Part 1

Transcriber’s Notes

Text printed in italics have been transcribed _between underscores_, underlined text =between equal signs=, and spaced out text ~between tildes~. Small capitals have been changed to ALL CAPITALS.

More Transcriber’s Notes may be found at the end of this text.

PICTURED PUZZLES AND WORD PLAY

_=BY THE SAME AUTHOR=_

UNIFORM WITH THIS VOLUME

THE TWENTIETH CENTURY STANDARD PUZZLE BOOK

Crown 8vo. Cloth Extra. Gilt.

PICTURED PUZZLES AND WORD PLAY

A COMPANION TO THE TWENTIETH CENTURY STANDARD PUZZLE BOOK

EDITED BY A. CYRIL PEARSON, M.A. AUTHOR OF “100 CHESS PROBLEMS,” “ANAGRAMS, ANCIENT AND MODERN,” ETC.

_PROFUSELY ILLUSTRATED_

LONDON GEORGE ROUTLEDGE & SONS, LTD. NEW YORK: E. P. DUTTON & CO.

CONTENTS.

FRONTISPIECE PUZZLE

PAGE PICTURED PUZZLES AND WORD PLAY 1 ENIGMAS, CHARADES, PUZZLES, &C., &C. 130 ODDS AND ENDS 188 SOLUTIONS TO PICTURED PUZZLES 202 „ „ WORD PLAY 283 „ „ ODDS AND ENDS 375

PICTURED PUZZLES

No. I.--A GOOD SPECIMEN

Here is a nest of magic squares, seven of them within the four corners of one diagram:--

╔═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╗ ║149│ 16│ 33│196│ 47│197│ 44│208│ 42│203│ 57│194│ 38│ 54│217║ ╟───╆━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╅───╢ ║177┃ 62│183│ 52│213│ 59│160│ 15│161│ 85│156│190│105│ 28┃ 49║ ╟───╂───╆━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╅───╂───╢ ║ 56┃147┃201│146│ 75│155│ 2│220│ 3│153│ 53│ 26│209┃ 79┃170║ ╟───╂───╂───╆━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╅───╂───╂───╢ ║162┃ 76┃148┃180│ 83│187│ 41│104│ 22│195│145│ 60┃ 78┃150┃ 64║ ╟───╂───╂───╂───╆━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╅───╂───╂───╂───╢ ║ 74┃176┃ 4┃124┃119│ 37│154│ 48│186│138│109┃102┃222┃ 50┃152║ ╟───╂───╂───╂───╂───╆━━━┿━━━┿━━━┿━━━┿━━━╅───╂───╂───╂───╂───╢ ║221┃ 24┃175┃ 63┃ 86┃116│ 93│135│ 94│127┃140┃163┃ 51┃202┃ 5║ ╟───╂───╂───╂───╂───╂───╆━━━┿━━━┿━━━╅───╂───╂───╂───╂───╂───╢ ║ 10┃215┃ 69┃159┃134┃ 95┃ 98│126│115┃131┃ 92┃ 67┃157┃ 11┃216║ ╟───╂───╂───╂───╂───╂───╂───┼───┼───╂───╂───╂───╂───╂───╂───╢ ║219┃ 19┃165┃ 1┃136┃ 97┃130│113│ 96┃129┃ 90┃225┃ 61┃207┃ 7║ ╟───╂───╂───╂───╂───╂───╂───┼───┼───╂───╂───╂───╂───╂───╂───╢ ║ 8┃205┃ 84┃191┃ 87┃158┃111│100│128┃ 68┃139┃ 35┃142┃ 21┃218║ ╟───╂───╂───╂───╂───╂───╄━━━┿━━━┿━━━╃───╂───╂───╂───╂───╂───╢ ║214┃ 34┃144┃ 27┃112┃ 99│133│ 91│132│110┃114┃199┃ 82┃192┃ 12║ ╟───╂───╂───╂───╂───╄━━━┿━━━┿━━━┿━━━┿━━━╃───╂───╂───╂───╂───╢ ║ 14┃123┃ 55┃106┃117│189│ 72│178│ 40│ 88│107┃120┃171┃103┃212║ ╟───╂───╂───╂───╄━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╃───╂───╂───╂───╢ ║206┃ 89┃181┃166│143│ 39│185│122│204│ 31│ 81│ 46┃ 45┃137┃ 20║ ╟───╂───╂───╄━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╃───╂───╂───╢ ║ 58┃101┃ 17│ 80│151│ 71│224│ 6│223│ 73│173│200│ 25┃125┃168║ ╟───╂───╄━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╃───╂───╢ ║118┃198│ 43│174│ 13│167│ 66│211│ 65│141│ 70│ 36│121│164┃108║ ╟───╄━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━┿━━━╃───╢ ║ 9│210│193│ 30│179│ 29│182│ 18│184│ 23│169│ 32│188│172│ 77║ ╚═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╝

