Twenty-Three Moves Suffice

After solving more than 200,000 cosets, we have been able to show that every position of Rubik's cube can be solved in 23 or fewer face turns.

The key contribution for this new result was 7.8 core-years of CPU time contributed by John Welborn and Sony Pictures Imageworks, using idle time on the render farm that was used for pictures such as Spider-Man 3 and Surf's Up.

No distance 21 positions were found in this search, despite solving a total of more than four million billion cube positions.

The same techniques for the proof of twenty-five moves were used, just on many more computers.

To prove 22 would require, using this technique, solving somewhere between 1 and 1.5 million cosets. We are investigating refinements to our techniques to reduce the CPU time required.

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Wow great site in the world.S

Wow great site in the world.Such a great site in the world.This site is very helpful for me and others.The key contribution for this new result was 7.8 core-years of CPU time contributed by John Welborn and Sony Pictures Imageworks, using idle time on the render farm that was used for pictures such as Spider-Man 3 and Surf's Up.This is very nice site Take care God bless you



Thanks
geogre

That can be done?

Never knew that the Rubik's cube can be figured out virtually. Maybe I'll be more adept in playing with it via the computer rather raw logic. Never good with my hands anyway.

Dang it! I congratulate yo

Dang it!

I congratulate you.

I wish i had your brains!

I'd love to understand life the way you do (math) but my brains are just not cut-out for that!

A hug.

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Thanks.Very interesting data

Thanks.Very interesting data have been frankly surprised..

This is a big reduction from

This is a big reduction from any previous known cosets. What a great discovery.
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:-)))) Very interesting! Than

:-)))) Very interesting! Thanks!!!
Great site well done!
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mootzie

Wow! Many congratulations.

Wow!

Many congratulations.

In a little more than a month you jumped from 25 to 23!. This is absolutely amazing.

I am convinced now the Rubik's diameter will be first found using computational techniques.

Thanks

Two things enabled this jump, actually:

1. Scads of CPU time from Imageworks, and

2. A suggestion from Herbert Kociemba on improving the way the coset solver worked. This suggestion simplified some of the code and lifted the "restriction" that the rubik25 paper discusses.

The amount of CPU time required to prove 20 (my ultimate goal) is still absolutely insane; it's on the order of 3500 core-years. So there's still some work to do to reduce this (or we just wait on Moore's Law).

And there's always the chance some position will actually require more than 20 moves; if I find a 21, suddenly the problem is easier.

that's nothing

3500 core-years is nothing

did you ever heard of FOLDING@HOME?

Impressive graph

Yeah, Folding@home is very impressive. 250K CPUs would crank through this (a final proof of 20) in about five days.

My congratulations Tom! This

My congratulations Tom! This is a fantastic result. I am at a loss for words.