Two-Player Tower of Hanoi

Jonathan Chappelon (1) , Urban Larsson (2) , Akihiro Matsuura (3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Department of Mathematics and Statistics [Canada]
3 School of Science and Engineering [TDU]

The Tower of Hanoi game is a classical puzzle in recreational mathematics, 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 2n−1, to transfer a tower of n disks. But there are also other variations to the game, involving for example move edges weighted by real numbers. 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 heaps.

Mots clés: scoring game; weighed Tower of Hanoi; winning strategy; normal play; Tower of Hanoi; Two-player game

Domaines: Informatique et théorie des jeux [cs.GT]; Mathématique discrète [cs.DM]; Mathématiques [math]

Jonathan Chappelon, Urban Larsson, Akihiro Matsuura. Two-Player Tower of Hanoi. 2015. ⟨hal-01130010v1⟩