Math Digest# Mathematical Digest

### Short Summaries of Articles about Mathematics

in the Popular Press

"Why Mathematicians Now Care About Their Hat Color," by Sara Robinson.

*New York Times,* 10 April 2001, page D5.

A new puzzle has been circulating among mathematicians. It goeslike this: Three players enter a room and a hat is placed on each person'shead. The color of the hat, either red or blue, is assigned randomly. Each player can see the color of the others' hats, but not his own. Without communicating, the three players must simultaneously guess thecolor of their own hats, or pass. A hypothetical US$3 million prize is awardedif at least one person guesses correctly and none guesses incorrectly. The interesting part of the game comes in the strategy session before theplayers get their hats. The game becomes yet more complicated whenmore players are included. It turns out that the best strategiesfor winning can be described by Hamming codes, a standard tool in theoreticalcomputer science.

*--- Allyn Jackson*