Talk:Rubik's Cube/Archive 2

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Archive 1 Archive 2 Archive 3


"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)

I'm not surprised the number of possible positions is questioned. The fact is that the six centre squares cannot be moved, only rotated. They are always in exactly the same position relative to each other. And the position of the other twenty pieces are not mutually exclusive. The actual number of possible genuinely distinct arrangements of the cube is therefore much less than generally stated. 8 pieces have only three colours on them, and 12 pieces have only 2 colours on them, so that limits the number of genuinely distinct positions that they can occupy. 10:39, 16 August 2007 (UTC)
We only need to consider distinguishable combinations (positions plus rotations). The centers don't move, so they can be used as reference points. The eight corner pieces can only be in one of the eight corner positions. The remaining twelve edge pieces can be interchanged.
To place an upper limit on the number of valid combinations, here are some calculations: For each of these sets, we consider the number of positions that they occupy (N!) multiplied by the number of rotations for each piece (M) multiplied by the number of pieces in that set (N), but (through experience) I have found that one piece from each set can have only one position. This means N! · (N - 1) · M. For corners, there are 8! · (8 - 1) · 3. For edges, there are 12! · (12 - 1) · 2. So the final result is: 8! · 21 · 12! · 22.
Are there any other combinations that aren't allowed? — Val42 13:54, 18 August 2007 (UTC)
It seems a roundabout way to find the possible positions by considering the illegal/impossible combinations. Finding the actual number is straight forward: There are 6 faces, each can take 4 distinct positions independently of each other. If a given position was not reached through a number combinations of rotations of one of the sides, its not a possibility. While the discussions of permutations are interesting in a mathematical discourse on multidimensional figures, I find it irrelevant in regard to the Rubik cube. —Preceding unsigned comment added by (talk) 21:08, 15 January 2008 (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)
You're right. Its made up of 3*3*3 - 1 smaller cubies. The right number is 26. Rubik123 03:01, 10 October 2007 (UTC)

Cheap imitations

This article doesn't mention the cheap imitation Rubik's Cubes. Whenever I try to work with those cheap things, all of the colorful stickers fall off. :) — Stevey7788 (talk) 20:45, 5 August 2005 (UTC)

True. It's very hard to find real Rubik's cubes nowadays. -- Eagleamn 05:18, 10 October 2005 (UTC)
Isn't "Rubik's" the so called official Rubik's cube maker? --- Acdx 23:29, 24 December 2005 (UTC)
Try buying them online from Calculusfreak 20:42, 7 August 2006 (UTC)
The actual rubik's standard can be bought at Walmart for $10-15 CAN. Now these are more expensve because of the sticker duration, it turns better (does not get stuck), has the nice little sticker in the middle of the white cube, and can be taken apart easier. The Professor cube, or the 5X5X5 is more expensive at about $35, and is harder to turn because of the amount of cubes on one layer, but once you get used to it, it turns fairly well. Androo123 (talk) 21:26, 28 April 2008 (UTC)

Rubik's Tesseract

Someone with a better understanding than mine might want to write about higher-dimensional analogs such as Rubik's Tesseract Archola 08:03, 26 December 2005 (UTC)

Then you might be interested in this which lets you actually play with a (simulated) 4D cube. Have fun!—Tetracube 05:08, 12 January 2006 (UTC)
The GabbaSoft cube is the best that i have found. a free demo is available here 04:56, 5 May 2007 (UTC)
Basically, 4d in the Cartesian Coordinate system would mean that there is an extra variable added. Thus, in 3d, (3,4,5) and (3,4,5) would be the same point. However, if the latter point moved +4 in the fourth dimension, (3,4,5,0) and (3,4,5,4) would not be the same point. I like to think of tetraspace as an infinite number of three-dimensional "realms" that a 4d person could move through. —Preceding unsigned comment added by Cubie Newbie (talkcontribs) 23:15, 4 April 2008 (UTC)

Originally posed as a problem for students

I read somewhere that Rubik ogininally devised the cube as a an exercise for his students, to help them think logically and geometrically. Anyone know more about this?

As I recall, Professor Rubik was a professor in industrial design and wanted his students to see that it was possible to create highly complex structures from simple concepts. Unfortunately I have no official source. --Blonkm 20:40, 1 July 2006 (UTC)
I remember that on there is a section that says that he built it to challenge the students with 3-d geometry —Preceding unsigned comment added by (talk) 05:41, 18 May 2008 (UTC)

alternative (imitation) "cube" dodecahedron

i used to have one of these, it was mechanically identical to the cube but each corner piece was sliced at a 45 degree angle to create a new face, this intersected the adjacent cubies so that the original faces were now smaller sqares at a 45 degree angle to the grid and there were now 8 additional triangular faces

the effect was somthing similar to this:

edit: sig 09:41, 26 June 2006 (UTC)

The shape being described is more like this:

Both of these have 14 faces (dodecahedron=12). Personally, I have never seen either of these as a Rubik puzzle. Does anyone have a picture? However, I have seen this one;

which is possibly what the OP had in mind.

Spinningspark (talk) 13:51, 30 December 2007 (UTC)

Permutations section

There needs to be more of an explanation of the mathematical formula in the section called "Permutations" that illustrates step-by-step.

I agree. I think some of the information is actually altogether incorrect. For instance, "261 light years" and "256 times around the earth." I'm not a professional by any means, but I'm fairly certain it wouldn't take more than a year for light to go the same distance as the circumfrence of the earth at it's equator. Tekemperor 06:23, 4 May 2007 (UTC) I just realized it was referencing the entire surface of the earth, not just the circumference.Tekemperor 06:29, 4 May 2007 (UTC)

Invisible cube?

The article says: "The 3×3×3 version, which is the version usually meant by the term "Rubik's Cube," has nine square faces on each side, for a total area of fifty-four faces, and occupies the volume of twenty-six unit cubes (not counting the invisible cube in the center)." (bolding added by me).