As each border is removed a fresh magic square remains, in which the numbers in the cells of each row, column, and diagonal add up to the same sum, while each of these sums is a multiple of the central 113.

No. II.--A BORDERED DIAMOND

By G. Slater

┌ │ ┌───┘ │ 91 ┌───┘ ┌ │ 3 │ ┌───┘ ┌───┘ │ 27 │ 25 ┌───┘ ┌───┘ ┌ │156 │154 │ ┌───┘ ┌───┘ ┌───┘ │161 │ 15 │138 ┌───┘ ┌───┘ ┌───┘ ┌ │130 │153 │136 │ ┌───┘ ┌───┘ ┌───┘ ┌───┘ │162 │147 │120 │ 69 ┌───┘ ┌───┘ ┌───┘ ┌───┘ │ 39 │ 22 │ 55 │112 ┌───┘ ┌───┘ ┌───┘ ┌───┘ │ 4 │152 │ 76 │ 57 56 ┌───┘ ┌───┘ ┌───┘ ┌───┘ │168 │146 │139 │100 99 ┌───┘ ┌───┘ ┌───┘ ┌───┘ │ 6 │ 21 │ 29 │ 45 44 43 ┌───┘ ┌───┘ ┌───┘ ┌───┘ │157 │ 80 │ 30 │ 88 87 86 └───┐ └───┐ └───┐ └───┐ │ 53 │ 41 │134 │123 122 121 └───┐ └───┐ └───┐ └───┐ │ 10 │132 │ 89 │ 74 73 └───┐ └───┐ └───┐ └───┐ │105 │ 67 │ 35 │109 108 └───┐ └───┐ └───┐ └───┐ │ 5 │116 │137 │ 60 └───┐ └───┐ └───┐ └───┐ │144 │ 19 │107 │ 95 └───┐ └───┐ └───┐ └───┐ │ 11 │106 │ 68 │ └───┐ └───┐ └───┐ └ │118 │ 77 │ 37 └───┐ └───┐ └───┐ │ 92 │ 38 │ └───┐ └───┐ └ │163 │148 └───┐ └───┐ │ 12 │ └───┐ └ │ 66 └───┐ │ └

───┐ 1│ └───┐ 117│ ───┐ └───┐ 20│ 160│ └───┐ └───┐ 129│ 65│ ───┐ └───┐ └───┐ 42│ 38│ 165│ └───┐ └───┐ └───┐ 36│ 103│ 26│ ───┐ └───┐ └───┐ └───┐ 124│ 81│ 54│ 159│ └───┐ └───┐ └───┐ └───┐ 75│ 135│ 151│ 52│ └───┐ └───┐ └───┐ └───┐ 111 110│ 33│ 64│ 78│ └───┐ └───┐ └───┐ └───┐ 62 61│ 63│ 93│ 7│ └───┐ └───┐ └───┐ └───┐ 98 97 96│ 102│ 142│ 158│ └───┐ └───┐ └───┐ └───┐ 49 48 47│ 133│ 51│ 104│ └───┐ └───┐ └───┐ └───┐ 85 84 83 82│ 140│ 90│ 13│ ┌───┘ ┌───┘ ┌───┘ ┌───┘ 127 126 125│ 52│ 145│ 79│ ┌───┘ ┌───┘ ┌───┘ ┌───┘ 72 71 70│ 34│ 16│ 167│ ┌───┘ ┌───┘ ┌───┘ ┌───┘ 114 113│ 50│ 155│ 143│ ┌───┘ ┌───┘ ┌───┘ ┌───┘ 59 58│ 115│ 17│ 14│ ┌───┘ ┌───┘ ┌───┘ ┌───┘ 101│ 94│ 23│ 9│ ┌───┘ ┌───┘ ┌───┘ ┌───┘ 46│ 31│ 148│ 40│ ───┘ ┌───┘ ┌───┘ ┌───┘ 41│ 18│ 8│ ┌───┘ ┌───┘ ┌───┘ 128│ 24│ 131│ ───┘ ┌───┘ ┌───┘ 149│ 166│ ┌───┘ ┌───┘ 130│ 2│ ───┘ ┌───┘ 164│ ┌───┘ 169│ ───┘

