Geodesic
The Hats game. The power of constructors
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 26-37 
K. P. Kokhas; A. S. Latyshev. The Hats game. The power of constructors. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXXI, Tome 498 (2020), pp. 26-37. http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a2/
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     author = {K. P. Kokhas and A. S. Latyshev},
     title = {The {Hats} game. {The} power of constructors},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_498_a2/}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We analyze the following general variant 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.

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[2] X. He, Y. Ido, B. Przybocki, Hat guessing on books and windmills, 2020, arXiv: 2010.13249v1

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[6] K. P. Kokhas, A. S. Latyshev, “Kliki i konstruktory v igre “Hats”. I”, Zap. nauchn. semin. POMI, 488, 2019, 66–96 | MR

[7] K. P. Kokhas, A. S. Latyshev, V. I. Retinskii, “Kliki i konstruktory v igre “Hats”. II”, Zap. nauchn. semin. POMI, 488, 2019, 97–118 | MR