FRONTISPIECE

The words which describe this picture can be recast, letter for letter, into the perfect anagram—

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No. IV.

It is said that there are 86 ways in which the numbers in this model magic square can be added up so that they make 34.

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It is not difficult to discover more than half this number that are symmetrical, including, of course, the 4 rows, 4 columns and 2 diagonals. Here are a dozen samples, from which others can be seen—

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No. VIII

Here is the completed magic square—

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Every row, column and diagonal adds up to exactly 1908.

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No. IX

This up-to-date magic square adds up to 1908 in quite 56 different symmetrical ways.

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Here are 44 of them—

There are a dozen other ways, more or less symmetrical, such as 481, 474, 483, 470; or 474, 485, 470, 479.

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No. X

This is the rearrangement of the domino magic square—

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The three-ace, which was a corner stone in the former diagram now occupies the centre, and the rearrangement was effected by first transferring the two bottom rows to the top, and then the fourth and fifth columns to the extreme left. This method of shifting the stones does not affect the magic quality of the square.

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No. XI

The affinity between chess and numbers is well illustrated by the Knight’s tour on this diagram—

The Knight starts from the square marked 1, and returns at last to it. The constant difference between any opposite and corresponding numbers in cells that are equidistant from the centre is 18.

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No. XII

Here are the cells in the diagram of our Numbers Patience, so filled in that each of the rows across from side to side adds up exactly to 143.

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Each cell contains, in accordance with the conditions, a different number.

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No. XIII

This is the division of a square into fifteen parts, which will form the windmill:—

This puzzle may, of course, be reversed, the parts of the square being given, and the solver asked to form with them a symmetrical windmill.

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No. XIV

In this nest of 49 squares it is possible to count 784 distinct interlacing figures, whose opposite sides are equal, and whose angles are all right angles.

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Of these 784 rectangles 140 are squares.

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No. XV

This is the domino magic square, in which all the stones are used except double-six, double-five and six-five.

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All rows, columns and diagonals add up to 27, as do the stones in the four corner cells and the four central border cells of the full square, and of the square of nine cells in the middle.

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No. XVI

Those to whom games of Patience appeal will find an interesting and pretty form of it in the construction of a pyramid with a complete set of dominoes.

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Solvers may like to study the position given, which is one of many that are possible, and to discover for themselves the ruling conditions which are its characteristics.

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No. XVII

When the boy’s father came up just in time to stop him from breaking out of bounds, and said, “Never throw a leg, lad,”