A Dozen Hat Problems

In each of these problems, hats of specified colors are placed on players’ heads. Each player can see the colors of some or all of the other player’s hats, but not his own. The goal is to come up with a strategy players can agree on before the game that will allow as many players as possible to correctly guess the colors of their hats. Some of these problems are psychological or philosophical and many are deeply mathematical. At the very least, they are fun to think about! Compiled by Dr. Ezra Brown and Dr. James Tanton.

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