The Complexity of Clickomania
Abstract
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 onecolumn 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 NPcomplete for two columns and five colors, or five columns and three colors.
 Publication:

arXiv eprints
 Pub Date:
 July 2001
 arXiv:
 arXiv:cs/0107031
 Bibcode:
 2001cs........7031B
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Discrete Mathematics;
 Computer Science  Data Structures and Algorithms;
 F.2.2;
 F.1.3;
 F.1.1;
 G.2.1
 EPrint:
 15 pages, 3 figures. To appear in More Games of No Chance, edited by R. J. Nowakowski