TOYS, TRICKS, AND TEASERS ^{Gardner’s Mathemagic} _{By Donald E. Simanek}

Martin Gardner has had a long career writing about recreational mathematics, which includes games, puzzles, and magic tricks based on mathematical principles (see MAKE, Volume 12, page 80, “Mathemagician”). Gardner generously agreed to share with MAKE readers a few that can be described briefly and performed with no sleight-of-hand skills.

Random order? Not!

The Gilbreath Principle deck and find two adjacent cards of the same color. A number of card tricks are based on a principle that Don’t tell me the color, but cut the cards between magician Norman Gilbreath introduced to magic. It’s those two, and complete the cut.” an application of combinatorial mathematics (which The dirty work has been done. The deck is now we will spare you here). Gardner discusses it in ordered as a sequence of pairs, and each pair has his books New Mathematical Diversions from one red and one black card. The spectator doesn’t Scientific American, Chapter 9, and Mathematical know this and wouldn’t likely notice even when Magic Show, Chapter 7. We’ll describe here the looking at the card faces. simpler versions. Some versions of this trick suggest you take the

Prepare the deck ahead of time with the cards in deck under the table and pretend to be searching black/red alternation. No other order is necessary. for red and black cards by touch, then bring them When you start this trick, you can do any false shuffle out and show them as pairs. But people become that doesn’t change the card order. But if you don’t suspicious when the deck is out of their sight. have those skills, don’t bother. (I can’t imagine why. Don’t they trust magicians?)

Have a spectator cut the deck and riffle shuffle The following method keeps the deck in full view. the two parts together just once. Tell him to fan the Take the deck, facedown, and explain that when cards and look at their faces to confirm that they red and black cards are adjacent to each other, as are well mixed. Say, “Look near the middle of the many must be, their opposite polarities give off

Photography by Donald E. Simanek

174 Make: Volume 13