What is meant by this? I want to just remove that, but is what is meant that there is conceptually a space for a twenty-seventh cube? In an actual Rubik's Cube, there is no cube in the center (there is just the central axis) -- this makes it sound like there is. Any thoughts? --Twilightsojourn 12:33, 8 August 2006 (UTC)

Conceptually, if you cut the cube into sub-cubes, the center of the cube is the 27th "sub-cube" or "cubie". But it is not really relevant here, since the Rubik's Cube isn't actually made of 27 sub-cubes, but with a central axis, as you said. I vote to remove the bolded statement.—Tetracube 19:45, 8 August 2006 (UTC)
I agree. I also vote to remove the bolded section -- and perhaps reword the entire sentence, to make it a bit clearer (maybe saying that there are 26 cubies, instead of that it "occupies the volume of twenty-six unit cubes"?). --Twilightsojourn 20:15, 8 August 2006 (UTC)

It's been a while and I see that the word "volume" doesn't appear in the current version of the article, but I'll point this out nonetheless. If you're talking about the volume contained by the faces of the cube, then 27 unit cubes is correct. The volume occupied by solid material would be 26 unit cubes if each piece were a solid cube and the centre were completely hollow, but that isn't the case either. It's true that there are 26 pieces that are conceptually cubical, but it doesn't make sense to talk of 26 unit cubes as the volume of the cube. -- Smjg (talk) 16:34, 29 December 2007 (UTC)

Has a 6x6x6 cube really been made?

The introduction to this page suggests that it is possible to make one (I've only read the introduction so far). I've played with a virtual one on a website, but I'm sure I remember reading somewhere that it was impossible to physicaly make one. The same article said that it was possible to make a 7x7x7 one but nothing larger. (

See this. It claimed, a few years ago, that 6x6x6 cubes would be available to the public within a few months. They still aren't available, but some prototypes (such as the one in the video at the bottom of the page) exist. I haven't heard of any "limited edition" 7x7x7 cubes. I'll change the introduction accordingly. --Ravi12346 15:45, 7 October 2006 (UTC)

I saw a picture of a 7x7x7 on a fansite. it had curved sides. 05:03, 5 May 2007 (UTC)
I realize that this is a rather late comment on the issue, but the 6³ and 7³ cubes do exist. The 6³ cube also has its own article. I'll write an article on the 7³ cube when I get a hold of one, if someone else doesn't do it first. Hellbus (talk) 05:24, 5 July 2008 (UTC)

Game award in Pop Culture

I know its important to mention that the cube won an award for best puzzle, however I don't think that it belongs under the pop culture section. 19:56, 14 February 2007 (UTC)

First non-spherical 9x9x9 cube

As of Feb 22, 2007 Tony Fisher released some details of his non-spherical 9x9x9 cube at [1].

It's worth noting that 7x7x7 and larger cubes by Panagiotis Verdes are all somewhat spherical as shown at [2] which makes this 9x9x9 even more special.

Could someone add this information to the article. I'm not good enough in writing to do that by myself. 13:00, 24 February 2007 (UTC)

Sorry, that was a hoax, which is now mentioned in that thread. This section can be deleted. 09:00, 26 February 2007 (UTC)

Problem with "Rubik's Revolution"

I have a problem with this lines: "In 2007, the first electronic Rubik's Cube was created-- the Rubik's Revolution. The Rubik's Revolution is a traditional cube with six different ways to play. Each game features light, sound and voice effects and multiple levels to unlock, each challenging your mind and dexterity. The Rubik's Revolution offers not only individual play, but also multi-player gaming. The Rubik's Revolution will be in stores summer of 2007." I am afraid it's not an information, but more like an advertisment, and it should not be here. What do you think? Mozaik 15:03, 27 February 2007 (UTC)

If the information is true, maybe it just needs a rewrite. Insanephantom (my Editor Review) 22:39, 27 February 2007 (UTC)
its actually quoted as something someone else said —Preceding unsigned comment added by (talk) 05:56, 18 May 2008 (UTC)
The information is true but utterly irrelevant to this article. It definitely does not belong here. There has even been some dispute in the past on whether it should be mentioned in the template (which appears at the bottom of all Rubik articles). It is not a Rubik cube, it is not a derivative of the Rubik's cube, it is not even a sequential move puzzle. It is just one more item in a very large collection of products that try to sell tnemselves by using the Rubik name or using coloured cubes as a motif. SpinningSpark 10:32, 18 May 2008 (UTC)

External links section

Should the External links section be subdivided? Just giving it a brief look, seems there is three categories (though I can't rightly define the third) those being Official Links, Solution Links and other types. At the moment there seems to be chaos as they're all mixed up in a hodge podge. Anyone up to sorting them out? -Gohst 13:37, 9 March 2007 (UTC)

it's actually quoted —Preceding unsigned comment added by (talk) 05:55, 18 May 2008 (UTC)


There are many solutions and algorithms out there, however most of them are extremely complicated but i have found very simple solutions on youtube from a guy called RobH0629 And he can do every single rubik's cube.

The References that are used are:

T = Top face clockwise a quater turn F = Front face clockwise a quater turn R = Right face clockwise a quater turn L = Left face clockwise a quater turn B = Back face clockwise a quater turn

When a lower case 'i' is added, it means that you have to rotate it counter-clock wise a quater turn.

When '180' is added, it means that you have to rotate it a 180°.

He does a step by step vidio guide So have fun solving the cube!!

13thDiZiPLE 18:24, 6 October 2008 (UTC)

Color versus Colour

The words colour en centre have been changed back and forth to color and center a couple of times in this article now. Why are they changed all the time in this article? Perhaps we can settle on one or the other. Personally I have a preference for colour and centre, but I can live with either. The original article uses colour and center. Any opinions? Sander123 08:42, 22 March 2007 (UTC)

There is a standard guideline (WP:ENGVAR) about this sort of thing: go back in the history to the first instance where either American or English spelling was used, and use that same spelling for all subsequent editing. It isn't perfect, but at least it is an objective tie breaker. CMummert · talk 12:03, 22 March 2007 (UTC)
In this case, the very first edit used "colour". CMummert · talk 13:07, 22 March 2007 (UTC)
An even earlier edit ([3] probably not the first) used both! --Henrygb 18:40, 22 March 2007 (UTC)
I gave the wrong link - how did that happen? The first edit I see now is from 2001-11-21 [4]. You're right - it does use both. And you're right that, based on the edit summary, it was probably not actually the first edit. Were the very old histories lost in a crash or something? CMummert · talk 18:56, 22 March 2007 (UTC)
There was a cut-and-paste move from Rubiks Cube so I just merged the page histories. Not your error. --Henrygb 22:43, 22 March 2007 (UTC)

The original version doesn't give a clear answer then. First of all, we agree that the choice is between {colour, centre} and {color, center}? According to the oxford dictionary these are the British/Us variants.

I've looked at the first edition of this article in each year, starting at 2002. Here are the versions [5] [6] [7] [8] [9] [10]

From these I conclude the following. Up to 2004 there was no preference for colour or color but in 2005 and 2006 there was a preference for colour in 2007 it was changed to color. Up to 2006 there was no preference for centre/center but in 2007 it changed in center.

