cuBerBruce
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Tom Rokicki has now claimed that all Rubik's Cube position can be solved using no more than 32 quarter turns.
http://cubezzz.duckdns.org/drupal/?q=node/view/131
http://cubezzz.duckdns.org/drupal/?q=node/view/131
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So why 32 and not 25? Is it because he has only looked at a special group of cosets? Or is there a known position that requires 26 or even 32 moves?No coset I have run yet has required more than 26 moves to solve, and
the possible distance-26 positions that I have run through an optimal
solver have all yielded distances less than 26
I think 35 was the current bound. If I'm interpreting correctly, he ran all the "problem cosets" (396 of them) that took 33-35, and they all turned out to be solvable in 26. Which means that there are some leftover cosets at 32 (not in the 396), but perhaps too many to compute and reduce (below 32, perhaps to 26) the same way right now.So why 32 and not 25? Is it because he has only looked at a special group of cosets? Or is there a known position that requires 26 or even 32 moves?No coset I have run yet has required more than 26 moves to solve, and
the possible distance-26 positions that I have run through an optimal
solver have all yielded distances less than 26
Yes.Or is there a known position that requires 26 moves?
Remember for his 25 HTM bound he proved his cosets to be solvable in 20 HTM or less. I think the proof it's a two-phase technique.So why 32 and not 25? Is it because he has only looked at a special group of cosets?
Yes, Mike Reid found a 26q* in 1998:Or is there a known position that requires 26 or even 32 moves?
I think Lucas is entirely rightI am running phase one to a depth of 19 and letting phase two complete
the coset
Tom does, sorta. http://cubezzz.homelinux.org/drupal/?q=node/view/129 suggests it's not quite o impossible.Does anyone believe that a 21 (HTM) or a 27 (QTM) will ever be found (or even exists)?
It is a 2-phase proces
I think Lucas is entirely rightI am running phase one to a depth of 19 and letting phase two complete
the coset
And I like Stefans analogy
There are over a million 20f* positions and Tom has made a crude estimate of 700 million, so there seems like a very real possibility of a 21f* position, but it seems to becoming more and more doubtful. On the other hand, there are only 3 known 26q* positions (all symmetrically related to each other), and I believe even 24q* positions are rather rare, so it seems to me highly unlikely there is any positions deeper than 26q*.Does anyone believe that a 21 (HTM) or a 27 (QTM) will ever be found (or even exists)?
First of all that page needs some serious editing because they switch from QTM to HTM and back at will without noting the change in metric, but that aside. This statement was interesting to me because the super flip is the example of a proven 20 HTM case, so I'm going to guess this 26 QTM case is also solvable in 20 HTM?In 1998 Michael Reid found a new position requiring more than 24 quarter turns to solve. The position, named by him as 'superflip composed with four spot' needs 26 quarter turns.
Mr. Kociemba, it is certainly a privilege to have you contribute to our forum. Welcome!
This statement was interesting to me because the super flip is the example of a proven 20 HTM case, so I'm going to guess this 26 QTM case is also solvable in 20 HTM?
Mr. Kociemba, it is certainly a privilege to have you contribute to our forum. Welcome!
He's contributed before actually. His post count reads 1 (at the moment) because his other 2 posts were in a thread in the "Off-Topic Discussion" section, and posts there aren't currently counted in a user's post count.
Very cool, I'vn never come across his site before. Thank you.This statement was interesting to me because the super flip is the example of a proven 20 HTM case, so I'm going to guess this 26 QTM case is also solvable in 20 HTM?
Superflip is only one of at least 1,445,274 proven 20f* positions.
Edit: OK, I think that superflip may have a direct mathematical proof of being 20f* while other 20f* positions have probably only been "proven" so by use of computer analysis.
You happen to be correct that the 26q* position is also one of the known 20f* positions. From Reid's web site, it can be created by:
U2 D2 L F2 U' D R2 B U' D' R L F2 R U D' R' L U F' B' (26q*, 21f)
F U2 R L D F2 U R2 D F2 D F' B' U2 L F2 R2 B2 U' D (20f*, 28q)
See: http://www.math.ucf.edu/~reid/Rubik/x_symmetric.html
Never heard of that. Would like to know about it if it's true. Most in that direction that I know is Reid's original proof exploiting symmetries to reduce the computer analysis:OK, I think that superflip may have a direct mathematical proof of being 20f* while other 20f* positions have probably only been "proven" so by use of computer analysis.
... Superflip is only one of at least 1,445,274 proven 20f* positions. ...
Never heard of that. Would like to know about it if it's true. Most in that direction that I know is Reid's original proof exploiting symmetries to reduce the computer analysis:OK, I think that superflip may have a direct mathematical proof of being 20f* while other 20f* positions have probably only been "proven" so by use of computer analysis.
http://www.math.rwth-aachen.de/~Mar...l_reid__superflip_requires_20_face_turns.html
... Superflip is only one of at least 1,445,274 proven 20f* positions. ...
Please tell me that someone tried all 18 moves on all those proven 20f* positions.
And has any of that 18*1,445,275 positions given another 20f* position?
I am assuming that he meant to say NO other distance-26 positions exist.believe, based on this, that it is likely
that on other distance-26 positions exist
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