Parity Failure

Effect: After shuffling the pack, the performer hands it to someone and has him cut it. The spectator completes the cut, then deals out five face-down rows of five cards each. It is explained that he can turn over any four cards of the layout that form the corners of a rectangle. The rectangle can be of any size and shape, so long as the cards at its corners lie at the intersections of two rows and two columns. In Figure 244, two such rectangles are indicated; one by Xs at its corners, the other by Os.

The spectator can turn over as many quadruplets as he wishes, turning the same cards over again should they be shared by adjoining rectangles. The result is a haphazard arrangement of face-up and face-down cards, determined by the spectator's whims.

The performer does not watch as the cards are turned this way and that. Instead he walks to another part of the room, taking the balance of the deck with him. When the spectator has finished turning cards, he is asked to decide on one. It can lie either face-up or

face-down. He is told to mark the card by setting some small object on it: a coin, a matchbook, a pencil. This is to avoid confusion later in the trick.

He is now asked to call out the condition of each card, telling the performer only if it is face-up or face-down. However, when he comes to the card he has chosen, he is to lie about its condition. If it is faceup, he should say it is face-down, and if face-down, he should say it is face-up. As he calls his way through the twenty-five cards, the performer, at another table, lays out his cards in an identical pattern. He gazes a moment at his layout; then, without a question, he names the chosen card.

Method: Here is a variation on the "Pack of Lies" plot (pp. 100106), with a method founded on an entirely different principle. The deck must be secretly arranged in a simple stack. The only rule of this stack is that each pair of mates be twenty-six cards apart. That is, if the top card is the three of hearts, the twenty-seventh card must be the three of diamonds; if the card third from the top is the nine of spades, the card twenty-ninth from the top must be the nine of clubs. This stack may be given any number of straight cuts without upsetting its arrangement.

Besides the stacked deck, you will require two tables with surfaces large enough to lay out five rows of five cards each.

Begin by giving the deck a false shuffle or a quick series of straight cuts that simulates an overhand shuffle. When finished, hand the deck to a spectator and have him cut the cards and complete the cut. Then tell him to deal a row of five face-down cards from left to right. Below this have him deal a second row in the same fashion, and a third below that, and so on, until twenty-five cards have been dealt into five rows (Figure 244).

Take the balance of the pack from him and clearly explain how he is to turn over four cards at a time. As already explained, each group of four must fall at the corners of a rectangle, though each rectangle can be of any length and width the spectator desires. Cards turned once are turned again if they happen to rest at the corners of more than one rectangle. To make the rules of procedure clear, point out several examples of rectangles in the layout, but turn none of the cards over during the explanation.

Once the procedure is understood, walk across the room to the second table. While keeping your back to the spectator, repeat your instructions clearly and succinctly. "Now will you turn over any foursome. Have you done that? Good. Do the same thing again. Of course, if one of the four cards is one you have already turned face-up, this time turn it face-down. Keep turning over foursomes until the cards are well mixed, face-up and face-down.

"Are you satisfied? Fine. Now I want you to choose any one of your twenty-five cards. Don't move itâ€”just decide which one you want. It can be one of the face-up ones or one of the face-down. It doesn't matter. So that you don't forget which one it is, lay something on it; a coin, a pencil, a matchbook, anything that's handy.

"Now I want you to call out all your cards in the order you dealt them, from the first card to the last. Don't tell me what they are. Just say whether each is face-up or face-down. For example, you might call. 'Up, up, down, up, down,' and so on. But, when you come to the card you've chosen, lie about it. If it's face-down, say it's faceup; and if it's face-up, say it's face-down. Do you understand? Go ahead then."

As the spectator runs through his layout, form a duplicate of it, dealing cards from the top of the face-down packet you hold. When the layout is completed, two cards will remain in your hand. Keep them.

Because only twenty-five cards (one less than half the pack) were dealt by the spectator, the mates in the two layouts are staggered. The mate of each card in his layout lies one card further along in yours. With the cards turned randomly up and down, anyone comparing the two configurations would be hard pressed to detect this offset affinity.

To discover the location of the chosen card, first examine each of your five rows for an odd number of face-up cards. Any row with all its cards face-down is discounted in this search. You will find that only one row contains an odd number

of face-up cards. Now inspect the five columns. Again you will find there is but one with an odd number of face-up cards. Figure 245 shows one such configuration of the cards. The card that lies at the intersection of the odd row and odd column corresponds in position to the selection in the spectator's layoutâ€”and the card one position further in your layout is the mate of that card. Should the spectator's selection lie at the right end of the bottom row (that is, if it is the last card dealt), its mate is the top card of the pair in your hand.

If the mate lies face-up in your layout, note it and name the spectator's card. However, if it is face-down, rather than openly turn it over, sweep your cards together and glimpse the mate as you do this. Then, as you square the cards, name the selection and conclude.

See Karl Fulves* book, Curioser (sic), pages 59-61, for interesting variations on "Parity Failure" by Charles Hudson and Roy Walton.

In the next trick, another divination of a card is made possible by a spectator's lie. However, with this method, only three cards are dealt, and the spectator retains the entire deck throughout.

1979