It seems that historically there was a slight preference for British English. I propose to stick to British English then, and in particular {colour, centre} for this article. Opinions? Sander123 10:53, 26 March 2007 (UTC)

My opinion is the the longer we discuss it the less work we get done. Almost any English speaker will be able to read both versions, so it makes little difference which one we use. So the British spellings are fine with me. CMummert · talk 12:04, 26 March 2007 (UTC)
This discussion has been on the discussion page for a while now. As no others have expressed an opinion, I take it that everybody agrees with British spelling. I've updated the article accordingly. Thanks to all for participating. Sander123 14:48, 6 April 2007 (UTC)

Date of Invention

A recent edit changed the date of invention from 1974 to 1978. A quick google search reveals many sources that state that the cube was invented in 1974. This could be vandalism, but I thought I would bring the issue up on the talk page first before the date is changed again. Vvitor 06:04, 8 April 2007 (UTC)

If you could, find the best (most authoratative) reference to the creation date and add a footnote to the article with that link. This would help make it clear what the correct date is. CMummert · talk 12:58, 8 April 2007 (UTC)
I've done this, and the source I used was the official website of the cube (as listed in the "External Links" section). Thank you for your help in the matter. Vvitor 13:33, 9 April 2007 (UTC)

Removal of Simpsons quote

I undid your change to inlude the comment "including Homer's classic (... use your main finger) in the article Rubik's Cube. I feel that it did not add to the article in an encyclopaedic manner in the context of Rubik's Cubes. Feel free to argue against my action on my Talk page User A1 01:46, 10 April 2007 (UTC)

Centre faces

What's up with the Centre faces section. All the cubes in the pictures have colored center faces. --Apoc2400 05:40, 1 May 2007 (UTC)

I don't understand your question. Do mean that there should be a picture added with a cube with marked centre faces? Sander123 07:42, 1 May 2007 (UTC)

Massimiliano Iseppon

Does anybody know who Massimiliano Iseppon is? He was added as a fellow inventor of the cube. Can anybody confirm/source it? I removed it for now. Sander123 07:41, 1 May 2007 (UTC)

Will Smith

The article says that Will Smith's ability to complete a Rubik's cube is still under speculation, but he did solve a cube while appearing on the Oprah Winfrey show to advertise "The Pursuit of Happyness". —The preceding unsigned comment was added by (talk) 03:48, 9 May 2007 (UTC).

The following was taken from [11] The man who taught Smith how to solve the cube so fast was the organizer of Saturday's event. Tyson Mao, who recently graduated from Caltech, is one of the world's fastest speedcubers and a founder of the World Cube Association, which holds such events around the world.Algonquin 11:27, 9 May 2007 (UTC)

Alternative Competitions

"In addition, informal alternative competitions have been held, challenging participants to solve the cube under unusual situations. These include:"

This whole section needs to be reworded. As a speedcuber, I can tell you a few of these things (specifically one handed and blindfold) are not informal, but just as competitive as the standard 3x3 cube. There are also various other things that speedcubers do that are much less competetive; see for a full list.

Blasphemized 03:49, 14 May 2007 (UTC)


Can anyone verify the edit stating the origins are Chinese? I find this hard to believe. User A1 14:21, 24 May 2007 (UTC)

Im going to remove it. verifiability.

Rubik's Cube 1980-2005

Continued from the previous subject. When trying to search for it on Google I couldn't even find a reference to this anniversary cube at all. Can somebody confirm that? Sander123 08:03, 25 May 2007 (UTC)

Yes, Rubik's did release a 25th anniversary version of the cube. It has shiny stickers on it. Pictures and references can be found on google fairly easily by using the correct search terms. Blasphemized 05:02, 29 May 2007 (UTC)

Sorry, I tried but I didn't find them. Can you give me some? Thanks. Sander123 12:08, 30 May 2007 (UTC)

Lowest amount of moves needed

I'd like to add "Using mathmatical group theory, scientists from Northeastern Univeristy have proved that the maximum amount of necessary permutations is 26." to the article, but i dont know how to refrence it to, could someone else do that for me? -- 13:08, 4 June 2007 (UTC)

The Rubik's Cube - when available in England

Text keeps appearing at the top of the Rubik's Cube article to the effect that the Magic Cube was being sold by David Singmaster as "Rubik's Cube" in England "by 1976".

Two points:

1) The Cube had not even been manufactured in 1976 and was available absolutely nowhere. The first test batches of Cubes were manufactured in late 1977 in Hungary. This information is available on the official Rubik's Online site -

2) The Cube did not become Rubik's Cube until 1980 - it was renamed by Ideal Toys. This information is also available via the link to Rubik's Online above. David Singmaster sold Cubes to friends and colleagues in England from around 1978 onwards - but they were "Magic Cubes" and he did not rename them.

To prove my point further that David Singmaster did not rename the Magic Cube, a comment of his from 1980, quoted in the book "20th Century Words" by John Ayto (Oxford, 1999) (ISBN 0-19-860230-8):"

"... the Magic Cube is now being sold as Rubik's Cube... [the Ideal Toy Corp.] has renamed the cube as 'Rubik's Cube' on the grounds that 'magic' tends to be associated with magic."

So Concerned about Inaccuracies on Rubik's Cube Page I've Joined Wiki!

I sent the Rubik's Cube in England post above and have been so concerned about the "Rubik's Cube" sold in England in 1976 inaccuracies that were at the beginning of the Wiki article, I have decided to join you!

For better or worse, I am a 1980s historian, and it took quite a lot of trouble to get the history of the Cube sorted and understood as it is quite complicated. I would be grateful if an eye can be kept on this article. The inaccurate information may reappear.

The basic Cube timeline, as I'm sure you all know, is:

1974: Erno Rubik invents the Magic Cube

Late 1977: First test batches of Magic Cubes in Budapest toy shops.

1978 & 1979: The Magic Cube becomes popular in Hungary and some Western World academics become interested. In June 1979, English mathematician David Singmaster writes a newspaper article on the Magic Cube - the first to appear outside Hungary. In September,Ideal Toys sign a deal to bring the Magic Cube to the West.

1980: Magic Cube makes its debut in January and February at the toy fairs of London, Paris, Nuremberg and New York. The Cube is then manufactured to bring it in line with Western World safety and packaging norms. A lighter Cube is produced and renamed "Rubik's Cube".

Rubik's Cube makes it debut in the USA in May 1980 although, due to a shortage, there are delays in some other countries, including the UK, which has to wait until just before Christmas.