It is a perfect magic diamond as it stands, and equally perfect are the diamonds that remain when each border of cells is removed, as is indicated by the lines.

WORD PLAY

1. A PARADOX

Two words in our region of puzzledom pose, And claim, through the passage of years That neither the pages of Johnson disclose, While either in Murray appears.

No. III.--A MULTIFOLD MAGIC SQUARE

Here is a magic square of 81 cells.

┌───┬───┬───┬───┬───┬───┬───┬───┬───┐ │ 53│ 8│ 71│ 28│ 73│ 10│ 51│ 6│ 69│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 62│ 44│ 26│ 19│ 37│ 55│ 60│ 42│ 24│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 17│ 80│ 35│ 61│ 1│ 46│ 15│ 78│ 33│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 66│ 21│ 30│ 14│ 59│ 50│ 34│ 79│ 16│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 3│ 39│ 75│ 77│ 41│ 5│ 25│ 43│ 61│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 48│ 57│ 12│ 32│ 23│ 68│ 70│ 7│ 52│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 31│ 76│ 13│ 72│ 27│ 36│ 11│ 56│ 47│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 22│ 40│ 58│ 9│ 45│ 81│ 74│ 38│ 2│ ├───┼───┼───┼───┼───┼───┼───┼───┼───┤ │ 67│ 4│ 49│ 54│ 63│ 18│ 29│ 20│ 65│ └───┴───┴───┴───┴───┴───┴───┴───┴───┘

If divided, as is shown, into 9 small squares, each of these is also a magic square, and yet another magic square is formed by the totals of these 9 squares arranged thus:--

┌───┬───┬───┐ │396│333│378│ ├───┼───┼───┤ │351│369│387│ ├───┼───┼───┤ │360│405│342│ └───┴───┴───┘

No. IV.--A MODEL MAGIC SQUARE

This magic square, which has in its cells the first sixteen numbers, is so constructed that these add up to 34 in very many ways.

╔═══╤═══╤═══╤═══╗ ║ 4│ 15│ 14│ 1║ ╟───┼───┼───┼───╢ ║ 9│ 6│ 7│ 12║ ╟───┼───┼───┼───╢ ║ 5│ 10│ 11│ 8║ ╟───┼───┼───┼───╢ ║ 16│ 3│ 2│ 13║ ╚═══╧═══╧═══╧═══╝

How many of these, in addition to the usual rows, columns, and diagonals, can you discover? They must, of course, be in some sort symmetrical.

2. A PREDOMINANT VOWEL

Can you fill in the missing letters which are needed to turn the oft-repeated “u” below into rhyming verse:--

.u.. .u.u. .u..u.., ..u...u. .u.. u..u.., .u... .u.., .u. .u..u.. .u..u... ..u...u. ..u..; ...u.. .u...., .u.. .u..u.. ..u... .u... .u... u..u.., U. .u...., .u.. ..u..-.u.u., .u..u.’. .u...u. .u..

