### The Hats game. The power of constructors [article]

Aleksei Latyshev, Konstantin Kokhas
<span title="2021-02-14">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
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
more &raquo; ... h for which the sages win for k = 14. We also give an easy proof of the theorem about the Hats game on "windmill" graphs.
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