I hope that you will help to keep the Wiki Rubik's info accurate. A great deal of work goes into recording the pop culture of recent decades, and it's a shame when bizarre and inaccurate information infects the system!

A Wiki page which (wrongly) informs people that the Rubik's Cube was on sale at the Open University in England in 1976, before going on (rightly) to tell the story of the Cube's invention, its release in Hungary in 1977 and its renaming as Rubik's Cube in 1980, contradicts itself, makes nonsensical reading - and is a little frustrating to those of us who devote time to writing the decades as they really were.

Looking forward to being a part of the Wiki community...

(Brett1980s 01:54, 9 June 2007 (UTC))

Any relation to timecube?


I've never heard this term and a Google search of "supercubing" and "rubik's" gives nothing appreciable. There's one mention of bigger cubes, but nothing else. Does anyone have the courage to remove it? Hyperneural 02:24, 26 August 2007 (UTC)

this is a very common thing among speedcubers and nothing special. It means the cube is solved with the centres in the original orientation. --Blonkm 17:40, 27 September 2007 (UTC)

A four-side pyramid?

I seem to remember someone solving a four-sided Rubik's 'cube' many years ago. Does anyone else recall seing them? —Preceding unsigned comment added by (talk) 00:37, 1 September 2007 (UTC)

A Pyraminx? Hyperneural 04:25, 7 October 2007 (UTC)

Rubik's cube software

I added a section on software. Now without having it loaded with external links soon, maybe we can have a List of Rubik's cube software puzzle. --Blonkm 17:43, 27 September 2007 (UTC)

complete list of solutions & algorithms

I was thinking, should there be another page of every algorithm and solution technique? I mean, I know that the monkeys & typwriters theory would say there are an infinite number of possible solutions, but there doesn't seem to be (anywhere on wikipedia) a page with links to all the solutions. 03:12, 4 November 2007 (UTC)

How about a list of every distinct algorithm? AFAIK these are:
  1. No particular order (e.g. Thistlethwaite's?)
  2. By layers (Singmaster's and many others)
  3. Corners first, then edges (the first solution I bought was like this)
  4. Edges first, then corners
I think there are at least two other possibilities. -- Korax1214 (talk) 12:31, 1 July 2008 (UTC)
How would you define "every", given the infinite monkey theorem you quite rightly cite? Even with a list, ISTM you can never prove it's complete. But an approach you could add to this list is one layer, then remaining corners, then remaining edges. This book uses this method. Moreover, if you have this sequence [12]
  1. Do the first layer except for one corner
  2. Do the middle layer
  3. Fill in the final first layer corner
  4. Do the last layer
then does this count as a by layers method? -- Smjg (talk) 14:57, 1 July 2008 (UTC)
Actually, it was the person to whom I was replying who cited the infinite monkeys theorem. What I propose is the same kind of filter as is applied to other puzzle solutions; just as, in the Eight queens puzzle for instance, two solutions are not regarded as different if they differ only by rotation or reflection, so Rubik's-Cube-solution algorithms should (IMO) not be regarded as different if they differ only in the sequences used to perform individual steps. Given that, I think this section is already near to being a complete list. -- Korax1214 (talk) 22:47, 1 July 2008 (UTC)

inconsistent figures

Given that the world record for the 5x5x5 is listed on the speedcubing page as 1hr 38 mins, I find it hard to reconcile that with the claims made here: "In May 2005, the Greek inventor Panagiotis Verdes constructed a 6×6×6 Rubik's Cube; on May 23, 2006, Frank Morris, a world champion Rubik's Cube solver, tested this version. He had previously solved the 3×3×3 in 15 seconds, the 4×4×4 in 1 minute and 10 seconds, and the 5×5×5 in 1 minute and 46.1 seconds. The 6×6×6 took him 5 minutes and 37 seconds to solve. " The figure for the basic cube seems reasonable, all the others sound fictional. 18:10, 10 November 2007 (UTC)

He prob'ly meant 1 min 38 sec —Preceding unsigned comment added by (talk) 23:03, 13 December 2007 (UTC)

The world record for the 5x5x5 is 1 minute 29 seconds at the moment. --M1ss1ontomars2k4 (talk) 23:27, 8 March 2008 (UTC)

Bad Dates

The dates given in the Conception and Development section are all screwed up. Almost all of them seem to be a decade later than they should be. I'd fix it, but I'd be assuming that the only thing incorrect would be the decade, and I could very well be wrong about that. But I know Rubik's cube was around well before I was in high school (1990).

I've been on a few bad dates myself... Oh wait, that's not what you mean. heh..
Seriously though, good spot. Earlier today, somebody came in and shifted all the dates in that section by a decade, and nobody spotted it. I undid their edit, so it should be good now. Thanks for the tip! ---- Jaysweet (talk) 21:19, 16 November 2007 (UTC)

Some Possible Vandalism to article

I have noted over the last two or three days that somebody has been visiting the Rubik's Cube article and making small, inaccurate changes to the text. For instance, when I visited a day or two ago, somebody had changed the original name "Magic Cube" to "Logic Cube" in the opening paragraphs. I corrected this.

Today, somebody had altered several of the dates. I have corrected this, but it might be an idea if we keep an eye on the article for a while.

(Dorgan65 (talk) 01:37, 17 November 2007 (UTC))

Inventor's name altered - possible prank/vandalism?

I visited the Cube article this evening to find that somebody had altered the name of the Cube's inventor in the opening paragraph from Erno Rubik to a name I didn't recognise. I have changed it back to Erno Rubik. —Preceding unsigned comment added by Dorgan65 (talkcontribs) 00:03, 30 November 2007 (UTC) (Dorgan65 (talk) 02:46, 30 November 2007 (UTC))

Rubik's Cube in Popular Culture

I noticed that this section was removed with the rationale that it is nn trivia with no value to the article, and that references of this kind could fill 20 pages or more. I have a few qualms with this:

  • The two trivia references left in the article have no rationale as to why they are more notable than the others.
  • Trivia sections should not simply be removed if you follow WP:TRIVIA but rather incorporated into the article somehow. If it could not be incorporated, it could always be moved into another page.
  • No discussion before removing the section.

