Journal
SIAM REVIEW
Volume 56, Issue 4, Pages 645-670Publisher
SIAM PUBLICATIONS
DOI: 10.1137/140973499
Keywords
group theory; algorithm performance; Rubik's Cube
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We give an expository account of our computational proof that every position of the Rubik's Cube can be solved in 20 moves or fewer, where a move is defined as any twist of any face. The roughly 4.3x10(19) 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 seconds of CPU time donated by Google. As a byproduct of determining that the diameter is 20, we also find the exact count of cube positions at distance 15.
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