# Twenty-Five Moves Suffice

Submitted by rokicki on Thu, 03/20/2008 - 14:26.

On March the 3rd I finally finished the last coset required to prove that 25 moves suffice.

I have finally finished a draft version of a paper detailing the technique and result:

http://tomas.rokicki.com/rubik25.pdf

The technique uses the coset solver I have described previously here (over the past two years)

but I have also made it faster, and also gotten a new machine that is faster and has more memory to run these cosets more quickly.

In the end, it required about 4,000 cosets to be solved to prove a bound of 25.

By solved, I mean an upper bound on the largest distance in that coset was found;

this can be done much more quickly than actually computing the exact distance for a

coset.

I think proving a bound of 24 is well within reach.

I have finally finished a draft version of a paper detailing the technique and result:

http://tomas.rokicki.com/rubik25.pdf

The technique uses the coset solver I have described previously here (over the past two years)

but I have also made it faster, and also gotten a new machine that is faster and has more memory to run these cosets more quickly.

In the end, it required about 4,000 cosets to be solved to prove a bound of 25.

By solved, I mean an upper bound on the largest distance in that coset was found;

this can be done much more quickly than actually computing the exact distance for a

coset.

I think proving a bound of 24 is well within reach.