No. V.--TESSELATED DIAMOND

By G. Slater

┏ ┃ ┏━━━╃ ┃ 13│ ┏━━━╃───┼ ┃113│ │ ┏━━━╃───┼───┼ ┃ 12│ │110│ ┌───╄━━━╅───┼───┼ │ 42│ ┃ 9│ │ ┌───┼───┼───╄━━━╅───┼ │ 74│ │ 81│ ┃112│ ┌───┼───┼───┼───┼───╄━━━╅ │ 67│ │ 53│ │ 87│ ┃ ┏━━━╃───┼───┼───┼───┼───┼───╄ ┃ 27┃ │ 49│ │ 50│ │ 35│ ┏━━━╃───╄━━━╅───┼───┼───┼───┼───╆ ┃ 96│ │ 26┃ │ 46│ │ 72│ ┃ ┏━━━╃───┼───┼───╄━━━╅───┼───┼───╆━━━╃ ┃ 30│ │ 95│ │ 97┃ │ 76│ ┃ 75│ ┏━━━╃───┼───┼───┼───┼───╄━━━╅───╆━━━╃───┼ ┃ 91│ │ 31│ │ 28│ │ 94┃ ┃ 40│ │ ┗━━━╅───┼───┼───┼───┼───╅━━━╃───╄━━━╅───┼ ┃ 92│ │ 90│ │ 25┃ │ 64│ ┃ 89│ ┗━━━╅───┼───┼───╆━━━╃───┼───┼───╄━━━╅ ┃ 29│ │ 93┃ │ 58│ │ 62│ ┃ ┗━━━╅───╆━━━╃───┼───┼───┼───┼───╄ ┃ 32┃ │ 66│ │ 60│ │ 57│ ┗━━━╃───┼───┼───┼───┼───┼───╆ │ 44│ │ 79│ │ 65│ ┃ └───┼───┼───┼───┼───╆━━━╃ │ 51│ │ 38│ ┃104│ └───┼───┼───╆━━━╃───┼ │ 88│ ┃ 22│ │ └───╆━━━╃───┼───┼ ┃ 99│ │ 23│ ┗━━━╅───┼───┼ ┃100│ │ ┗━━━╅───┼ ┃ 21│ ┗━━━╅ ┃ ┗

━━━┓ 106┃ ───╄━━━┓ │109┃ ───┼───╄━━━┓ 16│ │ 14┃ ───┼───┼───╄━━━┓ │107│ │ 15┃ ───┼───┼───╆━━━╃───┐ 11│ │100┃ │ 78│ ───┼───╆━━━╃───┼───┼───┐ │ 10┃ │ 56│ │ 71│ ───╆━━━╃───┼───┼───┼───┼───┐ 111┃ │ 83│ │43 │ │ 34│ ━━━╃───┼───┼───┼───┼───┼───╆━━━┓ │ 59│ │ 63│ │ 84│ ┃ 6┃ ━━━╅───┼───┼───┼───┼───╆━━━╃───╄━━━┓ 68┃ │ 39│ │ 37│ ┃115│ │ 7┃ ───╄━━━┓───┼───┼───╆━━━╃───┼───┼───╄━━━┓ │ 33┃ │ 85│ ┃ 3│ │116│ │114┃ ───┼───╄━━━╅───╆━━━╃───┼───┼───┼───┼───╄━━━┓ 61│ │ 82┃ ┃120│ │ 2│ │ 5│ │117┃ ───┼───╆━━━╃───╄━━━╅───┼───┼───┼───┼───╆━━━┛ │ 47┃ │ 41│ ┃119│ │121│ │ 8┃ ───╆━━━╃───┼───┼───╄━━━╅───┼───┼───╆━━━┛ 54┃ │ 69│ │ 86│ ┃ 4│ │118┃ ━━━╃───┼───┼───┼───┼───╄━━━╅───╈━━━┛ │ 73│ │ 52│ │ 80│ ┃ 1┃ ━━━╅───┼───┼───┼───┼───┼───╄━━━┛ 19┃ │ 45│ │ 48│ │ 36│ ───╄━━━╅───┼───┼───┼───┼───┘ │ 18┃ │ 55│ │ 70│ ───┼───╄━━━╅───┼───┼───┘ 103│ │105┃ │ 77│ ───┼───┼───╄━━━╅───┘ │ 20│ │102┃ ───┼───┼───╆━━━┛ 98│ │ 17┃ ───┼───╆━━━┛ │101┃ ───╆━━━┛ 24┃ ━━━┛

In this ingenious diamond all rows and both diagonals add up to 671; in the four corner diamonds all add up to 244; and in the central diamond, and the 16 rows of threes surrounding it, to 183.

3. AN ENIGMA

I see my first, I see my next, And both I sigh and see Joined to my third, which much perplexed And sorely puzzled me. ’Twas fifty, and ’twas something more, Reversed ’twas scarce an ell, With first and next it forms a whole Clear as a crystal bell. What is my whole? A splendid tear Upheld in cruel thrall; Blow soft, ye gales, bright sun appear! And bid me gently fall.

