International Journal of Game Theory

, Volume 47, Issue 2, pp 463–486 | Cite as

Two-player Tower of Hanoi

  • Jonathan Chappelon
  • Urban LarssonEmail author
  • Akihiro Matsuura
Original Paper


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 pegs.


Combinatorial game Scoring play Tower of Hanoi 

Mathematics Subject Classification




We thank the anonymous referees for their comments and suggestions.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Institut Montpelliérain Alexander Grothendieck, CNRSUniv. MontpellierMontpellierFrance
  2. 2.Department of Mathematics and StatisticsDalhousie UniversityHalifaxCanada
  3. 3.Division of Information System Design, School of Science and EngineeringTokyo Denki UniversitySaitamaJapan

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