Twentieth Century Standard Puzzle Book Three Parts in One Volume

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.

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.

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.

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.

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.

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.

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.

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.

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.

(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.

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?

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.

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.

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