# Thirty-Two QTM Moves Suffice

Submitted by rokicki on Wed, 01/14/2009 - 18:26.

I have modified my coset solver to work in the quarter turn metric, and

with 396 cosets solved, I can announce that every cube position can be

solved in 32 or fewer quarter turns.

I am running phase one to a depth of 19 and letting phase two complete

the coset; each run takes about 12 minutes and approximately 63% of

the runs yield an upper bound of 25; the other 37% yield an upper

bound of 26.

No coset I have run yet has required more than 26 moves to solve, and

the possible distance-26 positions that I have run through an optimal

solver have all yielded distances less than 26, so I do not have a

new distance-26 position yet. (Applying Radu's symmetrical coset

idea to explore only symmetrical positions in the QTM would probably

provide a large collection of "hardest positions", much as it did

for the half turn metric.)

There are some improvements I can make to my existing technology for

the quarter turn metric, including some speed improvements to the

coset solver and leveraging local maxima information when combining

cosets into an overall bounds proof, and I will be exploring some of

these ideas.

with 396 cosets solved, I can announce that every cube position can be

solved in 32 or fewer quarter turns.

I am running phase one to a depth of 19 and letting phase two complete

the coset; each run takes about 12 minutes and approximately 63% of

the runs yield an upper bound of 25; the other 37% yield an upper

bound of 26.

No coset I have run yet has required more than 26 moves to solve, and

the possible distance-26 positions that I have run through an optimal

solver have all yielded distances less than 26, so I do not have a

new distance-26 position yet. (Applying Radu's symmetrical coset

idea to explore only symmetrical positions in the QTM would probably

provide a large collection of "hardest positions", much as it did

for the half turn metric.)

There are some improvements I can make to my existing technology for

the quarter turn metric, including some speed improvements to the

coset solver and leveraging local maxima information when combining

cosets into an overall bounds proof, and I will be exploring some of

these ideas.