Talk:Rubik's Cube

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I copied this article (which I wrote) over from Nupedia since Wikipedia is getting much more traffic. Mark Jeays

Great article. Singmaster's book is certainly the definitive one, but perhaps some mention should be made of Thistlethwaite's "decent though nested subgroups" algorithm? --LDC

Good idea. I haven't used that method, though. Perhaps you or someone else could add a paragraph on it. I didn't want to get into lengthy discussions on the methods of solving the cube however perhaps an overview of some of the common methods would be good. Mark Jeays

I think so. Since we are not restricted by the five-paragraph-rule here, we can extend to our heart's content :-) For example, I would love to see an elaboration on the group theory aspect, and then I could make a link from group theory to here. --AxelBoldt

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I've added a link to someone's solution to the puzzle. It is listed as being GNU FDL licensed, so perhaps we can add it at Rubiks_Cube/Solution. However, I want to wait until I understand how subpages will be changed. -- Bignose

Oh, duh. Just realised the solution link is authored by Mark Jeays. Hi, Mark! Please add the solution to Wikipedia if you like. -- Bignose

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Hi! I was thinking of adding it (perhaps one solution only, since there is a good bit of extraneous stuff such as personal records and my ramblings that wouldn't be suitable). Also it could go in how-tos. I will try to do this later today (Nov. 21) but if someone else wants to, go right ahead. I think a separate page would be suitable. Mark Jeays

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Hi. I thought I'd say that I have a Rubik's Cube Java applet, which runs in a browser window! I think it may be a ask-permission before you place it on your site, but if I got permission, do you think we'd be allowed to have a virtual Rubik's Cube on this page?

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That's exactly the kind of thing I'd love to see more of here (along with images in general). Yes, you'd have to get the author's permission not just to post it here, but to release it under the GFDL. I also don't think the present Wiki software can handle Java applets directly yet, so it won't be possible to directly put it into the Wiki--it would have to be a page of its own with a link to it from the Wiki. --LDC

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I think Wikipedians should not only be writing and editing articles, but promoting the site, and creating multimedia content suitable for articles - Mark Ryan

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To comply with GFDL, we'd probably have to show the full source code to the Java applet too (which is a good idea in any event). --AxelBoldt

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I returned the spoiler warning. Many details of the cube's mechanics, such as the fact that centre squares cannot be moved and the fact that each cubie is unique, are not obvious to people when they first encounter the puzzle; figuring those things out can be part of the challenge. -- Jod

really? Those two facts can be deduced in about 30 seconds. We're not revealing the solution here. -- Tarquin 22:27 May 8, 2003 (UTC)

Well, you can and I can deduce it, but honestly many people can't, at least not right away, or not if it doesn't occur to them at all to look at it that way. I really think it's just fair to add the warning, even if only Great Fools need it. Anyhow, I think your repositioning of the warning works fine.

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Who calculated the number or positions and how? Are all those positions reachable from the solved puzzle? I ask because by taking the cube apart and then putting it together many positions that are unsolvable can be created. Just try taking one piece and then reinsert it rotated in 180 degrees.--AstroNomer 01:02, Aug 16, 2003 (UTC)

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Well, the rubik's cube is an interresting mathematical problem but also an interresting mechanism who knows about the internal of the rubik's cube ? Can someone put a cube in part to take photos ? Ericd 01:45, 16 Aug 2003 (UTC)

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A semidirect product isn't a direct product! Phys 17:01, 28 Aug 2003 (UTC)

\semidirect does not work.

Okay, which should we be using: the direct product or the semidirect product? -- Anon

The sub/sup stuff needs to be sorted out... we're mixing math with it, and it looks funny. -- Taral 18:07, 7 Sep 2004 (UTC)

Contents

1 Rubik's Cube as a mathematical group 2 "Positions" vs. "Permutations" 3 Patent issues 4 Typing error?

Rubik's Cube as a mathematical group

the text "One choice is the following group, given by generators: (The last generator is a 3 cycle on the edges). C_p = [U², D², F, B, L², R², R²U'FB'R²F'BU'R² ]" has me wondering about that last 3-cycle 'generator'. Wouldn't the simpler R²UD'F²U'D or equivalent be a better example? I'm confused by the extra pooh. 69.195.36.86 06:01, 17 Jan 2005 (UTC)

I wrote the original section. I needed a three cycle, and I took the first that I could find. Its effect on the cube is nice and clean. The resulting group was checked with GAP, to see that it indeed has the stated properties. If you are convinced that you get the same group with the generator you indicate, and it is easier to understand that way, then feel free to change it. (If you need them, GAP definitions for the cube group can be found on the Net). Sander123 15:32, 17 Jan 2005 (UTC)

"Positions" vs. "Permutations"

I find the explanation of the solution a bit confusing. There's a blurring of the distinction between "positions" and "permutations". The Rubik's cube group is not a group of "positions", whose elements are actual fixed positions of the cube. The elements of the groups are permutations, the group of which acts on the set of all possible positions of the cube. In other words, the Rubik's cube group acts on the symmetric group S₂₇, where the symmetric group represents actual positions. Of course, the action is really on some suitably nice subgroup of the symmetric group, namely the group of all realisable positions.

The "cube group" is first described as a group of "positions", then later it is intersected with another group generated by various "flips, twists", and so on. The positions themselves are not flips or twists, so this doesn't make sense. Revolver 01:13, 16 Apr 2004 (UTC)

Patent issues

A recent news article (http://abcnews.go.com/US/wireStory?id=206591) mentioned the possibility that the patent on Rubik's Cube had expired. Anyone know if this is the case? -- blahpers 17:28, 2004 Oct 29 (UTC)

Typing error?

This sentence: "The puzzle consists of the 26 unique miniature cubes ("cubies") on the surface" should probably have the number 27 instead as mentioned in the section above. Sir48-DK.

What you are referring to is,

This gives the impression that the cube is made up of 27 smaller cubes (3 × 3 × 3).

But there is no 27th cube in the center of Rubik's Cube. —Sean κ. + 00:25, 6 Jun 2005 (UTC)