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We analyze the following general version of the deterministic Hats game.Several sages wearing colored hats occupy the vertices of a graph. Each sagecan have a hat of one of $k$ colors. Each sage tries to guess the color of hisown hat merely on the basis of observing the hats of his neighbors withoutexchanging any information. A predetermined guessing strategy is winning if itguarantees at least one correct individual guess for every assignment ofcolors. 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.

The Hats game. The power of constructors