -three wine-glasses, and be solid enough to support a fourth set upon it? - -[Illustration] - -This picture shows how it is to be done. - - -The _elephant_, according to its anagram, is the animal to which the -command “Leap then!” would be the least appropriate. - - -The answer by anagram to “Whom should we employ to make ‘alterations’ in -our overcoats?” is _Neat tailors_. - - -Where do we go to remedy “disease?” - - To the _seaside_. - -Who should make a good “manager?” - - _A German._ - - -No. XCIX.--FROM THE MATCHBOX - -Here is quite a simple match problem:-- - - ----- ----- ----- - | | | | - | | | | - ----- ----- ----- - | | | | - | | | | - ----- ----- ----- - | | | | - | | | | - ----- ----- ----- - -Can you remove eight of these matches, that now form nine squares, so as -to leave only two squares upon the table? - - -When Cato and Chloe, at the Popular Café, decided to order for their -afternoon tea a pot of what is formed by the mixture of the letters of -their names, they called for _Chocolate_. - - -The answer by anagram to “Why may the scenery round Bournemouth be said -to be ‘quite spruce’?” is--because it is _picturesque_. - - -Lord Roberts’ motto, “Virtute et Valore,” is by its anagram _True to -avert evil_, a happy indication of his character. - - -No. C.--LIFT NINE WITH ONE - -To arrange ten matches on a table, so that with one hand you can lift -nine of them with the tenth, lay them, as is shown in Fig. 1, with the -heads of eight pillowed on one, and pointing in opposite directions, and -the tenth placed across the ridge at the top. - -[Illustration: Fig. 1] - -[Illustration: Fig. 2] - -Then lift all, as shown in Fig. 2. - - -A MAN HIS OWN ANAGRAM - -The enigma-- - - Behold in me a man forlorn, - Who, though with sound limbs he was born, - His anagram alas is! - For he has found out to his cost, - While all his nimbleness is lost, - How slippery wet grass is! - -is solved by _Male, lame_. - - -The answer by anagram to the question, “Whom do ‘our big hens’ -frequently annoy?” is _neighbours_. - - -No. CI.--FREEHAND DRAWING - -This is the way to draw in three strokes an old woman looking out of a -window:-- - -[Illustration] - - -Here is a puzzle anagram:-- - - Tell how to spell my name, - As on the stall you spy me, - For the letters are the same - Which bid you how to buy me. - - _Peach--cheap._ - - -The eglantine is the flower which quite contradicts its anagram, -_inelegant_. - - -The touching epitaph in memory of little Alice formed from the letters -of her name was _à ciel_! - - -No. CII.--A NOTABLE ANAGRAM - - sparkle - +-------+ - | Cats | - we | on | on. - | Truck | - +-------+ - Yes! - -Treated as an anagram the words “Cats on truck” can be recast into _Nuts -to crack_, and the surrounding motto, “Yes! we sparkle on” into -_Pearsons Weekly_; so that the whole design resolves itself into--_Nuts -to crack, in Pearson’s Weekly_. - - -The old saying that a man who is his own doctor has a fool for his -patient, seems to be borne out by the curious fact that the words, -“Dangers of amateur physicking,” resolve themselves into the perfect -anagram--“_The sick men pay for drugs again_.” - - -A ’VARSITY ANAGRAM - - What every “undergraduate” hates-- - - _A great rude dun_. - - -The food for a crocodile which seems to be indicated by its name is -_cool’d rice_! - - -No. CIII.--WITH DRAWN SWORD - -Here is a very simple and ingenious method of representing roughly an -officer with drawn sword. - -[Illustration] - -Six wax vestas, shredded to form the hair and sword-belt, are fastened -together by the application of a little heat. - -Anyone with handy fingers and an ingenious turn of mind can easily -construct other quaint figures in this style. - - -“Time and tide wait for no man.” - -ITS ANAGRAMS - -A fine mandate to mind, I trow. - -_and_ - -A firm intent made, a “do it now.” - - -No. CIV.--SHADOWGRAPHS - -Here are three excellent shadowgraphs, which can be produced with good -effect by flexible fingers in a strong light on the wall. - -[Illustration] - - -“Norway’s Olaf is in old England.” - -ITS ANAGRAMS - - Elf-lad, so loyal and so winning. - - A darling son and noisy fellow. - - Of winning lads, lead, royal son! - - On London’s air wing safely lad. - - -ANSWERS BY ANAGRAM - - Why should _city life_ be happy? - - Because the same letters spell _felicity_. - - -What is the best proof that “real stickphast paste sticks?” - -The same letters spell--_Keep this, stick scraps at last_! - - -ANSWERS BY ANAGRAM - -What place have our puzzles “in magic tale?” - - They are _enigmatical_. - - -What great assembly would seem from its name to consist of “partial -men?” - - _Parliament._ - - -CHARACTER BY ANAGRAM - -What did Douglas Jerrold, by his name anagram, declare himself to be? - - _Sure, a droll dog I!_ (_i for j_) - - -What in the old-fashioned days caused “the wig” to be discarded? - - _Weight._ - - -The following curious peace anagrams are appropriate in these days of -disturbance. Each set of words between inverted commas contain exactly -the same letters:-- - - “To escape fray” I ever “stay for peace,” - In “quiet times,” too, “I’m quite set” at ease: - Let no “vile words” provoke the “evil sword,” - Lest “red war” come, and bring its own “reward.” - - -Why does the old proverb “Birds of a feather flock together” form a -mystic link between us and our cousins in America? - -Because the same letters recast spell out the patriotic sentence, _It -rocks the broad flag of the free_! - - -What, by their anagram, are “platitudes?” - - _Stupid tales._ - - -Why is there a measure to “disappointment?” - - Because it is _made in pint pots_. - - -What is the purpose of a “catalogue?” - - It is _got as a clue_. - - -If “porcus” is Latin for pig, what is Latin for its body? - - _Corpus._ - - -What may “laudation” easily become? - - _Adulation._ - - -What is “revolution?” - - _To love ruin._ - - -Define “The Griffin” (Temple Bar). - - _Fine fright._ - - -Why is there room for variety in “twelve sentences?” - - Because we can _select new events_. - - -How do we know that “potatoes” in the singular should not have an “e” at -the end? - - Because they spell _O stop at e_! - - -What should be done to a “misanthrope?” - - _Spare him not._ - - -What was the owl of “Minerva?” - - _A vermin!