Two-player Tower of Hanoi

Jonathan Chappelon (), Urban Larsson () and Akihiro Matsuura ()
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Jonathan Chappelon: Univ. Montpellier
Urban Larsson: Dalhousie University
Akihiro Matsuura: Tokyo Denki University

International Journal of Game Theory, 2018, vol. 47, issue 2, No 5, 463-486

Abstract: Abstract The Tower of Hanoi game is a classical puzzle in recreational mathematics (Lucas 1883) which also has a strong record in pure mathematics. In a borderland between these two areas we find the characterization of the minimal number of moves, which is $$2^n-1$$ 2 n - 1 , to transfer a tower of n disks. But there are also other variations to the game, involving for example real number weights on the moves of the disks. This gives rise to a similar type of problem, but where the final score seeks to be optimized. We study extensions of the one-player setting to two players, invoking classical winning conditions in combinatorial game theory such as the player who moves last wins, or the highest score wins. Here we solve both these winning conditions on three pegs.

Keywords: Combinatorial game; Scoring play; Tower of Hanoi; 91A46 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00182-017-0608-4

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