The Mathematical Intelligencer

, Volume 32, Issue 1, pp 33–40 | Cite as

Twenty-Two Moves Suffice for Rubik’s Cube®

  • Tomas RokickiEmail author
Mathematical Entertainments Michael Kleber and Ravi Vakil, Editors


Move Sequence Search Phase Middle Edge Inverse Position Cube Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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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


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Palo AltoUSA

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