_ - - - These, wherever they are found, - Cluster lightly overhead. - Should you chance to turn them round - Blows may tell of weight instead. - Twisted in a foreign tongue, - You will see them as they are. - Changed again they need a bung - When you move them full and far. - -This is solved by the anagram words _nuts_, _stun_, _sunt_, _tuns_. -(_Sunt_ is Latin for “they are.”) - - -IPSISSIMA VERBA - -A discussion arose one day, in the winter season, between several -members of a West-end Club, as to the value of flannel underwear. A -London physician, who was appealed to, upheld the need for this, and it -was afterwards found that his name, Alfred James Andrew Lennane, treated -as an anagram, becomes “Man needs aired flannel wear.” This was -singular, but a much more curious coincidence of similar sort was -discovered by an expert in anagrams. - -Another member took quite an opposite view, and declared that all should -wear linen. By a wonderful chance his name, Edward Bernard Kinsila, -resolves itself into the _actual words_ that came from his lips--“A -d---- bad risk Dr., wear linen!” - - -A CHRISTMAS CARD - - | | - -+----------------------------------+- - | AN ANAGRAM | - | | - |“Christmas comes but once a year.”| - |So by Christ came a rescue to man.| - -+----------------------------------+- - | | - - -PALINDROMES - -OR - -SENTENCES THAT READ BOTH WAYS - - -NAPOLEON’S PALINDROME - - Able was I ere I saw Elba. - - -ADAM AND EVE’S PALINDROME - - Madam, I’m Adam! - - -When Charles Grant, Colonial Secretary, was made Lord Glenelg, in 1835, -he was called Mr Facing-both-ways, because his title Glenelg was a -perfect palindrome, that could be read with the same result from either -end. - -It was a member of the same family who sought to prove the antiquity of -his race by altering an “i” into an “r” in his family Bible, so that the -text ran, “there were Grants on the earth in those days.” - - -A GOOD PALINDROME - -“Roma, ibi tibi sedes, ibi tibi amor,” which may be rendered, “At Rome -you live, at Rome you love;” is a sentence which reads alike from either -end. - - -A QUAINT PALINDROME - - Eve damned Eden, mad Eve! - -This sentence reads alike from either end. - - -A good specimen of a palindrome is this German saying that can be read -from either end:-- - - Bei Leid lieh stets Heil die Lieb - (In trouble comfort is lent by love.) - - -Here are some ingenious palindromes, which can be read from either -end:-- - -Repel evil as a live leper. - -Dog, as a devil deified, lived as a god. - -Do Good’s deeds live never even? Evil’s deeds do O God! - - -A SCHOOLBOY’S PALINDROME - - “Subi dura a rudibus” - -“I have, endured roughness from the rod” which can be read alike from -either end. - - -Very notable as a long palindrome, even if it is not true record of the -great surgeon’s experience, is this quaint sentence:--“Paget saw an -Irish tooth, sir, in a waste gap.” - - -A PEACE PALINDROME - - Snug & raw was I ere I saw war & guns. - -This sentence reads alike from either end. - - -A PALINDROME PUZZLE - - A turning point in every day, - Reversed I do not alter. - One half of me says haste away! - The other bids me falter.--_Noon._ - - -Very remarkable for its length and good sense combined is the following -palindrome, which can be read from either end with the same -result:--“No, it is opposed, art sees trades opposition.” - - -A PERFECT PALINDROME - -Perhaps the most perfect of English palindromes is the excellent adage-- - - “Egad, a base tone denotes a bad age.” - - -Here is the most remarkable Latin palindrome on record:-- - - SATOR AREPO TENET OPERA ROTAS - -Its distinguishing peculiarity is that the first letters of each -successive word unite to form the first word, the second letters spell -the second word, and so on throughout the five words; and as the whole -sentence is a perfect palindrome, this is also true on reversal. - -[Illustration] - - -SOLUTIONS - - -No. III.--A BOOK AND ITS AUTHOR - -The well-known book and its author which are represented by - -[Illustration: A||] - -are “Innocents Abroad,” by Mark Twain. (In no sense A broad, by mark -twain.) - - -No. IV.--ON THE SHUTTERS - - +-----------------+-----------------+ - | No.|I | - | JOHN MAR|SHALL | - | IN ATTEN|DANCE | - | FROM 8 A.M.|DAILY | - | BARBER|AND | - | HAIR C|UTTER | - | THE BALD CRY A|LOUD | - | FOR HI|S CREAMS | - | AS DISPLAYED|IN THIS WINDOW | - |WHICH MAKE HAIR G|LISTEN | - | CLOSES|AFTER 8 P.M. | - +-----------------+-----------------+ - -The shutter on the left blew open, leaving the other to tell its strange -tale. - - -No. VI.--SOLVITUR AMBULANDO - -A man, tracing step by step the various readings of ROTATOR on this -chequered floor, can exhaust all of them, according to the arrangement -on our diagram, in 21,648 steps, spelling out the word as he goes in the -many directions 3608 separate times! - - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - |=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=| - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O |=R=| O | T | A | T | O | T | A | T | O |=R=| O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | O |=R=| O | T | A | T | A | T | O |=R=| O | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | A | T | O |=R=| O | T | A | T | O |=R=| O | T | A | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | A | T | O |=R=| O | T | O |=R=| O | T | A | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O | T | A | T | O |=R=| O |=R=| O | T | A | T | O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - |=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=| - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O | T | A | T | O |=R=| O |=R=| O | T | A | T | O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | A | T | O |=R=| O | T | O |=R=| O | T | A | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | A | T | O |=R=| O | T | A | T | O |=R=| O | T | A | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | T | O |=R=| O | T | A | T | A | T | O |=R=| O | T | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - | O |=R=| O | T | A | T | O | T | A | T | O |=R=| O | - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - |=R=| O | T | A | T | O |=R=| O | T | A | T | O |=R=| - +---+---+---+---+---+---+---+---+---+---+---+---+---+ - -This large total is due mainly to the fact that ROTATOR is a palindrome, -and lends itself to both backward and forward reading. The man, a -veritable rotator, will thus have walked more than four miles within a -compass of one hundred and forty-four square feet. - - -No. VIII.--AN OLD SAMPLER - - | | - -+----------------------------+- - | AL. IT. | - |T.L. EW. O. MA! | - |N.T. Ho! UGH AVE. Ryli. | - |T.T. Let. Hi! N.G.I. | - |S.S. We. Et. Erf. Art. Ha!| - |N.S. Ug. Ara. N.D.F. Lo! | - |W.E. R.S.T. Ha! TB. | - |L.O. O! Mins. Pri. | - | N. G. | - -+----------------------------+- - | | - -The cross-stitch legend on the old sampler, if its letters are read in -regular sequence, runs thus:-- - - A little woman, though a very little thing, - Is sweeter far than sugar, and flowers that bloom in spring. - - -No. XII.