Morpion Solitaire

Authors:
Erik D. Demaine;Martin L. Demaine;Arthur Langerman;Stefan Langerman
Affiliations:
Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA 02139, USA;Computer Science and Artificial Intelligence Laboratory, MIT, Cambridge, MA 02139, USA;Langerman Diamonds, 62 Pelikaanstraat, 2018 Antwerpen, Belgium;Departement d'informatique, Universite Libre de Bruxelles, B-1050 Brussells, Belgium
Venue:
Theory of Computing Systems
Year:
2006

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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 $\epsilon0$ unless P = NP.