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{\bf Maura B. Paterson and Douglas R. Stinson}
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{\bf Yet Another Hat Game}
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Several different ``hat games'' have recently received a fair amount
of attention.  Typically, in a hat game, one or more players are
required to correctly guess their hat colour when given some
information about other players' hat colours.  Some versions of these
games have been motivated by research in complexity theory and have
ties to well-known research problems in coding theory, and some
variations have led to interesting new research.

In this paper, we review {\bf Ebert's Hat Game}, which garnered a
considerable amount of publicity in the late 90's and early 00's, and
the {\bf Hats-on-a-line Game}.  Then we introduce a new hat game which
is a ``hybrid'' of these two games and provide an optimal strategy for
playing the new game.  The optimal strategy is quite simple, but the
proof involves an interesting combinatorial argument.

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