--STRIKE A BALANCE - -This diagram shows how, while the odd and even numbers of the nine -digits add up to 25 and 20 respectively, they can be arranged in two -groups so that the odd and the even add up to exactly the same sum. - - +----------------------+ - /| |\ - +-+----------------------+-+ - | | 1 | | - | | 3 2 | | - | | 5 4 | | - | | 7 6 79 | | - | | 9 8 5¹⁄₃ 84²⁄₆ | | - | | -- -- ----- ----- | | - | | 25 20 84¹⁄₃ 84¹⁄₃ | | - | | ==================== | | - +-+----------------------+-+ - \| |/ - +----------------------+ - - -No. XIII.--PUZZLE LINES - -The puzzle lines-- - - HKISTA! - MRS LR’S SR - MR LR KRS. - “BLR MR LR!” - MRS LR HRS-- - -when read according to the usual pronunciation of Mr and Mrs, and taking -the title from the Greek, become, by affinity of sound-- - - _He kissed her!_ - Mrs Lister’s sister - Mr Lister kisses. - “Blister Mr Lister!” - Mrs Lister hisses. - - -No. XIV.--IN MEMORIAM - -The puzzle epitaph-- - - | | - -+-------------------------+- - |WEON . CEW . ERET . WO | - |WET . WOM . ADEO . NE | - |NON . EFIN . DUST . WO | - |NO . WLI . FEB . EGO . NE| - | WILLIAM and MARGARET | - | TAYLOR | - | Anno Domini 1665 | - -+-------------------------+- - | | - -reads thus-- - - We once were two, - We two made one. - None find us two - Now life be gone. - - -No. XVI.--A QUAINT EPITAPH - - | | - -+------------------------------+- - |IT - OBIT - MORTI - MERA| - |PUBLI - CANO - FACTO - NAM | - |AT - RES - T - M - ANNO - XXX | - |ALETHA - TE - VERITAS | - |TE - DE - QUA - LV - VASTO | - |MI - NE - A - JOVI - ALTO | - |PERAGO - O - DO - NE - AT | - |STO - UT - IN - A - POTOR - AC| - |AN - IV - VAS - NE - VER - A | - | =R - I - P= | - -+------------------------------+- - | | - -reads into English thus:-- - -“I Tobit Mortimer, a publican of Acton, am at rest. Man, no treble X ale -that ever I tasted equal was to mine. A jovial toper, a good one at -stout in a pot or a can, I was never a rip!” - - -No. XIX.--SHAKESPEARE RECAST - -If you start with the first =T= in this combination, and then take every -third letter-- - - +----------------------+ - |HOUSE.CANOE.AFTER. | - |HOUR.PRINT.CAVE.CHILD | - |SASH.SLEVE.ACORN. | - |AMPLE.SAD.TATTA.HENA | - |MAT.ACHE.CAKE.TACHES, | - |HELIAC.SACQUE.USUAL. | - |ARBOR.SEE.MULCH.JACUR.| - | USE.STOP. | - +----------------------+ - -you will form the popular quotation, “Thrice is he armed that hath his -quarrel just.” - - -No. XX.--A DOUBLE ACROSTIC - -The excellent double Acrostic-- - - An old Italian bird we know - Whose heart was ever touched by snow. - - 1. None can press me without pain, - Pressure is against the grain. - 2. I am a king without my head. - 3. Here is another king instead. - -is solved thus:-- - -CORNIX - - 1. C or N - 2. (R) O -- I - 3. R e X - -We may tell those of our readers who have not studied the dead languages -that _cornix_ is the Latin for a crow, and that the word can be broken -up into _cor_, heart, and _nix_, snow, while _rex_ is, of course, a king -in Latin, as _roi_ is in French. The double meaning of corn is brought -out by “against the grain.” - - -No. XXI.--HIDDEN PROVERBS - -The five hidden proverbs are:-- - - “A rolling stone gathers no moss.” - - “Too many cooks spoil the broth.” - - “A live dog is more to be feared than a dead lion.” - - “You cannot eat your cake and have it.” - - “Peace hath her victories no less renowned than war.” - -Start from the central A, and work round and round. - - -No. XXVII.--WAS IT VOLAPÜK? - -Read backwards it becomes “Old birds are not caught with chaff.” - - -No. XXVIII.--ANOTHER EPITAPH - -(_On an Old Pie Woman_) - - BENE AT hint HEDU S.T.T.H. emo Uldy O - L.D.C. RUSTO F.N.E. L.L.B. - AC. hel orl AT Ely - W ASS hove N.W. how ASS Kill’d - Int heart SOF pi escu Star - D. sand Tart Sand K N ewe, - Ver yus E oft he ove N.W. Hens he - ’Dliv’ Dlon geno - UG H.S. hem Ade he R la STP uffap - UF FBY HE RHU - S. B an D. M. - Uchp R.A. is ’D no Wheres He dot - H L. i.e. TOM a Kead I.R.T.P. Iein hop est - Hat he R.C. Rust W I - L.L.B. ERA IS’D----! - -This puzzle epitaph, written aright, runs thus:-- - - Beneath in the dust the mouldy old crust - Of Nell Bachelor lately was shoven, - Who was skilled in the arts of pies, custards, and tarts, - And knew every use of the oven. - - When she’d liv’d long enough she made her last puff, - A puff by her husband much prais’d; - Now here she doth lie to make a dirt pie, - In hopes that her crust may be rais’d. - - -No. XXXI.--BY LEAPS AND BOUNDS - - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | tle | to | a |cat- |life | and |live | In | - | | | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | By | tle | ow- |bro | of | non |tle |fall | - | | | |wse | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | ter |tur- | gain| like|land |one’s|quiet| And | - | | | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | of | ar | Bet-| me | and |Than | a- |bat- | - | | m | | ad- | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - |bask | Be | lau-| or | tle |ness |done |wan- | - | | t- | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | rel | let |Than |die |With | der | of | smo | - | | | | | | | | ke | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | ter | in |brain|myr- | on | and |har- | un- | - | | | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - | | | | | | | | | - | Ch | or |to |sun |with |work | In |heat | - | ap- | | | | | | | - +-----+-----+-----+-----+-----+-----+-----+-----+ - -The “Knight’s Tour” verses run as follows:-- - - Better to die with harness on - In smoke and heat of battle, - Than wander and browse, and fall anon - In quiet of meadow-land cattle. - Better to gain, by arm or brain, - Chaplet of laurel or myrtle, - Than bask in sun, with work undone, - And live one’s life like a turtle, - -beginning with “Bet,” and ending in the top left-hand corner. - - -No. XXXII.--A BROKEN SQUARE - -The Broken Word Square is made perfect thus-- - - S O B E R - O L I V E - B I S O N - E V O K E - R E N E W - - -No. XXXIII.--A KNIGHT’S TOUR PROVERB - - +-+-+-+-+-+-+-+ - | | | | | | | | - +-+-+-+-+-+-+-+ - | | | | |E| | | - +-+-+-+-+-+-+-+ - | | |E| | | |T| - +-+-+-+-+-+-+-+ - | | | |L|H| | | - +-+-+-+-+-+-+-+ - | |E| |R| |S| | - +-+-+-+-+-+-+-+ - | | |E|A|S| | | - +-+-+-+-+-+-+-+ - |D| |E| |O| |S| - +-+-+-+-+-+-+-+ - | | | |S|P| |M| - +-+-+-+-+-+-+-+ - -To solve the “Knight’s Tour” proverb start with M, and by a succession -of moves, as of a knight on the chess-board, you can spell out the -proverb “More haste less speed.” - - -No. XXXIV.--GUARINI’S PROBLEM - -The solution of Guarini’s Problem, to transpose the positions of the -white and black knights on the subjoined diagram on which they appear, -is made clear by following the moves on the lettered diagram:-- - - +---+---+---+ - | N |...| N | - +---+---+---+ - |...| |...| - +---+---+---+ - | n |...