WORD PLAY

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

Solution

Here is a magic square of 81 cells.

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 arrangedthus:—

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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.

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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

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

.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

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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.

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

Solution

Here is a magic square, in which the rows, columns, and diagonals yield the same product, 4096, bymultiplication:—

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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.

Here is quite a good example of a bordered magic square of sixty-fourcells:—

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

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

Solution

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 pageI 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!

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 pageI 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

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.

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

Solution

This magic square adds up in rows, columns, and diagonals to1908:—

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

Solution

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

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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

I am bright as a wholeTill you cut off my head;Then as black as a coal,Or a mortal instead.Shaken up and recastWe with science are found,Read us back from the lastAnd we live underground.

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

Shaken up and recastWe with science are found,Read us back from the lastAnd we live underground.

Solution

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

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Can you follow this out?

Solution

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 expressA 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.

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

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 twofigures:—

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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

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