English

The Hats game. The power of constructors

Combinatorics 2021-02-16 v1

Abstract

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 kk 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=14k = 14. We also give an easy proof of the theorem about the Hats game on "windmill" graphs.

Keywords

Cite

@article{arxiv.2102.07138,
  title  = {The Hats game. The power of constructors},
  author = {Aleksei Latyshev and Konstantin Kokhas},
  journal= {arXiv preprint arXiv:2102.07138},
  year   = {2021}
}

Comments

8 pages