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E-Mail Magic

Alice and Bob have an e-mail card trick they wish to show Eve. First Eve selects five random cards from a standard deck. She e-mails the list of five cards to Bob. Bob then replies to Eve with a list of four of the cards. Eve forwards this message to Alice who immediately replies with the identity of the fifth card. How do Alice and Bob do it?

We use e-mail here to avoid the possibility of any signaling between Bob and Alice. They exchange no information directly. In fact, this is an effective trick done with two people in separate rooms.

Original source: "Math Miracles" by W. Wallace Lee, publ. by Mickey Hades International, Calgary, 1976; attributed to William Fitch Cheney, University of Hartford.

Thanks to Loren Larson (St. Olaf College) for the suggestion, and Arthur Benjamin (Harvey Mudd College) for the source.

[There is a very nice Web site devoted to this trick. You can even perform the trick over the Web (once you know how)! -Jeff]

Bonus Puzzle

Speaking of cards, Denis Borris (borrisd@magi.com) has sent me a most amusing puzzle. It is not appropriate as a PoW since the reader must know cribbage. But I do and it's cute:
Show how in cribbage one player can win 121 to n in only two rounds, where n is as small as possible. Well, I dont think he has a proof that his n is as small as possible, but it is pretty small: In fact, 121 to 8 is a possible score!