I do not think that the section should be removed entirely. Of course, it's not suitable in its present state, but it does provide an indicator of the cube's status in popular culture, and in this case something is better than nothing, in my opinion. Paiev (talk) 02:41, 5 December 2007 (UTC)

While I like trivia, there are those who don't and think that such sections have no place here on Wikipedia. To accomplish what you want to do, just go back in the history to the revision with the trivia then integrate the information that you think belongs in this article. — Val42 (talk) 03:10, 11 December 2007 (UTC)
None of the bullets in that section seemed to have any references. The prize, which is good to include, is already mentioned in the lede. The rest seem just like passing appearances. I would be more convinced they are worth mentioning here if any source that describes them as important appearances of the cube could be found. I don't see the encyclopedic benefit of listing apparently random movies (etc.) in which the cube has appeared. — Carl (CBM · talk) 02:03, 20 December 2007 (UTC)

calculation correction

In the permutations section the article claims: "If they were laid side by side, it would cover the Earth approximately 256 times". I may be wrong but isn't it approximately 276 times:

  • Surface area of the Earth (see Earth) = 510,072,000 square km = 510072000000000 square metres.
  • Surface area covered by one cube = 57 mm * 57 mm = 0.003249 square metres.
  • Surface area covered by all permutations = 0.003249 * 43252003274489856000 = 140525758638817542.144 square metres.
  • Number of Earth's covered = 140525758638817542.144/510072000000000 = 275.501

Reply if you come to a different answer. --Bucephalus (talk) 23:46, 20 December 2007 (UTC)


In the film Hellboy (2004), the character Abe Sapien says of his Rubik's Cube "Listen, I'm not much of a problem solver. Three decades... and I've only completed two sides." [13]

I removed the above line here as it seems to me to be irrelevant trivia. I was reading the article and suddenly came across this and it definitely seems out of place. The world fair cube for example seems a lot more relevant. The fact that it was lost probably isn't so important but it's continouing on so I suppose it's okay. However the above hardly seems to be particularly relevant to me. I'm sure it's not the first nor will it be the last time the Rubik's Cube is mentioned in a film Nil Einne (talk) 15:33, 29 December 2007 (UTC)

I've reverted your edit. The fact that the Rubik's Cube makes a brief albeit telling appearance in a major feature film more than two decades after it was a major fad speaks to its iconic status as a puzzle. As a prop, it speaks volumes, savvy? kencf0618 (talk) 18:40, 29 December 2007 (UTC)

I've removed the quote because I've spent over fifteen years studying the history of the Cube, and I think it is illogical. The film character, "Abe Sapien", says of the Cube "three decades and I've only completed two sides." The character could not have spent three decades attempting to solve the Cube in 2004 because it was not available in Hungary as the Magic Cube until late 1977 and in the rest of the world as Rubik's Cube until 1980. The film's writer is muddling up the INVENTION year of the Magic Cube (1974) with the time it became available. The character Abe Sapien is talking nonsense, which does happen in everyday life, but in a factual Wikipedia piece the quote is misleading.

(Dorgan65 (talk) 23:22, 30 December 2007 (UTC))

Timeline aside, it was a striking cameo of the Cube as a virtually intractable puzzle –it definitely has staying power! kencf0618 (talk) 02:59, 31 December 2007 (UTC)
We should have a trivia section, it lets readers know how popular and well known the cube is- (talk) 21:41, 2 January 2008 (UTC)
Trivia sections are now discouraged in Wikipedia - see WP:TRIV. If it is relevant, it should be in the main article, if it is not, then it goes to another article or gets deleted altogether. Spinningspark (talk) 22:41, 2 January 2008 (UTC)

Doesn't make sense... Contradictory section?

This part of the article seems contradictory:

In 1982, David Singmaster and Alexander Frey hypothesized that the number of moves needed to solve the Rubik's Cube, given an ideal algorithm, might be in "the low twenties". In 2007, Daniel Kunkle and Gene Cooperman used computer search methods to demonstrate that any 3×3×3 Rubik's Cube configuration can be solved in a maximum of 26 moves. [12] [13] Work continues to try to reduce the upper bound on optimal solutions to 25 moves, or even lower. The arrangement known as the super-flip (U R2 F B R B2 R U2 L B2 R U' D' R2 F R' L B2 U2 F2), where every edge is in its correct position but flipped, requires 20 moves to be solved. No arrangement of the Rubik's Cube has been discovered so far that requires more than 20 moves to solve.

So, is it a maximum of 20, or 26? Jenglish02 (talk) 01:30, 19 February 2008 (UTC)

I think a computer found that the theoretical maximum SHOULD be 26, but in practice nobody has found one that takes more than 20... That's what i got out of that anyway, but someone please correct if I'm wrong. Brainmouse (talk) 05:55, 19 February 2008 (UTC)

How does the new logo on a rubik's cube look like now? (Master King (talk) 02:00, 8 March 2008 (UTC))


The "Conception and development" section had been removed without any explanation when I logged on this morning. I have replaced it. There is no reason for its removal - the information about the development and release of Rubik's Cube simply echoes the Rubik's Online "Cube History" and is absolutely correct. —Preceding unsigned comment added by Dorgan65 (talkcontribs) 12:42, 23 March 2008 (UTC) (Dorgan65 (talk) 12:47, 23 March 2008 (UTC))

Either a test edit or straightforward mistake I would say. I have left a warning on the users talk page. SpinningSpark 16:33, 23 March 2008 (UTC)

The search for optimal solutions

No arrangement of the Rubik's Cube has been discovered so far that requires more than 20 moves to solve

Won't a superflip plus a pair of corner twists do it?

SpinningSpark 19:55, 27 March 2008 (UTC)

Without considering any solution methodology or algorithm, one can note that a better solution, whatever its details, has fewer steps than the previous solution. For example, if the previous solution required 22 moves, and then a newer, better solution is discovered that requires only 20 moves, one can say that the present optimal solution requires 20 moves, but no one has yet found a solution that requires less than 20 moves to solve. The direction of improvement of an optimal solution is toward fewer moves, toward less moves, required to solve the cube. --Kensor (talk) 09:54, 11 October 2008 (UTC)

Twenty-Five Moves Suffice for Rubik's Cube

please check this link:

M.zdila (talk) 21:08, 27 March 2008 (UTC)

More coverage about that here: [14] The Seventh Taylor (talk) 22:29, 4 April 2008 (UTC)
ISTR Singmaster's Notes said 20 or 22. Also that a hypothetical algorithm to actually solve it in this number of moves is half-jokingly termed "God's Algorithm". -- Korax1214 (talk) 12:08, 1 July 2008 (UTC)

Small error corrected

I have removed this piece of information from the article which I know to be in error:

"In the countries of the former Soviet Union, the cube was sold with the colors embedded onto the individual cube sides, instead of stickers."

