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Infinite Hat Problems
by
Alan D. Taylor
Union College
Coauthors: Christopher S. Hardin
In general, a hat problem involves a collection of players who are to have hats of various colors placed on their heads. Typically, each player can see the hats worn by the others, but not his own. The goal is to find a strategy that will ensure correct (independent) guesses by most (e.g., all but finitely many) of the players. We concentrate here on the case in which the set of players is an ordered set and each can see only the hats of higher numbered players. One instance of this is our result that appeared in the February 2008 issue of the Monthly and which asserts that if time is modeled by the real line, then the state of any system at time t is completely determined by its past states for all but a countable, nowhere dense set of instants t.
Date received: June 7, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxi-30.