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Hat Guessing Games
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DOI：10.1137/080743470.png)
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Abstract
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Hat problems have become a popular topic in recreational mathematics. In a typical hat; problem, each of n players tries to guess the color of the hat lie or she is wearing by looking at the colors of the hats worn by some. of the other players. In this paper we consider several variants of the problem, united by the common theme that the guessing strategies are required to be deterministic and the objective is to maximize the number of correct answers in the worst case. We also summarize what is currently known about the worst-case analysis of deterministic hat guessing problems with a finite number of players.
Keywords:
hat game
deterministic strategies
sight graph
Tutte-Berge formula
hypercube
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