I have an extensive collection of early Hungarian Magic Cubes and Rubik's Cubes and all early models were manufactured with stickers. Special "deluxe" editions were released later with "embedded" colours, but these were available worldwide. —Preceding unsigned comment added by Dorgan65 (talkcontribs) 00:08, 30 March 2008 (UTC)

(Dorgan65 (talk) 00:10, 30 March 2008 (UTC))


Cool article, my best friend loves rubiks cube! She is actually an expert. But My other 2 classmates really are in to it and I think they could solve it more or less a minute.

Though, arent rubiks cube also made up of tiles? —Preceding unsigned comment added by Beatlesnicole (talkcontribs) 12:56, 4 April 2008 (UTC)

Conception And Development: Accurate Information Recently Removed And Now Reinstated With Citation

I have discovered that accurate, verifiable information was removed from the "conception and development" section today. This relates to the Magic Cube making its toy fair debut in the West in January/February 1980. This information is verifiable and is included in the official Cube History on

I have reinstated the information with a citation.

(Dorgan65 (talk) 10:54, 9 April 2008 (UTC))

As of today, I have discovered that the in-depth Rubik's Online Cube History is no more! More below. —Preceding unsigned comment added by Dorgan65 (talkcontribs) 14:18, 9 April 2008 (UTC)

In-depth Rubik's Online History Changed To A Brief Summary

I have just discovered that the wonderful in-depth Rubik's Online Cube History has been replaced by a brief summary -

It's a bit of a sad day for Cube scholars!

(Dorgan65 (talk) 14:16, 9 April 2008 (UTC))

UPDATE - There is a copy of the original Rubiks Online brief history of the Cube here -

(Dorgan65 (talk) 14:35, 9 April 2008 (UTC))

Move notation confusion

I'm confused by the move notation section. For example, U means turn the top side one quarter clock-wise. But this description does not make me feel confident on how to move it, since I can turn it left or right and I can't figure out which direction I should go.

So an easier explanation for the different notations would be nice so that I can and other people can try the super flip. —Preceding unsigned comment added by (talk) 14:29, 11 April 2008 (UTC)

I don't quite understand your problem. The article seems perfectly clear to me. The move is clockwise as viewed looking at the face. Do you mean that it could be anti-clockwise if you were looking at it from behind or is it that you just do not understand the meaning of clockwise? SpinningSpark 08:29, 12 April 2008 (UTC)

Digital clocks don't have any hands so clockwise is almost a lost meaning. However, there is a question, do I hold the top stationary and turn the bottom two rows or do I hold the cube and turn the top clockwise? A U move would mean holding the top stationary and moving the bottom two rows counter-clockwise, as viewed from the top, which would immediately make all future instructions meaningless, because the frame of reference was changed. Oakwillow (talk) 18:00, 24 April 2008 (UTC)
Saying that clockwise is losing its meaning because clocks no longer have hands is rather silly. First of all, it is not true that analog clocks are unheard of. They are still very popular, just look in the window of your local jeweller to see that I am right. Even digital clocks often display the time with virtual hands. This is because people find this mode of display familiar and convenient and, unlike a digital display can be "taken in" at a glance without first having to observe and interpret the digits. Secondly, clockwise means, always has meant, and always will mean even if analog clocks disappear, a rotation opposite to the right hand screw rule, that is, the negative of the scientific, mathematical and engineering conventionally positive direction. There is no ambiguity in its meaning whatsoever.
A U move is not holding the top stationary and moving the bottom and middle layers, at least not in the conventional cube notation. It is moving the UP side. The article consistently refers to sides. I think that is clear enough. What would you suggest changing? Even if U were defined as you suggest, it would not make following moves meaningless. It would be perfectly possible to develop a notation system that worked that way. SpinningSpark 20:55, 24 April 2008 (UTC)

The "Singmaster notation" as explained in the article makes perfect sense until it comes to the x, y, and z cube rotations. Using the letters FBUDRL to refer to the faces with the letter alone representing a right or clockwise rotation, prime noting a left or counterclockwise rotation, and 2 indicating a half turn makes sense even if it is made unnecessarily confusing by being too abbreviated. The x, y, and z cube rotations are odd, however, because they don't follow normal scientific convention. The described positive x, y, and z rotations imply a positive x-axis to the left, a positive y-axis down, and a positive z-axis directed away from the observer. This z-axis orientation violates the normal orientation of the z-axis relative to x and y by the right hand rule which would be toward the observer for this case. In addition the z-axis is typically (though not always) used for the vertical or height direction. If x and y are used to define the vertical left/right plane then it would be normal for positive x to be right and positive y to be up, which would make positive z toward the observer. This axis system would make sense, but then the described rotations about x, y, and z would all be negative (this conflicts with the convention for face moves). It seems odd that a notation with inconsistencies would become a "standard". I personally prefer notations that more explicitly designate rotation direction or an orientation independent notation using the first letter of each face's color to refer to a face. (talk) 08:44, 9 June 2008 (UTC)


I have reverted the change of all occurences of "algorithm" to "operator". The edit summary claims that the difference between an algorithm and an operator is that algorithm involves a decision process. I can find no definition of algorithm that matches this, including the Wikipedia article.[15][16][17] They all say that algorithm is a defined sequence of steps without requiring a decision to be in there (although I accept that in the computer programming world this would naturally be expected). I agree that in some instances operator would be a better choice of words, but the wholesale replacing of algorithm is going too far, especially as it seems to be common terminology in Rubiks cube circles. SpinningSpark 21:17, 24 April 2008 (UTC)

But algorithm is used by cubers all over the world, this may confuse new cubers. Masterwiki (talk) 05:57, 26 April 2008 (UTC)
Yes, I think we agree. That's why I reverted the change to operator. All I was trying to say above was that a U move or a simple combination like U-1L should not sensibly be called an algorithm. It would be mathematically correct to describe that as an operator, but I think the cubing community would prefer the simple term move. If this were a mathematical article, it would be fair to require mathematical rigour in terminology. However it is not a mathematical article (it is not in a maths category - it belongs to puzzles and toys categories) and should use terms appropriate to it's audience. SpinningSpark 08:32, 26 April 2008 (UTC)
Just saw the edit you made to the article. I think you are misreading the history of the article. The edit I reverted was the one which changed all occurences of algorithm to operator and vice versa. I put it back to algorithm. The two remaining mentions of operator were in the original version of the article and said words to the effect algorithm (or operator). It is redundant to change that to algorithm (or algorithm) as youd did.
I also notice that the Wikiproject Mathematics has rated this article GA, so presumably they were happy with the articles use of algorithm. SpinningSpark 08:55, 26 April 2008 (UTC)

FWIW, I've always used "algorithm" for a process to obtain an overall result (such as the solution or a particular pattern such as The Ring) and "operator", "sequence" or "move" for one of the sub-processes which combine to form the algorithm as a whole. This also fits the mathematical/computing sense of "algorithm". -- Korax1214 (talk) 11:42, 2 July 2008 (UTC)

Competitions & record times

I removed this sentence from the end of the competition times section due to the weasel-word ("many") and the uncited nature. If it can be verified in some way (and made more specific?) it can be added back, I suppose.

