Whether guessing a card or a number, or performing astonishing calculations, the magician always relies on a mathematical trick. Now it is your turn to uncover the mathematics behind the magician's success.
The seeker card
The magician has a deck of thirty-two cards and asks a spectator, S, to shuffle it, then deal the cards alternately, one at a time and face down, into two piles of sixteen. The magician asks S to choose one of the piles, cut it, and look at and remember the top card of one of the two resulting stacks. The card is left face down in place, and the two stacks remain separate. The magician now cuts the other pile of sixteen cards and turns over the top card of one of his two stacks, revealing its value. He then gathers the four stacks in the following order, without commenting on this step: first, the stack with his face-up card V on top; next, the spectator's stack that does not contain the chosen card; then the stack with S's chosen card face down on top; and finally the magician's remaining stack. The spectator's card is therefore sixteen cards above the face-up card.
The magician now deals the cards alternately, one at a time, into two piles. They are still face down, except for his face-up card. One of the piles will contain the face-up card: this pile is kept, while the other, in which every card is face down, is discarded. In fact, V identifies which pile to use, and the magician announces that V is a seeker card that leads to the spectator's card.
