  We analyze the following general version of the deterministic Hats game.
Several sages wearing colored hats occupy the vertices of a graph. Each sage
can have a hat of one of $k$ colors. Each sage tries to guess the color of his
own hat merely on the basis of observing the hats of his neighbors without
exchanging any information. A predetermined guessing strategy is winning if it
guarantees at least one correct individual guess for every assignment of
colors. We present an example of a planar graph for which the sages win for $k
= 14$. We also give an easy proof of the theorem about the Hats game on
"windmill" graphs.
