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 (1/2)

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SOLUTION TO 304. BACHET'S SQUARE. (2/4)

Dudeney's Amusements@dudeney_puzzles@mathstodon.xyzSOLUTION TO 304. BACHET'S SQUARE. (3/4)

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assuming that the A, K, Q, J must be arranged in the form 1, and the D,

S, H, C in the form 2. He thus included reflections and half-turns, but not quarter-turns. They may obviously be interchanged. So that the correct answer is 2 × 576 = 1,152, counting reflections and reversals as different. Put in another manner, the pairs in the top row may be written in 16 × 9 × 4 × 1 = 576 different ways, and the square then