# God's number proven at 20

#### penfold1992

##### Member
it was suspected to be 20 but mearly solving all cases still isnt satisfying... a nice mathematical explanation would do and the guy/girl who does it will probably get a group theory prize too

#### hawkmp4

##### Member
O.O
Awesome! I look forward to hearing more of the results.

#### riffz

##### Member
Well this is awesome but disappointing at the same time. The fact that it was brute forced before proven mathematically is somewhat disappointing.

#### CUB3R01

##### Member
This is awesome! I'm glad to see that this has finally been proven.

#### Kirjava

##### Colourful
You're disappointed? It can still be proven with maths - if that happened first humans would probably have never traversed every permutation that exists. We did well to take this route imo ^_^

Did anyone else think of Google's SECRET BEOWULF CLUSTER SUPERCOMPUTER like the Large Hadron Collider for cubers?

#### vgbjason

##### Member
God's number is 4:20, you need to edit that typo

#### Rinfiyks

##### Member
20 is such a nice round number, this makes me happy

#### rokicki

##### Member
Computational proof

Every bound since Thistlethwaite's 52 for this puzzle depended on exhaustive search. Earlier, higher bounds were based on the exhaustive search of smaller groups and factor spaces. Some might consider it a feature of Rubik's cube, that the distance of a position cannot be easily estimated by some structural property.

Personally, I was holding out hope for finding a distance-21 position. Now that would have been very nice.

I've been trying to simplify, analyze, and solve this problem using non-exhaustive methods for years, and have come up all but empty. There are some small observations (for instance, some small number of the H-cosets have distance 18) but, in the end, very little "simple structure" to the group that I could figure out how to exploit. For many of these puzzles, I fear that's the nature of the beast.

#### MTGjumper

##### Member
I wonder what time Faz gets on the "hardest scramble"

#### Tim Major

##### Platinum Member
New FMC goal for everyone... get a sub 20 official solution
Cool... 20 moves for any case...
"Distance-20 positions are both rare and plentiful; they are rarer than one in a billion positions, yet there are probably more than one hundred million such positions."
Haha, loved this sentence.
And what is the average required amount of moves? I realise 18 moves is the most common, but is 15-16 about average?
Coool

#### hic0057

##### Member
I'm wondering if it's a coincidence how there is exactly 20 pieces (12 edges and 8 corners.) This is excluding the core but that doesn't change position.

#### rokicki

##### Member
And what is the average required amount of moves? I realise 18 moves is the most common, but is 15-16 about average?
Coool
The average is 17.7; most positions (about 2 in 3) have an optimal solution 18 twists long.

#### amostay2004

##### Member
I wonder what's God's number in STM

#### Zubon

##### Member
This is a very significant achievement in the history of the Rubik's cube.

Glad it has finally been done but it does remove some of the mystique surrounding the 3x3.

#### hawkmp4

##### Member
On to 4x4!

Edit: This isn't serious. Not at this point in time, at least.

#### mrCage

##### Member
Exactly how many positions are of maximum distance from solved? And are all these symmetrical positions??

Per

#### Christopher Mowla

Exactly how many positions are of maximum distance from solved? And are all these symmetrical positions??

Per
"Distance-20 positions are both rare and plentiful; they are rarer than one in a billion positions, yet there are probably more than one hundred million such positions. We do not yet know exactly how many there are."

#### Kryptonite

##### Member
This is awesome. Though I agree, it would have been sweet if there was exactly one distance-21 position we could marvel at.

#### RCTACameron

##### Member
On to 4x4!

Edit: This isn't serious. Not at this point in time, at least.