| n | - +---+---+---+ - - +---+---+---+ - | a | C | d | - +---+---+---+ - | D | | B | - +---+---+---+ - | b | A | c | - +---+---+---+ - -First move the pieces from a to A, from b to B, from c to C, and from d -to D. Then move them from A to d, from B to a, from C to b, and from D -to c. The effect so far is as if the original square had been rotated -through one right angle. Repeat the same sequence of moves, and the -required change of positions is completed. - - -No. XXXV.--AN ANAGRAM SQUARE - -This is the solution of the Word Square. - - +-------------+ - | A M E N D S | - | M I N I O N | - | E N A B L E | - | N I B B L E | - | D O L L A R | - | S N E E R S | - +-------------+ - - -No. XXXVII.--A KNIGHT’S TOUR - -The letters on the board below, read aright in the order of a Knight’s -moves at chess, starting from the most central E form the following -popular proverb:-- - - +-+-+-+-+-+-+-+-+ - |R|L|T|E|Y|L|R|O| - +-+-+-+-+-+-+-+-+ - |Y|H|L|T|O|B|T|A| - +-+-+-+-+-+-+-+-+ - |T|A|A|A| |H|T|I| - +-+-+-+-+-+-+-+-+ - |E|L| |E|I|N|E|O| - +-+-+-+-+-+-+-+-+ - |D|H|W| |Y|E|S|Y| - +-+-+-+-+-+-+-+-+ - |R|T|E|S|D| |B|W| - +-+-+-+-+-+-+-+-+ - |Y|N|E|S|N|D|A|E| - +-+-+-+-+-+-+-+-+ - |H|A|A|A|W|I|D|E| - +-+-+-+-+-+-+-+-+ - - “Early to bed, and early to rise, - Is the way to be healthy, and wealthy, and wise.” - - -No. XXXVIII.--A WORD SQUARE - -Dr Puzzlewitz completed his Word Square thus:-- - - E R A S E - R A V E N - A V E R T - S E R V E - E N T E R - - -No. XXXIX.--THE SQUAREST WORD - -This is completed thus:-- - - D E L F - E V I L - L I V E - F L E D - -It will be seen that there are four distinct readings of each word. - - -No. XL.--A PUZZLE DIAMOND - -The Diamond is completed thus:-- - - D - T I P - T I A R A - D I A M O N D - P R O U D - A N D - D - - -No. XLI.--A DEFECTIVE DIAMOND - -The Defective Diamond is completed thus:-- - - S - G E M - P E R I L - G E N E R A L - S E R E N A D E R - M I R A C L E - L A D L E - L E E - R - - -No. XLIII.--LETTER PUZZLE - -The word is _Level_, filled in thus:-- - - L E V E L - E E E E - V V V - E E E E - L E V E L - - -No. XLVII.--THE CIRCLE SQUARED - -The Circle can be squared thus:-- - - C I R C L E - I N U R E S - R U L E S T - C R E A S E - L E S S E E - E S T E E M - - -No. XLVIII.--A BROKEN SQUARE - -This is the completed Square:-- - - +-+-+-+-+-+-+-+ - |B|O|A|S|T|E|R| - +-+-+-+-+-+-+-+ - |O|B|S|C|E|N|E| - +-+-+-+-+-+-+-+ - |A|S|S|E|R|T|S| - +-+-+-+-+-+-+-+ - |S|C|E|P|T|R|E| - +-+-+-+-+-+-+-+ - |T|E|R|T|I|A|N| - +-+-+-+-+-+-+-+ - |E|N|T|R|A|N|T| - +-+-+-+-+-+-+-+ - |R|E|S|E|N|T|S| - +-+-+-+-+-+-+-+ - - -No. XLIX.--A CARD PROBLEM - -Here is the arrangement of the aces, kings, queens, and knaves of a pack -of cards in a kind of Magic Square:-- - - +--------+--------+--------+--------+ - | CLUBS | SPADES | HEARTS |DIAMONDS| - | ACE | KING | QUEEN | KNAVE | - +--------+--------+--------+--------+ - |HEARTS |DIAMONDS| CLUBS | SPADES | - | KNAVE | QUEEN | KING | ACE | - +--------+--------+--------+--------+ - |DIAMONDS| HEARTS | SPADES | CLUBS | - | KING | ACE | KNAVE | QUEEN | - +--------+--------+--------+--------+ - | SPADES | CLUBS |DIAMONDS| HEARTS | - | QUEEN | KNAVE | ACE | KING | - +--------+--------+--------+--------+ - -In each row, column, and diagonal, one, and one only, of the four suits -and of the four denominations is represented. - - -No. L.--TURF-CUTTING - -The eight thin strips of turf, cut from my lawn to form the four sides -of two square rose-borders, can be placed on a level surface of soil -thus without being broken or bent:-- - -[Illustration] - -This forms a framework for the three flower-beds of similar shape and -size. - - -No. LI.--A READY RECKONER - -The gardener decided that the water-butt was more than half-full thus:-- - -[Illustration] - -He tilted it steadily, and some of the water ran over its edge before -the bottom corner _A_ came into sight; but as soon as the water level -stood at _A B_ the cask was exactly half full. - - -No. LII.--A TRANSFORMATION - -The flat-headed 3 can be turned into a 5 by one continuous line, without -scratching out any portion of the 3, by treating the flat top of the 3 -as part of a square drawn round the 5, thus:-- - -[Illustration] - - -No. LIII.--A CLEAR COURSE - -Here is a list of ninety-two positions, in which eight pieces can be -placed upon the chess or draughtboard so that each has a clear course in -every direction. - - ++==+====+====+==+====+====+==+====+====+==+====+====++ - || 1|1586|3724|24|3681|5724|47|5146|8273|70|6318|5247|| - || 2|1683|7425|25|3682|4175|48|5184|2736|71|6357|1428|| - || 3|1746|8253|26|3728|5146|49|5186|3724|72|6358|1427|| - || 4|1758|2463|27|3728|6415|50|5246|8317|73|6372|4815|| - || 5|2468|3175|28|3847|1625|51|5247|3861|74|6372|8514|| - || 6|2571|3864|29|4158|2736|52|5261|7483|75|6374|1825|| - || 7|2574|1863|30|4158|6372|53|5281|4736|76|6415|8273|| - || 8|2617|4835|31|4258|6137|54|5316|8247|77|6428|5713|| - || 9|2683|1475|32|4273|6815|55|5317|2864|78|6471|3528|| - ||10|2736|8514|33|4273|6851|56|5384|7162|79|6471|8253|| - ||11|2758|1463|34|4275|1863|57|5713|8642|80|6824|1753|| - ||12|2861|3574|35|4285|7136|58|5714|2863|81|7138|6425|| - ||13|3175|8246|36|4286|1357|59|5724|8136|82|7241|8536|| - ||14|3528|1746|37|4615|2837|60|5726|3148|83|7263|1485|| - ||15|3528|6471|38|4682|7135|61|5726|3184|84|7316|8524|| - ||16|3571|4286|39|4683|1752|62|5741|3862|85|7382|5164|| - ||17|3584|1726|40|4718|5263|63|5841|3627|86|7425|8136|| - ||18|3625|8174|41|4738|2516|64|5841|7263|87|7428|6135|| - ||19|3627|1485|42|4752|6138|65|6152|8374|88|7531|6824|| - ||20|3627|5184|43|4753|1682|66|6271|3584|89|8241|7536|| - ||21|3641|8572|44|4813|6275|67|6271|4853|90|8253|1746|| - ||22|3642|8571|45|4815|7263|68|6317|5824|91|8316|2574|| - ||23|3681|4752|46|4853|1726|69|6318|4275|92|8413|6275|| - ++==+====+====+==+====+====+==+====+====+==+====+====++ - -The numbers indicate the position on the eight successive columns of the -cells on which the men are to be placed. Of course, many similar -arrangements arise from merely turning the board. - - -No. LIV.--QUARRELSOME NEIGHBOURS - -This diagram shows, by the dotted lines, how the three unfriendly -neighbours made the covered pathways to their gates, so that they might -never meet or cross each other’s paths. - -[Illustration] - - -No. LVI.--THE CROSS KEYS - -The Cross Keys puzzle when put together takes the form shown below. - -[Illustration] - -The method is as follows:--Hold _a_ upright between forefinger and thumb -of left hand. With the right hand push _b_ through the slot until the -further edge of the middle slot is nearly even with the outer edge of -_a_. Then lower _c_, held with the short arm of the cross nearest to -you, over the top of _a_, so that the central portion passes through the -cross cut in _b_. Finally push _b_ towards the centre, until the -transverse cut is hidden, and the puzzle is completed. - - -No. LVII.