The operation is exactly the same when the number of persons is greater. If, instead of 3, there are 4, or 5 persons, four or five cards must be presented to each.

PROBLEM XIV.

Three cards being presented to three persons, to guess that which each has chosen.

As it is necessary that the cards presented should be distinguished, we shall call the first A, the second B, and the third C. Let the persons, whom we shall distinguish by first, second, and third, choose privately which ever of the cards they think proper, and when they have made their choice, which is susceptible of six varieties, give the first person 12 counters, the second 24, and the third 36: then desire the first person to add together the half of the counters of the person who has chosen the card A; the third of those of the person who has chosen B; and the fourth part of those of the person who has chosen C; and ask the sum, which must be either 23 or 24; 25 or 27; 28 or 29, as in the following table:

This table shews, that if the sum is 25, for example, the first person must have chosen the card B, the second the card A, and the third the card C; and that, if it be 28, the first person must have chosen the card B, the second the card C, and the third the card A; and so of the rest.

PROBLEM XV.

To tell the number of spots on all the bottom cards of several heaps, arranged on a table.

Arrange each heap of cards in such a manner, that the spots on the bottom one, added to the cards above it, may always amount to 12; continue to make as many heaps as possible, in the manner above prescribed, and place the remaining cards on one side. Then separate in your mind four heaps, and multiply the heaps which remain, after these are deducted, by 18; this product, added to the number of cards, will be that of the spots required. We shall give the solu tion of this problem by an analysis in another place.

PROBLEM XVI.

To name all the cards of a pack.

Have a complete pack of 52 cards, and arrange them according to the order of the following words, which you must retain in your memory:

Unus quinque novem famulus sex quatuor duo Ace five nine knave six four two

Rex septem octo fæmina trina decem King seven eight queen three ten

Besides this first order, you must arrange them also according to the order of the colours, spades, hearts, clubs, and diamonds; so that the 52 cards may be disposed as follows:

ORDER OF THE CARDS.

1 Ace of spades

2 Five of hearts

3 Nine of clubs

4 Knave of diamonds

5 Six of spades
6 Four of hearts
7 Two of clubs

8 King of diamonds

This order is of such a nature, that, by knowing any one of the 52 cards, that which follows it may be also

Thus, for example, if it were required to know what card follows the king of spades, it will be sufficient to recollect that septem, in the two Latin lines above given, which follows that of rex, denotes that it is a seven; and as the colour which follows the spades is hearts, it is the seven of hearts, and so of the rest.

Every thing being thus arranged, having retained in your memory the above words, and the order of the colours, desire any person to cut the pack as many times as he chooses; for it will be easy to name all the cards in order, provided you have found means, by some dexterous manœuvre, to observe that one which is at the top of the pack.

The same arrangement of the cards may be employed for various amusements.

1st. To make a person believe that you can distinguish the cards by their smell.

The pack being disposed in the above order, present it to any one, that he may choose a card at pleasure; open the pack at the place where it has been drawn out, and dexterously observe that which precedes it, by seeming to smell the place from which it was taken. It will then be very easy to name it, as it can be only that which follows in the order already indicated.

2d. A pack of cards being divided into two parts; to discover whether the number in each be odd or even.

First, find out whether the last card in the pack be black or red; then, on the pack being cut into two parts, if the card found at the bottom of the upper division is of the same colour as that at the bottom of the pack, the two parts which have been separated, contain each an even number; on the other hand, if it be of a different colour, they contain each an odd number.

3d. To tell the number of spots on several cards which any person has chosen.

Having presented the pack, that the person may choose several succeeding cards at pleasure, privately observe the card which is above those he has chosen, and how many he has drawn from the pack; it will then be easy to count how many spots they ought to contain.

For example, if the observed card be a nine, and four cards have been drawn, it may readily be seen that those drawn must be a knave, equivalent to 10 spots; a six, a four, and a two. You may then announce, that the cards, in the persons hand, contain 22 spots.

PROBLEM XVII.

Having desired a person to draw four cards from a pack and to think of one of them, to tell the one he has thought of.

Suffer the person to draw four cards from the pack at pleasure, and desire him to think of one of them; then take these four cards back, and place two of them at the top and two at the bottom of the pack, in a dexterous manner, so as not to be perceived: under the two last, place any four cards whatever; then display the lower part of the pack on the table, shewing only 8 or 10 cards, and ask the person whether the one he thought of be among them. If he says No, you may be sure that it is one of the two which you put at the top of the pack; in that case you must transfer them to the bottom, and then, shewing the bottom of the pack, say, Is not this your card? If he replies No, turn aside that card with your third finger, which you must have previously moistened, and desire him to draw out his card himself from the bottom of the pack.

If the person should say, that the card he thought of is among the first shewn to him, dexterously remove the four cards put at the bottom of the pack, in order that the two, one of which is the card he thought of, may be the lowermost of the pack, and you may then either shew him his card or make him draw it out himself, as above explained.

PROBLEM XVIII.

Three things being privately distributed to three persons, guess that which each has got.

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Let the three things be a ring, a shilling, and a glove. Call the ring A, the shilling E, and the glove 1; and in your own mind distinguish the persons by calling tnem first, second, and third. Then take 24 counters, and give one of them to the first person, two to