Instead of white, the ordinary playing cards may be used, blacking the back of one to represent _c_. These are much more showy than the plain white ones, and the trick is not so easily discovered if slight bits of black are seen, as those having black spots are generally taken for the purpose.
One day a little fellow who had been repeatedly mystified by this trick, saw the cards which his brother had prepared lying on the table. He took them up, examined them carefully for a moment, then, with his little face all aglow at the revelation, he exclaimed, “Ha! I’ve found out how you do it now, you just blow charcoal on the other part.” How he got rid of the part already black, he did not explain, nor did we think to ask him, but he had at last solved the puzzle of their turning black, and that was all he cared to do at the time.
Hold a ring between thumb and forefinger at some distance from the boy addressed, and giving him a crooked stick, ask him to close one eye and try to catch the ring on the stick. This game looks so very simple, that any boy is certain he can do it at one thrust, and is only made aware of its difficulties after several unsuccessful attempts.
TO TELL THE NUMBER THOUGHT OF BY A PERSON.
Desire the person who has thought of a number to triple it, and to take the exact half of that; triple that half if the number was even, or if odd multiply the larger half by 3; and ask him how many times that answer contains nine: for the answer will contain the double of that number of nines, and one more if it be odd. Thus if the number thought of is 5, its triple will be 15, which cannot be divided by 2 without a remainder. The greater half of 15 is 8. If we multiply this by 3 we have 24, which contains 9 twice. So we shall have 2 + 2 + 1 = 5, the number first thought of.
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.