No. VI.--MAGIC SQUARE BY MULTIPLICATION

Here is a magic square, in which the rows, columns, and diagonals yield the same product, 4096, by multiplication:--

╔═══╤═══╤═══╗ ║128| 1 | 32║ ╟───┼───┼───╢ ║ 4 | 16| 64║ ╟───┼───┼───╢ ║ 8 |256| 2 ║ ╚═══╧═══╧═══╝

It will be seen that the numbers in this square, 1, 2, 4, 8, 16, 32, 64, 128, 256, are in regular progression, and 4096 is also the cube of the central 16.

No. VII.--ANOTHER BORDERED MAGIC SQUARE

Here is quite a good example of a bordered magic square of sixty-four cells:--

┏━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┯━━━┓ ┃ 1│ 56│ 55│ 11│ 53│ 13│ 14│ 57┃ ┠───╆━━━┿━━━┿━━━┿━━━┿━━━┿━━━╅───┨ ┃ 63┃ 15│ 47│ 22│ 42│ 24│ 45┃ 2┃ ┠───╂───╆━━━┿━━━┿━━━┿━━━╅───╂───┨ ┃ 62┃ 49┃ 25│ 40│ 34│ 31┃ 16┃ 3┃ ┠───╂───╂───┼───┼───┼───╂───╂───┨ ┃ 4┃ 48┃ 28│ 37│ 35│ 30┃ 17┃ 61┃ ┠───╂───╂───┼───┼───┼───╂───╂───┨ ┃ 5┃ 44┃ 39│ 26│ 32│ 33┃ 21┃ 60┃ ┠───╂───╂───┼───┼───┼───╂───╂───┨ ┃ 59┃ 19┃ 38│ 27│ 29│ 36┃ 46┃ 6┃ ┠───╂───╄━━━┿━━━┿━━━┿━━━╃───╂───┨ ┃ 58┃ 20│ 18│ 43│ 23│ 41│ 50┃ 7┃ ┠───╄━━━┿━━━┿━━━┿━━━┿━━━┿━━━╃───┨ ┃ 8│ 9│ 10│ 54│ 12│ 52│ 51│ 64┃ ┗━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┷━━━┛

It is a perfect specimen itself, and as each border is removed a fresh perfect magic square is revealed.

4. A CHARADE

Take for my first a quadruped, Transpose one for my second; My whole, a biped, quick or dead, Is dainty reckoned.

5. BYRON’S ENIGMA

I am not in youth, nor in manhood, nor age, But in infancy ever am known; I’m a stranger alike to the fool and the sage, And though I’m distinguish’d in history’s page I always am greatest alone.

I am not in earth, nor the sun, nor the moon; You may search all the sky--I’m not there; In the morning and evening--though not in the noon-- You may plainly perceive me--for, like a balloon, I am midway suspended in air.

Though disease may possess me, and sickness and pain, I am never in sorrow nor gloom; Though in wit and in wisdom I equally reign, I’m the heart of all sin, and have long lived in vain, Yet I ne’er shall be found in the tomb!

No. VIII.--A HARDY ANNUAL

A magic square can be formed with the 81 numbers from 172 to 252 inclusive, which in all its rows, columns, and diagonals will total 1908. It may interest our solvers to complete the square.

╔═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╤═══╗ ║216│175│224│ │ │ │240│199│248║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║247│215│174│ │ │ │190│239│207║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║206│246│214│ │ │ │230│198│238║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║ │ │ │213│172│221│ │ │ ║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║ │ │ │244│212│180│ │ │ ║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║ │ │ │203│252│211│ │ │ ║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║186│226│194│ │ │ │210│178│218║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║217│185│234│ │ │ │250│209│177║ ╟───┼───┼───┼───┼───┼───┼───┼───┼───╢ ║176│225│184│ │ │ │200│249│208║ ╚═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╧═══╝

We have filled in, as a solid start, 45 of the 81 cells.

No. IX.--ANOTHER “ANNO DOMINI”

This magic square adds up in rows, columns, and diagonals to 1908:--

╔═══╤═══╤═══╤═══╗ ║469│484│472│483║ ╟───┼───┼───┼───╢ ║481│474│478│475║ ╟───┼───┼───┼───╢ ║482│471│485│470║ ╟───┼───┼───┼───╢ ║476│479│473│480║ ╚═══╧═══╧═══╧═══╝

Can you decide in how many other symmetrical ways the same total is to be made?

