384.—­THE CROSS TARGET.

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In the illustration we have a somewhat curious target designed by an eccentric sharpshooter.  His idea was that in order to score you must hit four circles in as many shots so that those four shots shall form a square.  It will be seen by the results recorded on the target that two attempts have been successful.  The first man hit the four circles at the top of the cross, and thus formed his square.  The second man intended to hit the four in the bottom arm, but his second shot, on the left, went too high.  This compelled him to complete his four in a different way than he intended.  It will thus be seen that though it is immaterial which circle you hit at the first shot, the second shot may commit you to a definite procedure if you are to get your square.  Now, the puzzle is to say in just how many different ways it is possible to form a square on the target with four shots.

285.—­THE FOUR POSTAGE STAMPS.

+—–­+——­+——­+——­+
| 1 |  2 |  3 |  4 |
+—–­+——­+——­+——­+
| 5 |  6 |  7 |  8 |
+—–­+——­+——­+——­+
| 9 | 10 | 11 | 12 |
+—–­+——­+——­+——­+

“It is as easy as counting,” is an expression one sometimes hears.  But mere counting may be puzzling at times.  Take the following simple example.  Suppose you have just bought twelve postage stamps, in this form—­three by four—­and a friend asks you to oblige him with four stamps, all joined together—­no stamp hanging on by a mere corner.  In how many different ways is it possible for you to tear off those four stamps?  You see, you can give him 1, 2, 3, 4, or 2, 3, 6, 7, or 1, 2, 3, 6, or 1, 2, 3, 7, or 2, 3, 4, 8, and so on.  Can you count the number of different ways in which those four stamps might be delivered?  There are not many more than fifty ways, so it is not a big count.  Can you get the exact number?

286.—­PAINTING THE DIE.

In how many different ways may the numbers on a single die be marked, with the only condition that the 1 and 6, the 2 and 5, and the 3 and 4 must be on opposite sides?  It is a simple enough question, and yet it will puzzle a good many people.

287.—­AN ACROSTIC PUZZLE.

In the making or solving of double acrostics, has it ever occurred to you to consider the variety and limitation of the pair of initial and final letters available for cross words?  You may have to find a word beginning with A and ending with B, or A and C, or A and D, and so on.  Some combinations are obviously impossible—­such, for example, as those with Q at the end.  But let us assume that a good English word can be found for every case.  Then how many possible pairs of letters are available?

CHESSBOARD PROBLEMS.

    “You and I will goe to the chesse.”

    GREENE’S Groatsworth of Wit.