Magic Trick: A Mathematical Problem

To pick out from a pack in one's pocket the card thought of, without asking a question.

This is one of the most brilliant and most incomprehensible tricks ever invented. Moreover, it requires little skill on the part of the performer, being the result of a cleverly devised mathematical formula. All that is necessary for its successful performance is to follow out the instructions found here. A euchre pack of thirty-two cards is used; the deuce, trey, four, five and six being laid aside.

Before beginning the trick, the performer arranges as follows, eight hands of four cards each, placing them face uppermost on a table:

Hand 1 consists of an Ace, a King, a Queen and a Jack.

Hand 2 consists of a 7, a King, a 9, and a Jack.

Hand 3 consists of an 8, a Queen, a 9 and a Jack.

In these hands the suits should be as varied as possible. "Hand 4" contains four indifferent cards.

Hand 5 contains two hearts and two spades, regardless of the spots.

Hand 6 contains two diamonds and two spades, regardless of the spots.

Hands 7 and 8 are made up, each, of four indifferent cards. When all are laid out, hand 2 is placed on hand 1; hand 3 on hand 2, and so on to the end, so that hand 1 will be on top of the pack, when it is turned over. Hands 4, 7, and 8, have no bearing on the trick, but are merely intended as a blind.

Hands 1, 2 and 3 have a certain spot value, as shown in

 Table I: Hand No. 1, has for spot value, 1 Hand No. 2, has for spot value, 2 Hand No. 3, has for spot value, 4

These numbers show the spots of the card thought of, as explained further.

 Table II: Hand No. 5 has for suit value, 1 Hand No. 6 has for suit value, 2

and determine the suit of the card thought of.

Eight cards are arranged mentally so that the highest card is followed by the lowest, as appears in

 Table III: 1. Ace 2. Seven 3. King 4. Eight 5. Queen 6. Nine 7. Jack 0. Ten

The order of the suits is that shown in

 Table IV: Hearts =1 Spades=3 Diamonds=2 Clubs=0

A formidable list, the reader may say, but one easily remembered, if studied carefully. The pack being arranged, as explained, and the tables memorized, the performer is ready for the trick. To do away with any suspicion of prearrangement, the performer begins by giving the pack a false shuffle, so that the order of the cards is not disarranged in the least.

One of the audience is now requested to think of a card, and, so that there may be no question after, to write the name of it on paper and keep the paper.

The performer, sitting at a table with the one who thought of the card, deals out the four top cards with the request what the other shuffles them, without allowing anyone to see them, and then selects and puts aside any and all cards, no matter of what suit, that have the same spot value as the card thought of. This is repeated four times until sixteen cards are dealt out. The performer, in the meanwhile, quietly makes a mental note of the "hands" from which the cards are selected. Of course, it is only the first three "hands" that he watches, the "fourth hand," as has been said, having no bearing on the trick.

If the card was selected from the "first hand," he recalls, mentally, Table I, and at once knows that this hand has a value of 1; then referring to Table III, he finds that No. 1 is an ace, and he knows that the thought of card is an ace. The suit he does not know yet.

Should the selected card be in the "second hand" only, he finds by consulting Table I that the value of the "second hand" is 2, and Table III tells that the card is a 7.

Should the card be selected from the "third hand," Table I tells that "hand three" has a value of 4, and Table III that 4 is an eight.

Should the selected card be in two different "hands" or in the three "hands," the performer simply adds the values of the several "hands" as found in Table I, and referring to Table III, at once knows the card.

For example: If the selected card is in "hands one" and "two," by turning to three in Table III = a King.

If in all three "hands," No. 7 in Table III 0 = Jack.

If in "hands two" and "three," the value being 6= Nine.

Should there be no value corresponding to the thought-of card in any of the three "hands," No. 0 in Table III shows that to be a ten.

To learn the suit, the performer watches "hands five" and "six." In dealing "hand five" he requests that any and all cards of the same color as the suit of the card thought of, without regard to the spot value, be put aside. This he repeats with "hands six," "seven," and "eight," but pays no regard to the last two.

Then he refers to Tables II and IV. Should the suit be in "hand five" only, which has 1 for value, Table IV shows the suit to be a heart.

If the suit is "hand six" only, it has a value of 2 and 2 in Table IV=a diamond. If in "hands five" and "six" the united values being 3, Table IV shows it to be a spade, and should the suit not appear in either "hand five" or "six," the suit shown by Table IV is a club.

It must be borne in mind that all references to the several tables must be done mentally.

While these instructions may appear complicated, a little thought will show them to be very simple, and the practice spent in memorizing them will be well repaid by the brilliancy of the trick.

Now for the wind-up of the trick. The performer requests that the cards be brought together, be thoroughly shuffled, and then returned to him. When he receives them he places the pack in one of his pockets, and then, putting his hand in, brings out the thought-of card. Wonderful as this seems, it is the easiest part of the trick. In each of four pockets, the performer has eight duplicate cards, arranged in order from 7 to Ace, Jack, Queen, and King; each pocket containing one suit only. When the pack is returned to him, he puts it in the pocket that contains the thought-of card. Then it is but a moment's work to locate the card wanted.