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 (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 $2^n-1$, 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 heaps.

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

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. International Journal of Game Theory, 2018, 47 (2), pp.463-486. ⟨10.1007/s00182-017-0608-4⟩. ⟨hal-01130010v3⟩