--THE NABOB’S DIAMONDS - -When the children of the Indian Nabob divided his diamonds, the first -taking one stone and a seventh of the remainder, the second two stones -and a seventh of what was left, the third three under similar -conditions, and so on till all were taken, there were 36 diamonds and 6 -children. - -The division is prettily illustrated thus:-- - - ○○○○○ - ○○○○○● ○○○○○ - ○○○○○● ○○○○○ - ○○○○○● ○○○○○ - ○○○○○● ○○○○○ - ○○○○○● ○○○○○ - ○○○○○● ●●●●●● - - ○○○○ - ○○○○● ○○○○ - ○○○○● ○○○○ - ○○○○● ○○○○ - ○○○○● ○○○○ - ○○○○● ○○○○ - ○○○○● ●●●●●● - - ○○○ - ○○○● ○○○ - ○○○● ○○○ - ○○○● ○○○ - ○○○● ○○○ - ○○○● ○○○ - ○○○● ●●●●●● - -This shows how the first three took their shares, indicated by black -dots, the remainder being carried down each time, and by similar process -three more claimants would exhaust all the diamonds. - - -No. LVIII.--A CARD CHAIN - -To solve the Card Chain puzzle take a card about 5 in. by 3 in., as -shown below, draw a light pencil line from _A_ to _B_ and from _C_ to -_D_, lay the card in water till you can split its edges down to the -pencil lines, and put it aside to dry. - -With a sharp knife cut quite through the straight lines, but only half -through the dotted lines on the split edges. The corresponding figures -show the bar of each link, marking its two parts, which are connected by -the upper and under halves of the split portion. A little patient -ingenuity will now release link after link, and thus complete the chain. - -[Illustration] - - -No. LIX.--STRAY DOTS - - +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+--+-----+-----●-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--+-----+-----+-----●--+--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--+-----●-----+-----+--+--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+--●-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--●--+ - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--●-----+-----+-----+--+--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--+-----+-----●-----+--+--+-----+-----+-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - |\ | / \ | / \ | / \ | /|\ | / \ | / \ | / \ | /| - +--+-----+-----+-----+--+--+-----●-----+-----+--+ - |/ | \ / | \ / | \ / | \|/ | \ / | \ / | \ / | \| - +--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+--+ - - -No. LX.--THE OPEN DOOR - - +-+-+-+-+-+-+-+-+ - |A | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | | - + + + + + + + + + - | x | - +-+-+-+-+-+-+-+-+ - -The prisoner who is placed in the cell marked A, and is promised his -liberty if he can reach the door at _X_ by passing through all the -cells, entering each once only, gains his freedom by passing from _A_ to -the cell below, and thence _returning_ to _A_, and leaving it again _by -the other door_; his further course then is quite simple. - - -No. LXII.--LEAP FROG - -[Illustration] - -Move 9 to 13, 3 to 9, 7 to 3, 22 to 7, 18 to 22, 24 to 18, 9 to 24, 13 -to 9, 7 to 13, 3 to 7, 18 to 3, 22 to 18. - - -No. LXIII.--MUSIC HATH CHARMS - -is explained by the couplet-- - - “From _Handel_ I learn - As my _handle_ I turn.” - - -No. LXVII.--A SWARM OF WORDS - -This is the key - - M - A - M A D A M - A - M - -If these letters form each of the five crosses the conditions are all -fulfilled. - -[Illustration] - -In each cross the words Madam, Adam, Ada can be traced in sixteen -different directions, and the words Dam, am and a in four directions, so -that there are no less than three hundred and twenty readings of these -words in the whole mystic cross, and sixty-four in each separate cross, -though only three different letters are used. - - -No. LXVIII.--AFTER SOME SAD REVERSE - -[Illustration] - - -No. LXX.--A PICTURE PUZZLE - - “A misunderstanding between friends.” - - -No. LXXIV.--A NERVOUS SHOCK - -[Illustration] - - -No. LXXVIII.--A TRANSPARENCY - -[Illustration: 7119791/1119] - - -No. LXXXII.--A RE-BUS - -It was _Incubus_ that the driver of a London Road car hurled as a -scornful charge, at his rival on a motor car. - - -No. LXXXV.--CHEQUERS AND STRIPES - - +---+ +---+ +---+ +---+ +---+ - | 2 | | 1 | | 3 | | 3 | | 3 | - | | | | | | | | | | - | 2 | | 4 | | 1 | | 4 | | 3 | - +---+ +---+ +---+ +---+ +---+ - - +---+ +---+ +---+ +---+ +---+ - | | | | | | | | | | - | | | | | | | | | | - | | | | | | | | | | - +---+ +---+ +---+ +---+ +---+ - - +---+ +---+ +---+ +---+ +---+ - | 1 | | 3 | | 3 | | 5 | | 5 | - | | | | | | | | | | - | 5 | | 6 | | 5 | | 6 | | 5 | - +---+ +---+ +---+ +---+ +---+ - - +---+ +---+ +---+ +---+ +---+ - | | | | | | | | | | - | | | | | | | | | | - | | | | | | | | | | - +---+ +---+ +---+ +---+ +---+ - -Put a finger on one of the black backs in the top row, and move that -stone round to the bottom of its column, then push upward, so that each -stone rises into the row above it. Repeat this with the other back, and -the stripes are formed. - - -No. LXXXVIII.--A PICTURE PUZZLE - -The eight animals hidden in this wood are-- _Giraffe_, _Lion_, _Camel_, -_Elephant_, _Hog_, _Horse_, _Bear_, _Hound_. - -[Illustration] - - -No. XC.--A REBUS - -[Illustration] - -The solution is _Wellington_. - - -No. XCV.--THE PUZZLED CARPENTER - -The carpenter, anxious to stop a leak, was able to cut a board a foot -square from a board two feet square, which was pierced at regular -intervals by sixteen holes, by the following ingenious method:-- - -[Illustration] - - -No. XCVI.--NOT EASY WHEN YOU KNOW - -The solution of the puzzling match rearrangement is as follows:--We -repeat the original five square diagram, from which four squares were to -be formed by rearranging three matches, and its solution below. - - +-----+ +-----+ - | | | | - | | | | - +-----+-----+-----+ - | | | | - | | | | - +-----+-----+-----+ - - +-----+ +-----+ - | | | | - | | | | - +-----+-----+-----+-----+ - | | | | - | | | | - +-----+ +-----+ - - -No. XCVII.--SIMPLICITY - -When we have constructed this figure with five matches, we can remove -three of the matches, and then replace two of them so as to form a -similar figure, by moving any three of them a short distance, and then -replacing the two that are left behind, in their original positions! -This “catch” finds many victims. - - /\ - / \ - / \ - ------ - \ / - \ / - \/ - - -No. XCIX.