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Pictured Puzzles and Word Play / A Companion to the Twentieth Century Standard Puzzle Book cover

Pictured Puzzles and Word Play / A Companion to the Twentieth Century Standard Puzzle Book

Chapter 13: No. VII.—ANOTHER BORDERED MAGIC SQUARE
By A. Cyril Pearson
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About This Book

A lively compendium of illustrated puzzles and verbal amusements, organized into pictured puzzles, word-play (including anagrams, charades, enigmas, and riddles), and a miscellany of odds and ends, each followed by complete solutions. It pairs visual problems—magic squares, tessellated and domino designs, and geometric dissections—with linguistic challenges that test anagramming, cryptic clues, and witty charades, and includes numerical recreations linking chess and arithmetic. Diagrams and step-by-step answers support independent solving and practical learning.

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.

Solution

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

Images

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

Image

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.

Solution

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..

Solution

No. V.—TESSELATED DIAMOND
By G. Slater

  106  
  13   109  
  113   16   14  
  12   110   107   15  
  42   9   11   100   78  
  74   81   112   10   56   71  
  67   53   87   111   83   43   34  
  27   49   50   35   59   63   84   6  
  96   26   46   72   68   39   37   115   7  
  30   95   97   76   75   33   85   3   116   114  
91   31   28   94   40   61   82   120   2   5   117
  92   90   25   64   89   47   41   119   121   8  
  29   93   58   62   54   69   86   4   118  
  32   66   60   57   73   52   80   1  
  44   79   65   19   45   48   36  
  51   38   104   18   55   70  
  88   22   103   105   77  
  99   23   20   102  
  100   98   17  
  21   101  
  24  

Image

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.

Solution

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

Image

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

Image

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.

Solution

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!

Solution

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

Image

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

Solution

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

Image

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

Solution

No. X.—A DOMINO MAGIC SQUARE

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

    ●   ●   ●   ●   ●   ●   ●   ●   ●
  ●     ●   ●   ●   ●             ●  
●       ●   ●   ●   ●   ●   ●   ●   ●
            ●           ●   ●        
  ●       ●                       ●  
        ●               ●   ●        
 
●   ●       ●           ●       ●    
  ●       ●                          
●   ●   ●                   ●       ●
●   ●   ●   ●   ●   ●           ●   ●
  ●               ●       ●     ●   ●
●   ●   ●   ●   ●   ●           ●   ●
 
                ●   ●   ●   ●   ●   ●
                ●   ●                
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●   ●   ●       ●   ●   ●   ●   ●    
                ●   ●     ●          
●   ●       ●   ●   ●   ●   ●       ●
 
●   ●       ●                       ●
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●   ●   ●   ●   ●   ●       ●       ●
  ●       ●               ●       ●  
●   ●   ●   ●   ●   ●   ●       ●    
 
●       ●           ●   ●   ●   ●   ●
                   ●     ●   ●   ●   ●
    ●       ●   ●       ●   ●   ●   ●
●       ●   ●   ●       ●   ●        
          ●                       ●  
    ●   ●   ●       ●   ●   ●        

Image

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?

Solution

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.

Solution

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

Image

Can you follow this out?

Solution

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.

Solution

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

Image

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.

Solution

No. XIII.—THE WINDMILL