The Diameter of the Rubik's Cube Group Is Twenty

@article{Rokicki2014TheDO,
  title={The Diameter of the Rubik's Cube Group Is Twenty},
  author={Tomas Rokicki and Herbert Kociemba and Morley Davidson and John Dethridge},
  journal={SIAM Review},
  year={2014},
  volume={56},
  pages={645-670}
}
We give an expository account of our computational proof that every position of Rubik’s Cube can be solved in 20 moves or less, where a move is defined as any twist of any face. The roughly 4.3 × 1019 positions are partitioned into about two billion cosets of a specially chosen subgroup, and the count of cosets required to be treated is reduced by considering symmetry. The reduced space is searched with a program capable of solving one billion positions per second, using about one billion… CONTINUE READING
Recent Discussions
This paper has been referenced on Twitter 59 times over the past 90 days. VIEW TWEETS

From This Paper

Figures, tables, and topics from this paper.

References

Publications referenced by this paper.
Showing 1-10 of 26 references

Close to God’s algorithm

  • H. Kociemba
  • Cubism For Fun, 28
  • 1992
Highly Influential
9 Excerpts

15f* = 91365146187124313

  • T. Rokicki
  • http://cubezzz.dyndns.org/drupal/?q=node/view…
  • 2010
1 Excerpt

God’s Algorithm out to 14f

  • T. Scheunemann
  • http://cubezzz.dyndns.org/drupal/?q=node/ view…
  • 2010
1 Excerpt

God’s Algorithm out to 15f

  • T. Scheunemann
  • http://cubezzz.dyndns.org/drupal/?q=node/ view…
  • 2010
1 Excerpt

Twenty-two moves suffice for Rubik’s cube

  • T. Rokicki
  • Math. Intelligencer, 32
  • 2010
3 Excerpts

New estimate for 20f*: 300,000,000

  • T. Rokicki
  • http://cubezzz.dyndns.org/drupal/?q=node/
  • 2009
2 Excerpts

Adventures in Group Theory: Rubik’s Cube

  • D. Joyner
  • Merlin’s Magic & Other Mathematical Toys, The…
  • 2008
1 Excerpt

Similar Papers

Loading similar papers…