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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.
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.
