Fitch Cheney's Five Card Trick

I n recent years a classic mid-20th century two-person card trick has resurfaced in the mathematical community. It goes something like this: A volunteer chooses five cards at random from a standard deck, hands them to you, and you show four of them to your confederate who promptly names the fifth card. This superb effect is usually credited to mathematician William Fitch Chcney, Jr. The original trick, and some generalizations discussed here, work as well with large audiences as with small ones. The tricks arc I 00% mathematical-though you may choose to dress them up a little, for instance as "mind-reading tricks." They will stump all but the most sophisticated onlookers; a general audience will be convinced that some sort of body language or verbal signaling is being used. To eliminate that possibility, one can utilize email, tclc.Phone, an innocent go-between, or some other form of"impersonal'' communication. Indeed, Cheney's trick, as published by W. Wallace Lee in I950, was intended to be carried out over the telephone.