Geodesic
The three colour hat guessing game on cycle graphs
Witold Szczechla1
1Institute of Mathematics, University of Warsaw
The electronic journal of combinatorics, Tome 24 (2017) no. 1
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We study a cooperative game in which each member of a team of N players, wearing coloured hats and situated at the vertices of the cycle graph with N vertices, 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 asymmetric game is an example of relational system using incomplete information about an unpredictable situation, where at least one participant has to act properly.
DOI : 10.37236/5135
Classification : 05C57, 91A43, 91A12
Mots-clés : cooperative games, games on graphs, hat puzzle, hat guessing problems, deterministic strategy, system reliability, information network, graph colouring

Witold Szczechla  1

1 Institute of Mathematics, University of Warsaw 
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Witold Szczechla. The three colour hat guessing game on cycle graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 1. doi: 10.37236/5135

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