Talk:Optimal solutions for Rubik's Cube
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http://cubezzz.homelinux.org/drupal/?q=node/view/117 Credibility? Update needed or not?Ithy (talk) 03:43, 10 May 2008 (UTC)
I changed the link from mathematical constructivism to constructive proof because, although IANAM, I feel the notion of constructive vs. non-constructive proofs does not depend on the philosophy of constructivism, and the latter is not really relevant to the topic at hand. Unfortunately I don't think I'm up to actually writing the article on constructive proofs... :(
Oh goody, Gandalf61 just did :)
24 quarter turns changed to 26 quarter turns by anonymous editor, can anyone cofirm? Κσυπ Cyp 22:51, 20 Jan 2004 (UTC)
I can confirm it. On the following page http://www.math.ucf.edu/~reid/Rubik/x_symmetric.html there is a positions that needs 26 quarter turns. Here is the solution
U2 D2 L F2 U' D R2 B U' D' R L F2 R U D' R' L U F' B'
User:Sander123 3 febuary 2004.
- I am not convinced this is correct. Reid's x_symmetric.html page is stating that his best algorithm (the optimal cube solver) needs 26 quarter turns to reach that position. This is not a proof that no algorithm can reach that position in fewer turns. For the superflip position the situation is different: as stated, Jerry Bryan has proved by brute-force search through depth 11 (exploiting the symmetry of superflip) that 24 is a real lower bound (http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers/Jerry_Bryan__Qturn_Lengths_of_M-Symmetric_Positions.html). Without a similar proof for the 26 quarter turn position (and if so, please give a reference), it is not a lower bound. Jim Mahoney 18:05, 8 June 2007 (UTC)
- After looking around further and re-reading the primary sources, I'm even more unconvinced. http://www.fact-index.com/o/op/optimal_solutions_for_rubik_s_cube.html states that the bounds are 20 for the face metric, and 24 for the quarter turn metric, both based on the superflip position. I'm therefore going to change the front page lower bound back to 24 for the quarter turn metric. Jim Mahoney 18:45, 8 June 2007 (UTC)
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- Update, I have a reference for the lower bound of 26q. See [2] (dated august 2 1998, subject: superflip composed with four spot)
Hmm. In this article http://www.americanscientist.org/template/BookReviewTypeDetail/assetid/25829;jsessionid=baa4XNTR6LdtGz it is claimed that there are also positions that need 21 face turns. I haven't found one yet though. User:Sander123 3 febuary 2004.
A position with 21 face turns has not been discovered up to now. User:Herbert Kociemba 9 febuary 2004.
The mathematics concerning Thistlethwaites and my algorithm was not correct. The subgroups there definitely are not normal and so the coset spaces are no groups! I changed it. User:Herbert Kociemba
The article Rubik's Cube says that "all cubes can be solved in 23 moves or fewer." Is this correct? Does it need to updated changed? Is this perhaps the correct number? (The Swami 05:54, 11 November 2005 (UTC))
According to the 6 Step Solution Guide that is included in all recent Rubik's Cubes sold today, all cubes can be solved in 20 twists or less. "RUBIK Fact: Most cubes can be solved in only 17 moves with the aid of a computer, and theoretically there is no cube that requires more than 20 twists to solve. Some people can solve the cube in under 45 moves from any scrambled positon; and a few can even solve the cube blindfolded!" This may prove to be a valuable addition to the article.User:Ring-Ding July 29, 2006.
Though 20 twist is suspected to be the actual lower bound, this has not been proven, afaik. Sander123 11:52, 31 July 2006 (UTC)
Contents |
[edit] "How to solve the Rubik's Cube" Link
How to solve the Rubik's Cube is no longer a valid link. Was that article deleted, or moved, or merged? This article seems to build off of that old one, so if it was deleted, at least a little information of it should be merged into this one. If it was moved, the link should be changed too. Fieari 06:51, July 23, 2005 (UTC)
It got moved to wikibooks:How to solve the Rubik's Cube -- Spoon! 05:19, 8 August 2005 (UTC)
[edit] Dedmore?
Why does no one speak of the excellent solution by Denny Dedmore? I have learned it this way, and it is much easier as a beginner's soulution, but can be executed quite quickly. Plus, it is highly visual and easy to understand, utilizing move sequences for the posistion of cubies on the cube face.Fishdert 22:46, 25 February 2007 (UTC)Fishdert —The preceding unsigned comment was added by Fishdert (talk • contribs) 22:45, 25 February 2007 (UTC).
- Because this page is about solution that are optimal. I don't know dedmore's method but very likely it can't solve a cube in worst case 27 turns. The solutions on this page are not intended to be used by humans for solving cubes in practice. Bye. Sander123 15:32, 26 February 2007 (UTC)
[edit] Scientist Solves Rubik's Cube In 26 Moves
http://www.sciencedaily.com/releases/2007/05/070531131326.htm
"It’s a toy that most kids have played with at one time or another, but the findings of Northeastern University Computer Science professor Gene Cooperman and graduate student Dan Kunkle are not child’s play. The two have proven that 26 moves suffice to solve any configuration of a Rubik's cube – a new record. Historically the best that had been proved was 27 moves."
Thank you 129.71.94.254 for deleting that awful overview paragraph. --72.192.8.238 (talk) 20:50, 23 March 2008 (UTC)
[edit] Lower Bounds section
Isn't this
"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. [2]"
in the Lower Bounds section now incorrect, because of http://arxivblog.com/?p=332, which shows that 25 moves is the (currently known) lower bound? Mattack (talk) 00:37, 28 March 2008 (UTC)
- There are two ways to count the number of moves: counting each quarter turn as a move, and one counting each face turn as a move. Using the face turn metric one gets lower numbers than using the quarter turn metric. Reid's position is the currently worsed known position in terms of the number of quarter turns needed. Most of the work on lower bounds focusses on the face turn metric. This difference is not always explicit in the article. Sander123 (talk) 05:20, 6 June 2008 (UTC)
