Geodesic
A combinatorial approach to Ebert's hat game with many colors
Uthaipon Tantipongpipat1
1University of Richmond
The electronic journal of combinatorics, Tome 21 (2014) no. 4
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This paper proves an optimal strategy for Ebert's hat game with three players and more than two hat colors. In general, for $n$ players and $k$ hat colours, we construct a strategy that is asymptotically optimal as $k\rightarrow \infty$. Computer calculation for particular values of $n$ and $k$ suggests that, as long as $n$ is linear with $k$, the strategy is asymptotically optimal. We conclude by comparing our strategy with the strategy of Lenstra and Seroussi and with the bound of Alon, and suggest our strategy is better when $2k \geq n \geq 7$.
DOI : 10.37236/4375
Classification : 91A46, 90C27, 05B40, 91A12
Mots-clés : Ebert's hat game, hat game, game, strong covering, generalized cover

Uthaipon Tantipongpipat  1

1 University of Richmond 
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     title = {A combinatorial approach to {Ebert's} hat game with many colors},
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Uthaipon Tantipongpipat. A combinatorial approach to Ebert's hat game with many colors. The electronic journal of combinatorics, Tome 21 (2014) no. 4. doi: 10.37236/4375

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