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Morpion Solitaire

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Abstract

We study a popular pencil-and-paper game called morpion solitaire. We present upper and lower bounds for the maximum score attainable for many versions of the game. We also show that, in its most general form, the game is NP-hard and the high score is inapproximable within \(n^{1-\epsilon}\) for any \(\epsilon>0\) unless P = NP.

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Authors and Affiliations

  1. Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA 02139, USA

    Erik D. Demaine & Martin L. Demaine

  2. Langerman Diamonds, 62 Pelikaanstraat, 2018 Antwerpen, Belgium

    Arthur Langerman

  3. Departement d'informatique, Universite Libre de Bruxelles, B-1050 Brussells, Belgium

    Stefan Langerman

Authors
  1. Erik D. Demaine
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  2. Martin L. Demaine
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  3. Arthur Langerman
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  4. Stefan Langerman
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Correspondence to Erik D. Demaine, Martin L. Demaine, Arthur Langerman or Stefan Langerman.

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Demaine, E., Demaine, M., Langerman, A. et al. Morpion Solitaire. Theory Comput Syst 39, 439–453 (2006). https://doi.org/10.1007/s00224-005-1240-4

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  • DOI: https://doi.org/10.1007/s00224-005-1240-4

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