No. X.--A DOMINO MAGIC SQUARE

In this magic square the rows, columns, and diagonals add up always to 33.

┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │ ● │ │ ● ● │ │ ● ● │ │ ● ● │ │ ● ● │ │ ● │ │ ● ● │ │ ● ● │ │ │ │ ● │ │ ● │ │ ● ● │ │ ● ● │ │ ● ● │ │ ● ● │ ├─────┤ ├─────┤ ├─────┤ ├─────┤ ├─────┤ │ │ │ ● │ │ │ │ ● ● │ │ │ │ ● │ │ ● │ │ │ │ │ │ ● │ │ │ │ ● │ │ │ │ ● ● │ │ │ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │ ● ● │ │ ● │ │ │ │ ● │ │ ● │ │ ● │ │ ● │ │ │ │ │ │ │ │ ● ● │ │ ● │ │ │ │ ● │ │ ● │ ├─────┤ ├─────┤ ├─────┤ ├─────┤ ├─────┤ │ ● ● │ │ ● ● │ │ ● ● │ │ │ │ ● ● │ │ ● │ │ │ │ ● │ │ ● │ │ ● ● │ │ ● ● │ │ ● ● │ │ ● ● │ │ │ │ ● ● │ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘

┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │ │ │ │ │ ● ● │ │ ● ● │ │ ● ● │ │ │ │ │ │ ● ● │ │ │ │ │ │ │ │ │ │ ● ● │ │ ● ● │ │ ● ● │ ├─────┤ ├─────┤ ├─────┤ ├─────┤ ├─────┤ │ ● ● │ │ ● │ │ ● ● │ │ ● ● │ │ ● │ │ │ │ │ │ ● ● │ │ ● │ │ │ │ ● ● │ │ ● │ │ ● ● │ │ ● ● │ │ ● │ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘

┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │ ● ● │ │ ● │ │ │ │ │ │ ● │ │ ● ● │ │ ● │ │ │ │ ● │ │ ● │ │ ● ● │ │ ● │ │ │ │ │ │ ● │ ├─────┤ ├─────┤ ├─────┤ ├─────┤ ├─────┤ │ ● ● │ │ ● ● │ │ ● ● │ │ ● │ │ ● │ │ ● │ │ ● │ │ │ │ ● │ │ ● │ │ ● ● │ │ ● ● │ │ ● ● │ │ ● │ │ ● │ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘

┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ ┌─────┐ │ ● │ │ ● │ │ ● │ │ ● ● │ │ ● ● │ │ │ │ │ │ ● │ │ ● ● │ │ ● ● │ │ ● │ │ ● │ │ ● │ │ ● ● │ │ ● ● │ ├─────┤ ├─────┤ ├─────┤ ├─────┤ ├─────┤ │ ● │ │ ● ● │ │ ● │ │ ● ● │ │ │ │ │ │ ● │ │ │ │ │ │ ● │ │ ● │ │ ● ● │ │ ● │ │ ● ● │ │ │ └─────┘ └─────┘ └─────┘ └─────┘ └─────┘

Can you rearrange it so that the first stone (three-ace) shall occupy the centre, now filled by the double six, and it shall still add up in all ways to 33?

6. SHIFTING LETTERS

I am bright as a whole Till you cut off my head; Then as black as a coal, Or a mortal instead.

Shaken up and recast We with science are found, Read us back from the last And we live underground.

No. XI.--CHESS AND NUMBERS

The arrangement of numbers in the 36 cells of this square discloses a very close affinity between chess and arithmetic.

╔═══╤═══╤═══╤═══╤═══╤═══╗ ║ 30│ 21│ 6│ 15│ 28│ 19║ ╟───┼───┼───┼───┼───┼───╢ ║ 7│ 16│ 29│ 20│ 5│ 14║ ╟───┼───┼───┼───┼───┼───╢ ║ 22│ 31│ 8│ 35│ 18│ 27║ ╟───┼───┼───┼───┼───┼───╢ ║ 9│ 36│ 17│ 26│ 13│ 4║ ╟───┼───┼───┼───┼───┼───╢ ║ 32│ 23│ 2│ 11│ 34│ 25║ ╟───┼───┼───┼───┼───┼───╢ ║ 1│ 10│ 33│ 24│ 3│ 12║ ╚═══╧═══╧═══╧═══╧═══╧═══╝

Can you follow this out?

