THE COUNTER PUZZLE.
In an old book published over half a century ago, I came across this puzzle; and finding it gave an evening’s entertainment to our young folks, I introduce it here for the benefit of those boys who take especial delight in games of an arithmetical nature.
Out of thin cardboard—old business cards answer this purpose nicely—make thirty-two blank counters, the size of a dime. Then upon a piece of note-paper mark off a figure just three inches square, and divide it by lines into nine compartments, each containing one square inch. The puzzle is, to arrange the counters in the external cells of the square four different times, and each time to have nine in a row, yet to have the sum of the counters different, and varying from twenty to thirty-two. If you will inspect the following figures you will see how this is possible: the first represents the original disposition of the counters in the cells of the square; the second, that of the same counters when four are taken away; the third, the manner in which they must be disposed when these four are brought back with four others; and the fourth with the addition of four more. There are always nine in each external row, and yet in the first case the whole number is twenty-four, in the second it is twenty, in the third twenty-eight, and in the fourth thirty-two. The numbers are substituted in the place of the counters in the above figures for convenience, but Fig. 5 represents the disposition of the counters, as indicated in Fig. 2.
—————◀▶—————