--FROM THE MATCHBOX - -The diagram below shows how eight matches can be removed from the -nine-square arrangement so as to leave two squares on the table. - - ----- ----- ----- - | | - | | - ----- - | | | | - | | | | - ----- - | | - | | - ----- ----- ----- - - -MISSING WORDS SOLUTIONS - - -1 - - What tempting _sprite_ beguiled the boy to sample - Fruit that hung _ripest_ on the parson’s trees? - _Stripe_ upon _stripe_ shall make him an example - When the stern _priest_ has brought him to his knees. - - -2 - - Man of the dark room, _traces_ none I find - Upon these _cartes_ of likeness to my features. - _Carest_ thou naught, O man of evil mind, - Who _racest_ thus to libel fellow creatures? - - Evil thus done _reacts_ upon the doer, - The _carets_ in thy conduct, sir, are many; - _Recast_ thy life, and let thy crimes be fewer, - Or all thy _crates_ of good won’t fetch a penny! - - -3 - - The missing words all spelt with the same - seven letters, are _tho’ near_, _a hornet_, _or neath_, _nor - hate_, _or then a_, _near hot_, _than o’er_, _ten hoar_, _the - roan_, and _eat horn_. - - -4 - - ’Neath _bluest_ Indian seas fierce battles spread - ’Twixt _subtle_ hermit-crabs and other shellfish! - With horrid _bustle_ when their foes are dead - These crabs declare their shells _sublet_, so selfish. - - -5 - - Though _seated_ secure and _sedate_ in his cage, - Our Polly, when _teased_, will fly into a rage. - - -6 - - All courtly honours are but light - As grains that from a _grater_ fly; - And he who wears the _Garter_ bright - May haply in a _garret_ die. - - -7 - - I’d rather from a _manger_ eat, - I give my sacred word, - Than dine in slums where _ragmen_ meet, - And _German_ pedlars herd. - - -8 - - A much married _grandee_ of Cadiz - Once _angered_ some riotous ladies. - To _derange_ him they chucked - A _grenade_, but he ducked, - Which _enraged_ these rude ladies of Cadiz. - - -9 - - A lass and her lover were _warned_ by the sky - Not to _wander_ too far where no shelter was nigh. - She lingered behind, and _drew an_ old church, - St. _Andrew_ by name, and was left in the lurch. - - She tried a short cut through the park on the grass, - But sternly the _warden_ forbade her to pass. - Then helplessly stood the disconsolate maid, - When the lad she was soon to _wed ran_ to her aid. - - -10 - - When _weather_ smiles, and sunbeams play - On flowers that _wreathe_ and deck the green, - _Whate’er_ can match the scene so gay - _Whereat_ they crown the May-day queen? - - -11 - - ’Tis said of William, while his forces rested - On Albion’s _shores_, when Harold had been bested, - He made the _shoers_ of his _horses_ fuse - Saxon spear-heads, to fashion into shoes. - - -12 - - Happiness, brighter than _rubies_, is dead; - Life’s battle, sterner and _busier_ now, - Heals the sore _bruise_ that love left as it fled, - _Buries_ remembrance of long-broken vow! - - -13 - - Press critics fall on me like sharks: - “A shameless _patcher_ of odds and ends, - No _chapter_ original,” and more remarks - In adverse mood. But stay, my friends, - He _carpeth_ best who hath his record clean; - My faults are published, yours are yet unseen! - - -14 - - _Plates_ are his _staple_, fashion-forms of grace - In _pastel_ deftly hinted. - _Pleats_ soft as _petals_, crowned by Beauty’s face, - In _palest_ hues are tinted. - - -15 - - When Kate _no heart_ _nor heat_ displayed - _He ran to_ hide a tear; - “All love is dead _on earth_,” he said. - “_Another_ I’ll _not hear_!” - - -16 - - Some grinding at the _tholes_ must toil, - Down-trodden _helots_ of to-day; - While other children of the soil - In vast _hotels_ their wealth display. - - -17 - - Betrayed by faithless friends, in _sadder_ mood - Man _dreads_ his fellows as the _adder’s_ brood. - - -18 - - With divers _inks_ his _skin_ is scarred, - He hangs a bangle in his nose; - Such marks secure his _kin’s_ regard, - Exalt his fame, and _sink_ his foes. - - -19 - - _Steward_, who, as we _west’ard_ roll, - _Drawest_ for me the foaming bowl, - And _wardest_ off unfriendly spray - With oilskin-cape, thou shalt not say - “In vain I’ve _strawed_ my favours here.” - I’ll think of thee when port is near! - - -20 - - With high _ideals_ for hearts and hands, - These _ladies_ _sailed_ for distant lands. - - -21 - - The _premiss_ of his speech did not - _Impress_ his audience a jot. - They greeted all he said thereafter - With _simpers_, smiles, and open laughter. - - -22 - - To convent shrine at break of day - With _palms_ together nuns repair; - Mid gleaming _lamps_ they kneel and pray, - And chanted _psalm_ allays each care. - - -23 - - Here once, as a hag is bedizened with paint, - A _devil_ _lived_, _veil’d_ in the garb of a saint. - - -24 - -The missing words of the lines “In praise of Sussex,” are _apers_, -_rapes_, _spear_, _spare_, _pears_, _reaps_, _parse_, _pares_, all spelt -with the same letters. - - -25 - -The missing words are _there_, _ether_, and _three_. - - -26 - -The missing words are _trades_, _daters_, _treads_, _darest_, and -_read’st_. - - -27 - - The _Tsar_ with _arts_ importunate - To rule his _tars_ may try; - His _star_ is so unfortunate - That “_rats_” they may reply! - - -28 - -The missing words are _mace_, _acme_, and _came_. - - -29 - -The missing words are _esprit_, _sprite_, _priest_, _stripe_, and -_ripest_. - - -30 - - Of all destructive country pests - The farmer _loves_ _voles_ least; - He cannot yet the puzzle _solve_ - How to suppress the beast! - - -31 - -The “Fresh Air Fund” missing words are given below in italics:-- - -OH THE _LUSTRE_ OF THE _RESULT_ - - The _slimes_ of darkest London are radiant with _smiles_, - You can _read_ it in their _dear_ little faces: - So wherever you _reside_ let it be your heart’s _desire_ - To ease the _cares_ and sorrows of all _races_! - - -32 - - She _rouges_ in vain, “Men are _rogues_, and as shy - As _grouse_ in October,” she says with a sigh. - -33 - - When good men lapse the _Serpent_ grins, - When one _repents_ he swears; - And strives to set his former sins - Against his _present_ prayers. - - -34 - - His hands and face were _swart_, and sad - Upon the _straw_ a gipsy lad - Lay: as the breeze his temples fanned - He counted _warts_ on either hand. - - -35 - - In yon grey _manse_ an old divine - Taught me my “_mensa_” to decline, - And verbs with _names_ of mood and tense; - But while I plodded on apace - I had to keep the _means_ of grace, - And close his prayers with loud _amens_. - - -36 - - No reckless _drawer_ of the sword, - He _warred_ his fatherland to save. - Fighting for freedom, not _reward_, - Now _warder_ of the eastern seas. - - -37 - - A fair _design_, though _singed_ and frayed, - The critic _deigns_ to own, - And it might interest the trade - If _signed_ by some one known. - - -38 - - In his _latter_ days, as when he was young, - The _tatler_ indulges in _rattle_ of tongue. - - -39 - -The missing words indicated in the lines which begin - - A cylindrical lock - Where no key can be found. - -are a _ringlet_, _triangle_, _relating_, _altering_, and _integral_, -which are all spelt with the same eight letters. - - -40 - -The lines with