7. A GOOD CHARADE

_By Horace Smith, one of the authors of_ “_Rejected Addresses._”

In arts and sciences behold my first the watchword still, All prejudice must bend the knee before its iron will; Yet “Onward!” is the Briton’s cry--a cry that doth express A holy work but half begun, and speaks of hopefulness.

In palace or in lonely cot its name alike is heard, And in the Senate’s lordly halls sit my second and my third. Strange paradox, though for my first my total is designed, Sad marks of vice and ignorance we in that whole may find.

No. XII.--NUMBERS PATIENCE

Those who combine a fancy for “Patience” with some skill in numbers will find amusement in filling the empty cells of this diagram with appropriate numbers, each of which must consist of two figures:--

╔═══╤═══╤═══╤═══╤═══╗ ║ 17│ │ │ │ 24║ ╟───┼───┼───┼───┼───╢ ║ │ 32│ │ 46│ ║ ╟───┼───┼───┼───┼───╢ ║ │ │ 14│ │ ║ ╟───┼───┼───┼───┼───╢ ║ │ 19│ │ 16│ ║ ╟───┼───┼───┼───┼───╢ ║ 22│ │ │ │ 20║ ╚═══╧═══╧═══╧═══╧═══╝

It is required that each of the rows across from side to side shall add up, when all the cells are filled, to 143 exactly. No number must be used more than once.

No. XIII.--THE WINDMILL

Can you divide a square into 15 parts, which can be built up into this windmill?

8. THRICE BEHEADED

Untouched I tell of budding growth and life; Beheaded I lead upward more or less; Again--with varied fragrance I am rife; Again--but little value I express.

No. XIV.--A NEST OF RECTANGLES

In this nest of 49 squares it is possible to count a great number of distinct and interlacing figures, whose opposite sides are equal, and whose angles are all right angles.

┌───┬───┬───┬───┬───┬───┬───┐ │ │ │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┼───┤ │ │ │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┼───┤ │ │ │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┼───┤ │ │ │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┼───┤ │ │ │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┼───┤ │ │ │ │ │ │ │ │ ├───┼───┼───┼───┼───┼───┼───┤ │ │ │ │ │ │ │ │ └───┴───┴───┴───┴───┴───┴───┘

Can you decide exactly the number of these rectangles, and say how many of them are square?

9. AN ENIGMA

Search Holy Writ and you will see A victory was won by me. Behead me, and I may be found In water or on hilly ground. Behead again, and then transpose, A snare my letters now disclose. If yet again my head you sever, No matter how sharp-set or clever ’Tis all in vain you look about, For no one yet has found me out.

No. XV.--ANOTHER DOMINO MAGIC SQUARE

Can you, using all the dominoes except double five, five-six, and double six, construct with the twenty-five stones a magic square that adds up in all rows, columns, and diagonals to 27, and in which the stones in the cells marked by the same figures in this diagram also add up to that number?

╔═══╤═══╤═══╤═══╤═══╗ ║ 2 │ │ 1 │ │ 2 ║ ╟───┼───┼───┼───┼───╢ ║ │ 4 │ 3 │ 4 │ ║ ╟───┼───┼───┼───┼───╢ ║ 1 │ 3 │ │ 3 │ 1 ║ ╟───┼───┼───┼───┼───╢ ║ │ 4 │ 3 │ 4 │ ║ ╟───┼───┼───┼───┼───╢ ║ 2 │ │ 1 │ │ 2 ║ ╚═══╧═══╧═══╧═══╧═══╝

No. XVI.--DOMINO PATIENCE

The problem is to construct, with all the twenty-eight stones, a domino pyramid of seven stages, starting with a single stone, and adding one stone on each successive stage.

The stones must be so arranged that the number of pips in any row or column are in all cases exactly three times the number of half-dominoes of which that line or column is composed. There are many solutions to exercise the solver’s patience.

10. LEGAL PLEASANTRIES

Said a lawyer aside to his friend in the court, “Now I’d bet, were we not in this place, That my first is my second a bottle of port,” Then bright with my whole shone his face.

11. RIVALS ON THE ROAD