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Morpion Solitaire is a pencil-and-paper game for a single player. A move inthis game consists of putting a cross at a lattice point and then drawing aline segment that passes through exactly five consecutive crosses. Theobjective is to make as many moves as possible, starting from a standardinitial configuration of crosses. For one of the variants of this game, called5D, we prove an upper bound of 121 on the number of moves. This is done byintroducing line-based analysis, and improves the known upper bound of 138obtained by potential-based analysis.

Morpion Solitaire 5D: a new upper bound of 121 on the maximum score