TO GUESS THE SPOTS ON A CARD.
Take a whole pack, consisting of 52 cards, and desire some person in company to draw out any card, at pleasure, without showing it. Having assigned to the different cards their usual value, according to their spots, call the knave 11, the queen 12, and the king 13. Then add the spots of the first card to those of the second; the last sum to the third; and so on, always rejecting 13, and keeping the remainder to add to the following card. It may be readily seen that it is needless to reckon the kings, which are counted 13. If any spots remain at the last card, you must abstract them from 13, and the remainder will indicate the card that has been drawn: if 12 remains, it has been an ace; but if nothing remains, it has been a king.
Demonstration.—Since a complete pack contains 13 cards of each suit, the values of which are 1, 2, 3, &c., as far as 13, the sum of all the spots of each of the different suits will be 7 times 13 (91), which is a multiple of 13; consequently the quadruple is also a multiple of 13: if we add the spots of all the cards, always rejecting 13, the remainder at last must be 0. Hence it is evident, that if a card, the spots of which are less than 13, be drawn, the difference between its spots and 13 will be what is wanting to complete the number. If, at the end, then, instead of attaining to 13, we attain only to 10, for example, it is plain, that the card wanting is a 3; and if we attain exactly to 13, the card missing must be equivalent to 13; that is, it must be a king.