"Many individuals have recorded shorter times, but these records are not accepted due to possible lack of compliance with standards." —Preceding unsigned comment added by Brainmouse (talkcontribs) 15:00, 7 May 2008 (UTC) (edit -- sorry I forgot to sign Brainmouse (talk) 21:22, 7 May 2008 (UTC))
Yea well many athletes break records in training but no one makes a song and dance about that because it doesn't count. I don't see why cube times should be any different. Official records are broken at official events under the oversight of officials. That's what makes them official records. I would not particularly be in favour of putting that text back even if someone does find a citeable quote of people claiming to have done it (which in all probability has happened). It's not relevant, official is official. SpinningSpark 20:02, 7 May 2008 (UTC)
If you guys had spent a few minutes looking it up, you would have found a huge list of unofficial records at, the definitive source for unofficial records. I'm not saying that it should go back in or it should stay out of the article, but it is true. --M1ss1ontomars2k4 (talk) 01:40, 8 June 2008 (UTC)

4D Image?

The picture of a 4D cube has 7 colors. Shouldn't it have 8? (I asked on the discussion page for that image, but, so far, no response there.) —Preceding unsigned comment added by (talk) 16:55, 10 May 2008 (UTC)

You are right inasmuch as there are indeed 8 cubes an a 4-cube and you need 8 colours to mark them all uniquely. However, the artist has used a number of "cheats" in order to succesfully represent a 4-cube Rubik. The 8th cube would enclose all the rest in a commonly used 4-cube projection (extreme foreshortening) but this would make the diagram very messy. Even line drawings of 4-cubes get messy so the artist has chosen to leave the 8th cube as hidden detail, much as you would leave out the back face of a drawing of a 3-cube. But actually, the artist is not using a "solid" projection of this sort, it is more of a 3-D version of architectural plan/front-elevation/side-elevation type projections. The artist could have chosen to draw the 8th cube off to one side and still remain true to the projection. So I suspect that it may have been left off more for artistic (symmetry) reasons.
Another point to bear in mind when looking at that diagram is that any given 4-cubie "owns" several of the cubies shown and these are not adjacent to each other. Edge cubies, for instance, are shared by three cubes, so there is a corresponding "edge" 4-cubie that owns three of them in the diagram. All three of them are a single piece, the 4-cubie, but are scattered across the diagram. Similarly, corner cubies are shared by 4 cubes and middle cubies are shared by two cubes. There is also one centre cubie in each cube which is not shared. No-one (except possibly me) ever thinks about the centre cubie in a 3-cube because a) you can't see it and b) it's solution is trivial. However, in a 4-cube the solution of the centre cubies is not trivial and requires algorithms.
Heck, there's enough material for an article on this beast - someone ought to post it! SpinningSpark 18:46, 10 May 2008 (UTC)
So I did it at N-dimensional sequential move puzzles. Snappy title or what? SpinningSpark 15:39, 25 May 2008 (UTC)

how to spot a fake cube

I think that we should add a section talking about how to spot a fake rubik's cube.

Hintss talk 15:48, 7 June 2008 (UTC)

We'd need reliable sources that provide this information. — Val42 (talk) 21:35, 7 June 2008 (UTC)
What you mean fake cube? Like non-rubik's brand? Masterwiki (talk) 04:13, 8 June 2008 (UTC)
I'm saying that if someone wants to add such a section (that was suggested by another user), we'd have to have a reliable source for this information. — Val42 (talk) 04:51, 8 June 2008 (UTC)

Inconsistent pictures

The images Image:Rubik's cube.svg and Image:Rubiks_cube_solved.jpg are inconsistent: it's impossible for the same cube to have both this red/white/blue corner piece (tilted image) and red/white/green corner piece (solved image). I have no idea what the official cube used in competitions is, so I don't know which one should be fixed. But it's certainly disturbing. Sam Hocevar (talk) 17:22, 26 June 2008 (UTC)

My collection of 3D combinatorial puzzles has Cubes in at least three different colour schemes ("opposite" here means "at the opposite ends of the same axis"):
  • Original Ideal / recent Ideal / pirate: white opposite yellow, green opposite blue, red opposite orange
  • Middle-era Ideal: white opposite blue, green opposite yellow, red opposite orange
  • Meffert: white opposite yellow, green opposite blue, red opposite purple
Take your pick. :-) -- Korax1214 (talk) 11:58, 1 July 2008 (UTC) (table edited 8 July)

I've now altered the image of the solved cube to match the other one; it was a simple matter of splitting it into its channels and recombining them with the green and blue channels reversed, and took about 5 seconds. -- Korax1214 (talk) 11:44, 2 July 2008 (UTC)

Alternatively, you could just have mirror-imaged the solved cube. --M1ss1ontomars2k4 (talk) 00:54, 7 July 2008 (UTC)
If the photograph had been of one of my cubes, which it wasn't (check the image's page). :-) And in any case, swapping the G and B channels of the existing picture was much quicker and easier than taking a new picture. -- Korax1214 (talk) 01:16, 7 July 2008 (UTC)
Wait, what? I meant you could mirror the image of the solved cube, so left becomes right and vice versa. Thus blue would be on the right and red on the left. Surely that's easier than whatever you did? Also, modern cubes are white opposite yellow. Early cubes are white opposite blue. Pirated cubes can be either, independent of when they were manufactured. --M1ss1ontomars2k4 (talk) 01:30, 7 July 2008 (UTC)
Mirroring the picture as it originally was would have put green on the left and red on the right, which is consistent with the colouring of the scrambled cube, but would also have put the shadow in front of the cube, which would not have been trivial (or quick) to fix; splitting and recombining the channels, so as to change green to blue (without having to individually find and change all of the hundreds of shades of green which were probably in the image) was far easier and quicker. Download the original version of the image (available via the image's description page), and use a top-flight bitmap editor (download the trial version of Corel Paint Shop Pro X if you haven't got one handy) and try both techniques yourself, and you'll see what I mean.
As for the colours, were you writing from actual (and long-term) experience, as I was? I know for a fact that the very first Ideal cubes (in 1981) were yellow-opposite-white, and all the pirate cubes I ever came across had that colouring (presumably to be as exact an imitation of Ideal as possible), because I actually saw them (and have several in my collection); however, I've noticed (from the keychain cube I bought about a month ago) that Ideal have now reverted to their original colour scheme, which is probably what confused you on this issue. I'll edit my table above to reflect this. -- Korax1214 (talk) 14:49, 8 July 2008 (UTC)