missing words, which are increased each time by one -letter, run thus:-- - - A lover of _an_ unkind fair - Were less than _man_ did he not _moan_, - “Mine is no _nomad_ life, I swear, - It dwells in this _domain_ alone. - Grant me thy love, like _diamond_ chaste - _On diadem_, lest thou live unwooed, - _Doomed in a_ lonely life to waste - The treasure of sweet _maidenhood_.” - - -41 - -The missing words are _bared_, _beard_, _debar_, _bread_. - - -42 - -THE PAUPER’S PLAINT - - Pale penury that _rivest_ social bands, - And any link that _rivets_ worth to fame, - Take ye the blame for my inactive hands, - I _strive_ in vain to build upon the sands, - Without a _stiver_, who can make a name? - - -43 - - Mr Backslide, afflicted with weakness of mind, - _Cantered_ over to Lushington’s inn, where he dined. - He _recanted_ the pledge he had taken as handy, - And emptied forthwith a _decanter_ of brandy. - - -44 - -The missing words are indicated below by italics:-- - - A _sutler_ sat in his _ulster_ grey, - Watching the moonbeams _lustre_ play - On a keg that in the bushes lay; - And these were the words of his song:-- - “Thou _rulest_ the weak, thou _lurest_ the strong, - To thee the _result_ of bad deeds doth belong.” - And the leaves with a _rustle_ took up the sad song. - -It would be difficult to find a better specimen than this of seven words -spelt with the same letters. - - -45 - -In these lines each of the words in italics is longer by one letter than -the one before, the same letters being carried on in varied order:-- - - Nature _I_ love _in_ every land, - On burning plain, by wooded rill; - Where _Ind_ is girt by coral strand, - Or _Edin_ rears her castled hill. - Then _deign_ from me the tale to hear, - How, true to one _design_, the bee - Once _singled_ out keeps year by year - The _leadings_ by her instinct given, - Which teach her, wheresoe’er she roam, - In every clime beneath the heaven, - To build the same _six-angled_ home. - - -46 - -The missing words are _smite_, _times_, _emits_, _items_, and _mites_. - - -47 - -The missing words of the Farmyard puzzle are printed in italics:-- - - All his flock from _danger_ rough, - To the _garden_ ran apace, - Where their _gander_, old and tough, - _Ranged_, the guardian of his race. - - -48 - - Come, landlord, fill the flowing _pots_, - Until their _tops_ run over; - For in this _spot_ to-night I’ll _stop_, - To-morrow _post_ to Dover! - - -49 - -The four missing words are _silent_, _listen_, _enlist_, and _tinsel_, -which are all spelt with the same letters. - - -50 - - Some men their _teams_ escorted on their way, - When “_Mates_ look here!” I heard a driver say: - “It _tames_ our pluck to toil like _steam_ all day, - When, wanting _meats_, we starve on wretched pay.” - - -51 - -WISDOM WHILE YOU WAIT - - As a _general_ _gleaner_ of facts you’ll find - Our Encyclopædia _enlarge_ the mind. - - -52 - -The missing words are _nectar_, _Cretan_, _canter_, _trance_, _recant_. - -53 - - _I Satan_ but for rebel act - Without _a stain_ should be; - But this _is at an_ end, in fact - None find _a saint_ in me. - - -54 - - “Oh for a _break_ in this vast solitude, - This endless rise and fall of _brake_ and moor!” - Soliloquised a _baker_ in sad mood, - As through the lonely hills the staff of life he bore. - - -55 - -THE SEA SERPENT - - ’Twas in _mid-ocean_ that we saw him play, - Like a _demoniac_ in his sports, and they - Amused us, as a good _comedian_ may. - - -56 - - Soup is _on table_ for a _notable_ divine, - Who with _no table_ is _not able_ to sit down and dine. - - -57 - - Sweet as the _rose_ and cruel as its thorn, - _Eros_ thy power is great, thy pity scorn. - Swift as the _roes_ that through the forest fly, - Deep as the _ores_ that deepest hidden lie, - Is thine own _sore_ to hapless mortals given, - Semblance of darkest hell or brightest heaven. - - -58 - -The missing words, dedicated to the Fresh Air Fund, read thus:-- - -GOOD _TIMES_ FOR CITY _MITES_ - - My pipe _emits_ for _me its_ charms, that yield - Pictures and _items_ of a children’s day. - Lest conscience _smite_ I _sit me_ down to say - My _mites_ shall send some City _mites_ afield. - - -59 - - He said “you _Cretan_,” when one lied, - He said “don’t _canter_,” when one hied, - His glass held _nectar_ at his side, - He can _recant_ what he denied. - - -60 - - Mr Snip, the _agnostic_, was _coasting_ a hill, - With a bag of new _coatings_ for stock; - When a runaway motor-car gave him a spill - Which scattered his doubts with the shock. - - -61 - - _Pales_ her fair cheek, and back o’er all - The _lapse_ of years _leaps_ memory. - Those wedding _peals_ to her recall - The _pleas_ he urged so tenderly. - - -62 - - Two burglars attempted to _rifle_ a house, - But the _filer_ was heard, though as still as a mouse. - When challenged at once he a _flier_ became, - But caught as a _lifer_ he finished his game. - - -63 - - The _licensed_ fool in olden days - Gave kings advice in jesting phrase; - He’s _silenced_ now: the modern throne - _Declines_ all follies but its own. - - -64 - - Days of _dearth_, and times of evil, - Starving girls with _thread_ do toil, - No man _dareth_ feast or revel, - Hushed is _hatred_ and turmoil. - - -65 - - Who _reineth_ in his pride and rage, - To _neither_ vice a prey, - May hope to reach a green old age, - And find _therein_ his stay. - - -66 - -This is the full text of Moore’s witty reply, when Limerick courted him -as her member, and the “boys for fun’s sake” asked him to what party he -belonged:-- - - “I’m of no party as a man, - But as a poet _am--a--tory_!” - - -67 - - Is England _Israel_? That this is so - A solemn _serial_ aspires to show. - By most ignored, the theme _is real_ to some, - Who gravely to the same conclusion come. - Like _Ariels_ o’er obstacles they soar, - And if an _earl is_ ’vert they rave the more. - - -68 - - Off to the links is now their cry, - For golf is man’s _idolatry_: - Be not _dilatory_ or slow, - _Adroitly_ hit the ball will go. - - -69 - - No maid e’er _resided_, North, South, East, or West, - More _desired_ than she who _derides_ Love’s request. - - -70 - - Though in _adversity_ I be, - It is, alas! _sad verity_ - No _vestry aid_ comes nigh to me. - - -71 - - _Mastering_ his pride the royal James - Came down upon the _streaming_ Thames; - Like _emigrants_ his court repair - To breath _St Germain_’s freer air. - - -72 - -The drop letter lines are as follows:-- - - With lily leaves his oars are _trifling_, - Her eager hands their treasures _rifling_. - To the fair winds all cares _I fling_, - And echo faintly answers _fling_! - - -73 - -The solution of the enigma with missing letters:-- - -“There was no good ... in the d...y, so the klim,” is-- - -There was no good