# 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.

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.