The Diameter of the Rubik's Cube Group Is Twenty

  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},
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
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