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Twenty-Eight QTM Moves Suffice
Submitted by rokicki on Fri, 06/06/2014 - 09:48.
Every position of the Rubik's Cube can be solved in at most
28 quarter turns. The hardest position known in the quarter-turn metric requires only 26 moves, so this upper bound is probably not tight. This new upper bound was found with the generous donation of computer time from Kent State University's College of Arts and Sciences. In order to obtain this new result, 7,000 cosets of the subgroup U,F2,R2,D,B2,L2 were solved to completion. Each coset took approximately an hour on a 6-core Intel CPU. No new positions at a distance of 26 or 25 were found in the solution of all of these cosets. Further details from the investigation will be presented in a future posting. |
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