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arXiv · 1412.3435

The three-colour hat guessing game on the cycle graphs

Witold W. Szczechla
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Abstract

We study a cooperative game in which each member of a team of $N$ players, wearing coloured hats and situated at the vertices of a cycle graph $C_N$, is guessing their own hat colour merely on the basis of observing the hats worn by their two neighbours without exchanging the information. Each hat can have one of three colours. A predetermined guessing strategy is winning if it guarantees at least one correct individual guess for every assignment of colours. We prove that a winning strategy exists if and only if $N$ is divisible by $3$ or $N=4$. This problem represents an example of a relational system using incomplete information about an unpredictable situation, where at least one participant has to act properly.

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Witold W. Szczechla. 2015-04-30. The three-colour hat guessing game on the cycle graphs. https://arxiv.org/abs/1412.3435

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