A mathematical model and a computer tool for the Tower of Hanoi and Tower of London puzzles

  • Authors:

  • Andreas M. Hinz;Anton Kostov;Fabian Kneiíl;Fatma Sürer;Adrian Danek

  • Affiliations:

  • Lehrgebiet Angewandte Mathematik, FernUniversität in Hagen, Lützowstraíe 125, 58095 Hagen, Germany;Fakultät für Informatik, Technische Universität München, Boltzmannstraíe 3, 85748 Garching, Germany;Institut für Informatik, Ludwig-Maximilians-Universität München, Oettingenstraíe 67, 80538 München, Germany;Neurologische Klinik und Poliklinik, Ludwig-Maximilians-Universität München, Marchioninistraíe 15, 81377 München, Germany;Neurologische Klinik und Poliklinik, Ludwig-Maximilians-Universität München, Marchioninistraíe 15, 81377 München, Germany

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

We propose a mathematical model for the Towers of Hanoi and London based on state graphs. The analysis of this model allows to address questions like equivalence of puzzles, difficulty of tasks and optimality of solutions using topological, metric and symmetry properties of the corresponding graphs. The mathematical model serves as a base for a computer program to administer tower puzzles in a variety of psychological test situations. It is suitable for bedside use and is equipped with numerous devices for post-processing of recorded data. Among these features is the graphical representation of the projection of the path taken by a test person onto the state graph.