Skip to main content
SpringerLink
Log in

Twenty-Two Moves Suffice for Rubik’s Cube®

  • Mathematical Entertainments
  • Michael Kleber and Ravi Vakil, Editors
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Joyner, David. Adventures in Group Theory: Rubik’s Cube, Merlin’s Magic and Other Mathematical Toys. Baltimore: The John Hopkins University Press, 2008.

    Google Scholar 

  2. Kociemba, Herbert. “Close to God’s Algorithm.” Cubism for Fun 28 (April), 1992, pp. 10–13.

    Google Scholar 

  3. Kociemba, Herbert. Cube Explorer (Windows Program). http://kociemba.org/cube.htm

  4. Kunkle, D., Cooperman, G. “Twenty-Six Moves Suffice for Rubik’s Cube.” Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC ’07), 2007. ACM Press, Waterloo.

  5. Korf, Richard E. “Finding Optimal Solutions to Rubik’s Cube Using Pattern Databases.” Proceedings of the Workshop on Computer Games (W31) at IJCAI-97, 1997, Nagoya.

  6. Radu, Silviu. “New Upper Bounds on Rubik’s Cube,” 2006. http://www.risc.uni-linz.ac.at/publications/download/risc_3122/uppernew3.ps

  7. Reid, Michael. “New Upper Bounds.” Cube Lovers, 7 (January), 1995. http://www.math.ucf.edu/^reid/Rubik/Cubelovers/

  8. Reid, Michael. “Superflip Requires 20 Face Turns.” Cube Lovers, 18 (January), 1995. http://www.math.ucf.edu/^reid/Rubik/Cubelovers/

  9. Rokicki, Tomas. “In Search Of: 21f*s and 20f*s; a Four Month Odyssey,” May 7, 2006. http://www.cubezzz.homelinux.org/drupal/?q=node/view/56

  10. Sloane, N. J. A. “Sequence A080601 (Sum of the First Seven Terms).” Online Encyclopedia of Integer Sequences.

Download references

Acknowledgments

This work was greatly helped by discussions with Silviu Radu; it was he who directed us to the subgroup (called H here) used by Kociemba. We are also grateful to Herbert Kociemba for both his original 1992 algorithm (and its implementation in Cube Explorer) and for ongoing e-mail discussions that have led to significant simplifications and performance improvements in the set solver. Many thanks also to John Welborn and Sony Pictures Imageworks, who donated massive computer time toward this project. The list of cosets and our calculated distance bounds are available at http://johnwelborn.com/rubik22/.

Author information

Authors and Affiliations

  1. Palo Alto, CA, USA

    Tomas Rokicki

Authors
  1. Tomas Rokicki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tomas Rokicki.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rokicki, T. Twenty-Two Moves Suffice for Rubik’s Cube® . Math Intelligencer 32, 33–40 (2010). https://doi.org/10.1007/s00283-009-9105-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-009-9105-3

Keywords

Search

Navigation