This difficult word puzzle is given as an example of the use of chessboard analysis in solving such things.  Only a person who is familiar with the “Eight Queens” problem could hope to solve it.

304.—­BACHET’S SQUARE.

One of the oldest card puzzles is by Claude Caspar Bachet de Meziriac, first published, I believe, in the 1624 edition of his work.  Rearrange the sixteen court cards (including the aces) in a square so that in no row of four cards, horizontal, vertical, or diagonal, shall be found two cards of the same suit or the same value.  This in itself is easy enough, but a point of the puzzle is to find in how many different ways this may be done.  The eminent French mathematician A. Labosne, in his modern edition of Bachet, gives the answer incorrectly.  And yet the puzzle is really quite easy.  Any arrangement produces seven more by turning the square round and reflecting it in a mirror.  These are counted as different by Bachet.

Note “row of four cards,” so that the only diagonals we have here to consider are the two long ones.

305.—­THE THIRTY-SIX LETTER-BLOCKS.

[Illustration]

The illustration represents a box containing thirty-six letter-blocks.  The puzzle is to rearrange these blocks so that no A shall be in a line vertically, horizontally, or diagonally with another A, no B with another B, no C with another C, and so on.  You will find it impossible to get all the letters into the box under these conditions, but the point is to place as many as possible.  Of course no letters other than those shown may be used.

306.—­THE CROWDED CHESSBOARD.

[Illustration]

The puzzle is to rearrange the fifty-one pieces on the chessboard so that no queen shall attack another queen, no rook attack another rook, no bishop attack another bishop, and no knight attack another knight.  No notice is to be taken of the intervention of pieces of another type from that under consideration—­that is, two queens will be considered to attack one another although there may be, say, a rook, a bishop, and a knight between them.  And so with the rooks and bishops.  It is not difficult to dispose of each type of piece separately; the difficulty comes in when you have to find room for all the arrangements on the board simultaneously.

307.—­THE COLOURED COUNTERS.

[Illustration]

The diagram represents twenty-five coloured counters, Red, Blue, Yellow, Orange, and Green (indicated by their initials), and there are five of each colour, numbered 1, 2, 3, 4, and 5.  The problem is so to place them in a square that neither colour nor number shall be found repeated in any one of the five rows, five columns, and two diagonals.  Can you so rearrange them?

308.—­THE GENTLE ART OF STAMP-LICKING.