Algorithms for Solving Rubik's Cubes

  title={Algorithms for Solving Rubik's Cubes},
  author={Erik D. Demaine and Martin L. Demaine and Sarah Eisenstat and Anna Lubiw and Andrew Winslow},
The Rubik’s Cube is perhaps the world’s most famous and iconic puzzle, well-known to have a rich underlying mathematical structure (group theory). In this paper, we show that the Rubik’s Cube also has a rich underlying algorithmic structure. Specifically, we show that the n×n×n Rubik’s Cube, as well as the n×n×1 variant, has a “God’s Number” (diameter of the configuration space) of Θ(n/ logn). The upper bound comes from effectively parallelizing standard Θ(n) solution algorithms, while the… CONTINUE READING


Publications referenced by this paper.

Is optimally solving the n × n × n Rubik’s Cube NP-hard

  • Andy Drucker, Jeff Erickson
  • Theoretical Computer Science — Stack Exchange…
  • 2010
2 Excerpts

The Cube: The Ultimate Guide to the World’s Bestselling Puzzle — Secrets, Stories, Solutions

  • Jerry Slocum
  • Black Dog & Leventhal Publishers,
  • 2009
1 Excerpt

The world’s first 12x12x12 cube

  • Leslie Le
  • forum post,
  • 2009
1 Excerpt

Jerrum . The complexity of finding minimum - length generator sequences

  • R Mark
  • Theoretical Computer Science
  • 1985

Similar Papers

Loading similar papers…