God's Number in QTM is 26

[Lucas Garron]

This was announced at US Nationals today.

http://cube20.org/qtm/

Tomas and Morley worked with the Ohio Supercomputing Center using 29 CPU-years.

The only known distance-26 position is superflip + 4 spots:
U U F U U R' L F F U F' B' R L U U R U D' R L' D R' L' D D

 

[Renslay]

Finally! I waited for this result for so long!
Huge, huge, huge congrats!

"We did not find optimal solutions to each position, but instead only solutions of length 20 or less." - uhm, is that state correct? Or just a copy-paste error from the 20f text?

 

[10461394944000]

o awesome !!

STM next

edit: what is the current lower bound for STM?

 

[qqwref]

Whoa! So awesome.

 

[Kirjava]

cool :U

STM next

totally

 

[Frubix]

Cool

 

[rokicki]

Thanks, all! Morley spearheaded getting the computer time, and that
was the main impediment.

You're right, there are some typos I'll have to fix. I'm editing this from
Hawaii (just got back from the beach) otherwise I'd be more "on" it.

I *think* the current STM lower bound is 18, but I'm not sure.

Also note that we did not prove there is only a single distance-26 position
(but I strongly suspect there is only that one, and indeed I have some
machines going right now looking for more deep positions.) More on that
when I get back to the mainland.

I hope everyone is having fun in Jersey City; I really wanted to go but
am having fun in Hawaii nonetheless.

Thanks to the event organizers for giving us space in the program.

 

[Renslay]

It surprised me that there so few 26q* positions! The number of 20f* positions are about 490,000,000, but there are only a handful of 26q*?! Mindblowing!

Also, what are the chances to explore the distance/#states table? For the face turn metric, 15 depth is the farthest where we know the exact number of positions, and that result is many years old by now. I noticed that the estimation of depth 20 is updated (from 300,000,000 to 490,000,000) some times ago, I don't know if that is true for the other depths. I guess it would require tons of computational resources; is there a chance that there will be an algorithm specifically aimed for this? Currently, how much work would be required for distance 16?

 

[Stefan]

Awesome!

And yes, STM next, please

Superflip with or without fourspot is 16s*, superfliptwist with or without fourspot is 17s*. Maybe superflip variations will finally not be among the hardest positions?

 

[guysensei1]

STM is HTM but with slices counting as 1 move right? Why not have SQTM where it's QTM but slices are counted as 1 turn?

 

[Stefan]

Why not have SQTM

We do have that. It's just not popular.

 

[Dane man]

Wow, nice work. Congrats on the find!

 

[Kirjava]

We also have ATM

 

[goodatthis]

I would really like to see ATM next, that's a really interesting metric.

EDIT: just saw kirjava's post

 

[10461394944000]

We also have ATM

that would be cool too

 

[G2013]

Wow! Amazing result, I wish I was there when they did the announcement!

And what program can be used to calculate the optimal QTM solve to a given scramble?

 

[Renslay]

And what program can be used to calculate the optimal QTM solve to a given scramble?

Hm, an update to CubeExplorer for finding sub-optimal and optimal solutions in QTM might be a good idea!
But on the other side... How many actually would use it?

 

[10461394944000]

is there a video of the announcement?

 

[cuBerBruce]

is there a video of the announcement?

This is my video of the main part of the announcement. I was not aware in advance that this announcement would be made, and so I had just had to shoot this from where I was and with the digital camera I had with me. The audio is distorted; there is much background noise; and people near me talking and drowning out what the speaker was saying, at times. Hopefully, someone else has a better recording.

 

[cubernya]

I just had the idea: I wonder what God's number is if we exclude all primes? So just R and R2 are allowed, not R'. Of course, we could require R2 and R' because of symmetry, but that is indifferent.