## All HMC Faculty Publications and Research

#### Title

An Amazing Mathematical Card Trick

Article

#### Department

Mathematics (HMC)

1-2010

#### Abstract

A magician gives a member of the audience 20 cards to shuffle. After the cards are thoroughly mixed, the magician goes through the deck two cards at a time, sometimes putting the two cards face to face, sometimes back to back, and sometimes in the same direction. Before dealing each pair of cards into a pile, he asks random members of the audience if the pair should be flipped over or not. He goes through the pile again four cards at a time and before each group of four is dealt to a pile, the audience gets to decide whether each group should be flipped over or not. Then the cards are dealt into four rows of five cards. The audience can decide, for each row, whether it should be dealt from left to right or from right to left, producing an arrangement like the one shown.

First published in The Mathematical Intelligencer, Volume 32, Number 2 (2010), 37-40.