  In this paper we study the Three Hat Problem which appeared in Puzzle Corner
of the Technology Review magazine. This puzzle gives a scenario in which three
players wearing hats are sitting together and each hat can be seen by everyone
except the player that is wearing that hat. Each player is told that all of the
hats contain a positive integer and that two of the integers add to the third.
In an ordered, turn-wise, modular fashion, each player truthfully states
whether or not he knows his integer. We give a strategy which allows for one of
the players to solve for his integer for all possible integer configurations of
the puzzle and prove it is the optimal such strategy.
