The Complexity of Clickomania

Details The Complexity of Clickomania The Complexity of Clickomania

2001-07-21

arxiv.org/abs/cs/0107031v1

Computer Science

Computational Complexity

15 pages, 3 figures. To appear in More Games of No Chance, edited by R. J. Nowakowski

Scientific paper

We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group of at least two square blocks, and any blocks above it fall down. We show that one-column puzzles can be solved, i.e., the maximum possible number of blocks can be removed, in linear time for two colors, and in polynomial time for an arbitrary number of colors. On the other hand, deciding whether a puzzle is solvable (all blocks can be removed) is NP-complete for two columns and five colors, or five columns and three colors.

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