ISTR (from Singmaster's Notes) that in group theory the accepted term for one of the 12 sets of Cube configuration is "orbit"; I don't know where "universe" came from. And after all, cube literature often (IME) uses terms from group theory, such as "conjugate" or "commutator". -- Korax1214 (talk) 12:15, 1 July 2008 (UTC)


Who keeps removing the links to good rubik's cube website and replaces them with youtube video lessons? As far as I'm concerned, video lessons only cover the beginner methods, and more advanced methods like the Friedrich method which was explained in other sites is omited. —Preceding unsigned comment added by (talk) 21:11, 7 July 2008 (UTC)

Edge-coloured or corner-coloured cubes

How can "neither of these alternative colourings has ever been produced commercially" be verified? Moreover, I'm sure I've seen a photo of an edge-coloured cube. Possibly in Don Taylor's book Cube Games. Though needless to say, this doesn't prove that it was ever a commercial product.

Moreover, I've just had a few more thoughts on these styles of cubes, though I'm not sure how much can be said here within WP:NOR. -- Smjg (talk) 15:39, 19 July 2008 (UTC)

there are aldo competitions —Preceding unsigned comment added by (talk) 20:08, 29 July 2008 (UTC)

New references

An editor has just added a large number of items to the references section with an annoyingly misleading edit summary of "alphabetizing". Since no new material has been added to the article at the same time, I find it hard to believe that all these new books really are the source of information in the article. I do not recognise any of the authors so propose to delete them unless someone thinks they really are sources. We could start a "Further reading" section but references should be reserved for the actual source material for the article. Even "Further reading" is a bit dubious, it is likely to attract a monster list of every book ever written on the cube. SpinningSpark 19:41, 3 September 2008 (UTC)

sequence of movements..

The 'sequence of movements' comment in the 'algorithms' section isn't clear. How would i perform the movements 116655224433, or whatever the sequence is? I don't think this is explained in the following section, either. (talk) 11:14, 26 September 2008 (UTC)

It actually seems clear to me. Could you explain which part you don't understand: how to label the sides, or, given that you know a side is labeled 1, you don't know what the movement "1" means? Brainmouse (talk) 11:36, 26 September 2008 (UTC)
I think that we should stick to the official notation (talk) 01:32, 7 October 2008 (UTC)
I have no problem with how you changed the notation. I added the rest of the paragraph back in though - was there a reason you removed it? It explained the whole point of the "algorithm" subsection and why that example was there to begin with.Brainmouse (talk) 01:46, 7 October 2008 (UTC)

The search for optimal solutions

An editor is insisting on changing

No arrangement of the Rubik's Cube has been discovered so far that requires more than 20 moves to solve.


No arrangement of the Rubik's Cube has been discovered so far that requires less than 20 moves to solve.

I believe this is incorrect syntax and have explained to the editor on their talk page why, but today it has again been changed back to less. Would other editors please indicate the consensus here. SpinningSpark 10:02, 11 October 2008 (UTC)

I didn't check what you wrote on that editor's page, so I apologize if I repeat your logic, but I think thatwhy it's "more" and not "less" can be explained by the fact that it is immediately clear that there are arrangements that require less than 20 moves to solve. Take a solved cube, and rotate one edge one turn. This arrangement of the Rubik's cube requires less than 20 moves to solve, thus immediately making the second statement false. On the other hand, take a completely scrambled cube. If done perfectly, as far as is known it should never take more than 20 moves to solve, thus making the first statement true.Brainmouse (talk) 14:34, 11 October 2008 (UTC)
I agree with Spinningspark. Saying that there is no arrangement of the Cube that requires less than 20 moves to solve is patently ridiculous, since the arrangement reached by making a single turn is a ready counterexample. I'm not sure why that particular editor insists on this change. He has been doing that persistently in spite of all efforts to convince him otherwise, and he has done that again early this morning.—Tetracube (talk) 15:24, 11 October 2008 (UTC)
P.S. On reading his comment on the matter, it seems that he is misreading the intent of the sentence in question, as though it was referring to a general solution scheme rather than specific solutions for specific arrangements. I don't think that was the intent here.—Tetracube (talk) 15:27, 11 October 2008 (UTC)
The heading of the section is the search for optimal solutions, that is, a general solution with the minimum number of steps. The first sentence of the paragraph states: "Work continues to try to reduce the upper bound on optimal solutions." The word reduce means to make less. Improvement of an optimal solution means the minimum number of steps is less. The final sentence of the paragraph gives the current status of the work to reduce the minimum number of steps by stating that no optimal solution has been found with a lower number of steps. The word less is appropriate to indicate that status.
If this section is intended to discuss some type of solution other than an optimal solution, that intention should be reflected in the section heading. Kensor (talk) 07:15, 15 October 2008 (UTC)
Your understanding of the topic is correct, but you have one important thing wrong: Improvement of an optimal solution means the MAXIMUM number of steps is smaller, not the minimum. Because of this, the sentence describing the optimal solution has to say that the current optimal solution makes it so no MORE than that is required. If we are reducing a maximum, saying "no more than" is in fact correct. I would be fine if you re-worded the sentence entirely, but hopefully you understand why it is obvious that just changing that one word is fundamentally incorrect?Brainmouse (talk) 23:33, 15 October 2008 (UTC)
That final sentence is not referring to a general optimal solution, it is referring to a particular solution. Potentially, this could be used as a counter-example of a proposed optimal solution. For instance, if a general optimal solution were proposed requiring 18 moves maximum, this can immediately be proved false from a known counter-example that requires at least 20 moves. No counter-example of more than 20 moves is known. Therefore no proposed optimal solution of more than 20 moves can be proved false by the method of counter-example. Your whole argument appears to be based on the semantics of the heading. Changing the truth content of a statement in order to achieve grammatical agreement is, in my view, a quite perverse thing to do. SpinningSpark 21:56, 17 October 2008 (UTC)