PSPACE-completeness of Bloxorz and of Games with 2-Buttons


Bloxorz is an online puzzle game where players move a 1 by 1 by 2 block by tilting it on a subset of the two dimensional grid. Bloxorz features switches that open and close trapdoors. The puzzle is to move the block from its initial position to an upright position on the destination square. We show that the problem of deciding whether a given Bloxorz level is solvable is PSPACE-complete and that this remains so even when all trapdoors are initially closed or all trapdoors are initially open. We also answer an open question of Viglietta [5], showing that 2-buttons are sufficient for PSPACE-hardness of general puzzle games. We also examine the hardness of some variants of Bloxorz, including variants where the block is a 1 by 1 by 1 cube, and variants with single-use tiles.

DOI: 10.1007/978-3-319-18173-8_30

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Showing 1-7 of 7 references

Buchin: Rolling block mazes are PSPACE-complete

  • K Buchin
  • 2012

Demaine: PSPACE-completeness of sliding-block puzzles and other problems through the nondeterministic constraint logic model of computation

  • Robert A Hearn, D Erik
  • 2005

Savitch: Relationships between nondeterministic and deterministic tape complexities

  • J Walter
  • 1970

Google Play Store. details?id=com.TwistedGames.Caveman 3. Ice Cube Caveman, iTunes App Store. ice-cube-caveman/id456179222?mt=8