Total Tetris: Tetris with Monominoes, Dominoes, Trominoes, Pentominoes,...
Author(s)Demaine, Erik D; Demaine, Martin L; Eisenstat, Sarah Charmian; Hesterberg, Adam Classen; Lincoln, Andrea I; Lynch, Jayson R.; ... Show more Show less
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We consider variations on the classic video game Tetris where pieces are k-ominoes instead of the usual tetrominoes (k = 4), as popularized by the video games ntris and Pentris. We prove that it is NP-complete to survive or clear a given initial board with a given sequence of pieces for each k ≤ 5, complementing the previous NP-completeness result for k = 4. More surprisingly, we show that board clearing is NP-complete for k = 3; and if pieces may not be rotated, then clearing is NP-complete for k = 2 and survival is NP-complete for k = 3. All of these problems can be solved in polynomial time for k = 1.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Journal of Information Processing
Information Processing Society of Japan
Demaine, Erik D. et al. "Total Tetris: Tetris with Monominoes, Dominoes, Trominoes, Pentominoes,...." Journal of Information Processing 25 (2017): 515-527 © 2017 Information Processing Society of Japan
Author's final manuscript