Paper by Erik D. Demaine

Nadia Benbernou, Erik D. Demaine, Martin L. Demaine, and Benjamin Rossman, “Coin-Flipping Magic”, in Exchange Book of the 8th Gathering for Gardner (G4G8), Atlanta, Georgia, March 2008.

This paper analyzes a variety of generalizations of a coin-flipping magic trick invented independently by Martin Gardner and Karl Fulves. In the original trick, a blindfolded magician asks the spectator to flip three coins, forcing them into an all-equal state by surprisingly few moves. We generalize to any number of coins, coins/dice with more than two sides, and multiple flips at once. Next we consider a generalization described by Martin Gardner in which the spectator can re-arrange the coins in certain ways in between each flip. Finally we consider the variation in which the magician equalizes the number of heads and tails, which can be achieved exponentially faster.

The paper is 12 pages.

The paper is available in PostScript (1901k), gzipped PostScript (877k), and PDF (217k).
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Last updated June 13, 2024 by Erik Demaine.