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God's number proven at 20

penfold1992

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Mar 31, 2009
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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
 

Kirjava

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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?
 

rokicki

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Oct 31, 2008
Messages
269
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.
 

Tim Major

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New FMC goal for everyone... get a sub 20 official solution :p
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 :D
 

rokicki

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Oct 31, 2008
Messages
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And what is the average required amount of moves? I realise 18 moves is the most common, but is 15-16 about average?
Coool :D
The average is 17.7; most positions (about 2 in 3) have an optimal solution 18 twists long.
 

Zubon

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Sep 25, 2009
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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

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May 17, 2008
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On to 4x4! ;)

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

mrCage

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Jun 17, 2006
Messages
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Exactly how many positions are of maximum distance from solved? And are all these symmetrical positions??

Per
 

Christopher Mowla

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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

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Jul 16, 2010
Messages
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This is awesome. Though I agree, it would have been sweet if there was exactly one distance-21 position we could marvel at.
 

RCTACameron

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On to 4x4! ;)

Edit: This isn't serious. Not at this point in time, at least.
What about 2x2?

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.
I wonder if God's Number for 2x2 would be 8 moves.

Anyway, this is amazing. :)
 
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