## HAT PROBLEMS |

**Alan Taylor**

Union College

May 15, 2006

4:45 pm

Bailey Hall 201

Pastries and drinks will be served at 4:30 in Bailey Hall 204

We consider the following kind of hat problem. Several people (perhaps finitely many, perhaps infinitely many) are to have hats of various colors placed on their heads. Each will be able to see at least some of the other hats, but not his or her own. No communication is allowed after the hats have been placed and each will be asked to guess (simultaneously and independently) the color of his or her own hat. But before the hats are placed, the people are allowed to get together to plan a strategy as to how they might guess. A remarkable observation of Yuval Gabay and Michael O'Connor is that if the number of people is infinite and each can see all but finitely many of the other hats, then there is a strategy ensuring that only finitely many guess incorrectly. We will present a general framework for this kind of question and a number of results, in both the finite and infinite case, obtained by Chris Hardin, myself, and others.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

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