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PARADOXICAL $n$-FACES DICE BUILT FROM MAGIC SQUARES
Keywords:
magic squaresDOI:
https://doi.org/10.17654/0972555525031Abstract
For any odd integer $n$, we exhibit dice $A_1, A_2, \ldots, A_n$ with $n$ faces which have the property that for $i=1,2, \ldots, n$, a player with the die $A_i$ is expected to beat the player with the die $A_{i+1} \left(\right.$ where $\left.A_{n+1}=A_1\right)$.
Received: July 1, 2025
Accepted: July 15, 2025
References
[1] E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways for Your Mathematical Plays, Volume 2, Academic Press, 2000.
[2] D. H. Eckhardt, Cyclic groups and the generation of De la Loubère magic squares, Math. Mag. 63(5) (1990), 315-320.
[3] D. C. Fischer and J. Syom, Optimal strategies for a generalized “Scissors, Paper, and Stone” game, Amer. Math. Monthly 99 (1992), 935-942.
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