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Problem of the Week 935

Three Hat Heads

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Alice, Bob, and Charlie each have either a red hat or a blue hat on their head. The hats were placed randomly (one's hat color has no effect on the others) and no person knows the color of his or her hat, but each can see the other two.

Once the hats are placed, no communication of any sort is allowed and once they have all seen the others's hats, they must simultaneously guess the color of their own hat or pass. The three will share a large monetary prize if at least one of them guesses correctly and none guesses incorrectly.

For example, they could decide that Alice will say RED and the others will PASS. This will yield the money half the time. Devise a strategy that will do better.

Source: Dr. Todd Ebert, University of California at Irvine via the NY Times

© Copyright 2001 Stan Wagon. Reproduced with permission.

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15 Apr 2001