Journal of Algorithms
Tetris is hard, even to approximate
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
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We analyze a new popular video-game called Lumines, which was developed by Sony for the PSP platform. It involves a sequence of bichromatic 2×2 blocks that fall in a grid and must be shifted or rotated by the player before they land. Patterns of monochromatic 2 × 2 blocks in the terrain are regularly deleted. The primary goal is to contain the terrain within a fixed height and, if possible, clear the grid. We deal with questions such as: (1) Can the game be played indefinitely? and (2) Can all terrains be eliminated? We examine how answers to these questions depend on the size of the grid and the rate at which blocks are deleted.