air in the dairy, so the milk turned. - - -74 - -But unmerciful disaster followed fast and followed faster. - - -75 - -If you write _stale_ _tales_, at _least_ do not _steal_ the _slate_. - - -76 - -The six missing words are _Siren_, _risen_, _Erin’s_, _reins_, _rinse_, -_resin_. - - -77 - - A man of _parts_ had caught a _sprat_, - And it was windy weather; - “Give me my _strap_,” he cried, “to fix - My fish and _traps_ together.” - - -78 - -The missing words are _Cesar_, _acres_, _races_, _cares_, _scare_. - - -79 - - Buy my ripe _melons_, my _lemons_ who’ll buy? - Don’t look so _solemn_, but take some and try! - - -80 - - He who _nips_ may _snip_ at last, - How to _spin_ we show; - Take a sixpence, hold it fast, - Press the _pins_ and blow! - - -[Illustration] - - - PRINTED BY M‘LAREN AND CO., LTD., EDINBURGH. - - - - - Transcriber’s Notes - - - Inconsistent spelling, hyphenation, capitalisation, etc. and lay-out - have been retained, except as mentioned below. The same applies to - repetitions, (factual) errors, mistakes, unclarities and - contradictions in the puzzles, riddles etc. and in the solutions - provided. - - Depending on the hard- and software and their settings used to read - this text, not all elements may display as intended. Several of the - puzzles will only display as intended if a fixed-width font is used. - - An attempt has been made to include, where possible, the illustrations - in this text. These are only rough approximations; the actual - illustrations (and therefore better representations of the book’s - contents) are available in the other formats provided at - www.gutenberg.org. Some of the larger elements have been split to fit - in the available width. Some of the symbols used for this graphic - representation are used to approximate the symbols used in the book - rather than for their usual meaning. - - Domino tiles are represented by blocks with the number of pips - inscribed rather than by the pip patterns (or they are left blank to - indicate back sides). For the chess problems, a schematic - representation has been used, in which dots represent black squares, - and K, Q, B, R, N, P and k, q, b, r, n, and p represent white and - black king, queen, bishop, rook, knight and pawn respectively. - - Page I-7, Monster Magic Square: row 2 column 2 should be 48, not 41; - row 3 column 9 should be 92, not 72. - - Page I-30, magic triangle, bottom row 0 should be 8 (as in the - solution on page I-150). - - Page I-89, "on opposite sides of the central line": this should be - read "on opposite sides of the central lines" (both horizontal and - vertical). - - Page I-130, mens’ tears: as printed in the source document. - - Page I-131, An Illusion of Type: the phenomenon described may not work - with every font. - - Page I-136, For the Children, last sentence: the opposite is true: If - this is an even quantity the coins or sweets in the right hand are - odd, and in the left even; if it is odd the contrary is the case. - - Page II-130, number 81: some words were misprinted or missing - altogether; these have been added based on the context: ... the man - [fe]ll sick ...; [Ho]w ought his estate ...; and ... to [the] widow, - son and daughter. - - Page II-148, Notable Chronogram: IAVDES should have read LAVDES, which - would result in the year 1894 (when the organ was blessed). - - Page II-176, Solution LXXX: The positions of the dots are indicated in - the text only, not in the diagram. - - Page II-204, Solution 65, 12 + ¹⁄₂ = ¹³⁄₂: the calculation only works - if the 12 were replaced with ¹²⁄₂ (or 6), which would be in accordance - with the description. - - Page II-206, Solution 77: _two_ and _twenty_ pence should probably - read _two and twenty_ pence. - - Page III-3 and III-111, No. III: The illustration in the question is - not the same as the one in the answer. - - Page III-25, Begins 2 U U U up: possibly an error for Begins 2 UU U up - (cf. other repeated letters). - - Page III-35, No. XXXV, five words: there are six words in the puzzle - (and in the solution). - - Page III-53, No. LIII: the occupied squares on the chess board are - indicated by an X. - - Page III-77, inspiréd strain: as printed in the source document. - - - Changes made - - Some obvious minor typographical and punctuation errors and misprints - have been corrected silently. - - Some minor lay-out inconsistencies have been standardised without - further remarks; where necessary, table and text-elements have been - re-arranged and aligned in accordance with the description given. - - The part numbers have been inserted on the blank pages preceding each - part. - - Throughout the book, items from one category (preceded by an Arabic - number) are occasionally printed split over two pages, with one or - more items from other categories (often preceded by a Roman numeral) - between the several parts. For this text, these split items have been - recombined on the page where they originally started, and references - to their respective parts have been deleted. - - The part numbers (I, II and III) have been added to the page numbers - for easier reference. - - Page I-141: "cigars" changed to "cigares" (French, 2x). - - Page II-99, 6¹ changed to 6¹⁄₂. - - Pages II-113 and II-185, illustration: reference letter "F" added. - - Page II-199: "there they sold" changed to "these they sold". - - Page II-225, Solution 6: "f _on_ d l _over_" changed to "a f _on_ d l - _over_". - - Page III-7, No. VII: "BVT In trVth" changed to "bVt In trVth". - - Page III-7 and III-44, No. VII and XLIV: The chronographs were printed - in small capitals and upper case letters; the former have been - transcribed as lower case letters to retain the meaning according to - the description. - - Page III-41, No. 67: "And if -- ---- is ’vert" changed to "And if an - ---- -- ’vert". - - Page III-46: "chêrit" changed to "chérit". - - Page III-67, illustration: unprinted asterisk added to the right-hand - arm of the cross. - - Page III-78: "a jamais" replaced with "à jamais". - - Page III-108: "stats" replaced with "stets". - - Page III-123, Solution XLIII: V inserted in bottom line cf. puzzle. - - Page III-124: "stripes" changed to "strips" cf. puzzle. - - Page III-128: "86 diamonds and 6 children" changed to "36 diamonds and - 6 children". - -*** END OF THE PROJECT GUTENBERG EBOOK TWENTIETH CENTURY STANDARD PUZZLE -BOOK *** - -***** This file should be named 63884-0.txt or 63884-0.zip ***** -This and all associated files of various formats will be found in: - http://www.gutenberg.org/6/3/8/8/63884/ - -Updated editions will replace the previous one--the old editions will -be renamed. - -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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