149. THE CHOCOLATE SQUARES. Here is a slab of chocolate, indented at the dotted lines so that the twenty squares can be easily separated. Make a copy of the slab in paper or cardboard and then try to cut it into nine pieces so that they will form four perfect squares all of exactly the same size.

SOLUTION TO 349. STALEMATE. (3/3) Show more

SOLUTION TO 349. STALEMATE. (2/3) Show more

SOLUTION TO 349. STALEMATE. (1/3) Show more

349. STALEMATE. Some years ago the puzzle was proposed to construct an imaginary game of chess, in which White shall be stalemated in the fewest possible moves with all the thirty-two pieces on the board. Can you build up such a position in fewer than twenty moves?

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

SOLUTION TO 304. BACHET'S SQUARE. (3/4) Show more

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

SOLUTION TO 304. BACHET'S SQUARE. (1/4) Show more

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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. (2/2)

304. BACHET'S SQUARE. One of the oldest card puzzles is by Claude Caspar Bachet de Méziriac,
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)

SOLUTION TO 76. THE BARREL OF BEER. (2/2) Show more

SOLUTION TO 76. THE BARREL OF BEER. (1/2) Show more

...
without manipulating in any way the contents. (2/2)

76. THE BARREL OF BEER. A man bought an odd lot of wine in barrels and one barrel containing beer. These are shown in the illustration, marked with the number of gallons that each barrel contained. He sold a quantity of the wine to one man and twice the quantity to another, but kept the beer to himself. The puzzle is to point out which barrel contains beer. Can you say which one it is? Of course, the man sold the barrels just as he bought them, (1/2)

SOLUTION TO 272. THE NINE SCHOOLBOYS. (3/3) Show more

SOLUTION TO 272. THE NINE SCHOOLBOYS. (2/3) Show more

SOLUTION TO 272. THE NINE SCHOOLBOYS. (1/3) Show more

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might be grouped on the first day as follows:--

A B C
D E F
G H I

Then A can never walk again side by side with B, or B with C, or D with E, and so on. But A can, of course, walk side by side with C. It is here not a question of being together in the same triplet, but of walking side by side in a triplet. Under these conditions they can walk out on six days; under the "Schoolgirls" conditions they can only walk on four days. (2/2)

272. THE NINE SCHOOLBOYS. This is a new and interesting companion puzzle to the "Fifteen Schoolgirls" (see solution of No. 269), and even in the simplest possible form in which I present it there are unquestionable difficulties. Nine schoolboys walk out in triplets on the six week days so that no boy ever walks _side by side_ with any other boy more than once. How would you arrange them?

If we represent them by the first nine letters of the alphabet, they (1/2)

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