Talk:N-dimensional sequential move puzzle

Rubik's example

Either the number of pieces should be 27 rather than 26 or the number of pieces with 0 stickers should be 0 not 1. It doesn't add up.

Also why is the number of cells 1? The rubik's cube doesn't have higher dimensions meeting, so this seems an anomaly here. -- SGBailey (talk) 08:31, 28 May 2008 (UTC)

The fact that the 0-sticker pieces are not being counted in the total is stated quite clearly at the top of the article under definitions. However, the count of 0-sticker pieces is still given, so of course if you add the numbers up it will come to something different. In fact it will come to sⁿ (Rubik 3³) rather than the total given. The difference is because solvers are only interested in (and hence naturally only count) pieces with stickers. Mathematicians, on the other hand, will count them all because the integer sequences only work properly if they are.

The number of cells is 1 for the Rubik cube because the whole cube is a cell. It does not meet any other cells or higher dimension polytopes because there are not any. The definition does say for objects of dimension greater than four which excludes Rubiks cube. SpinningSpark 14:05, 29 May 2008 (UTC)

I know that is what it says. That doesn't stop it being confusing. IMO either P should be redefined or revalued. Having the equation on one line that differs from the value in the table is awful. -- SGBailey (talk) 22:12, 29 May 2008 (UTC)

How about calling the total "Number of coloured pieces"? SpinningSpark 23:18, 29 May 2008 (UTC)

Sounds OK -- SGBailey (talk) 06:25, 1 June 2008 (UTC)

Sourcing

Are those really reliable sources? --NE2 09:10, 28 May 2008 (UTC)

If you are looking for sources published in peer reviewed journals, might be hard to come by on this subject. This is the best I could find, and they do seem to be mathematically competent. Open to suggestions though.

Or were you referring to the sources for the unsolved puzzles? In those cases the sites referred are keeping the records so they are correct almost by definition, however unreliable you might consider them in general. SpinningSpark 23:16, 29 May 2008 (UTC)

Notability

This article needs reliable, third-party sources to firmly establish the significance of its subject. The subject matter is very interesting and worthy of attention, but if its notability in the wider world cannot be supported, the article may not satisfy Wikipedia's inclusion threshold and should be moved elsewhere. ~ Jafet _{Speaker of many words} 14:26, 17 June 2008 (UTC)

Well, for a mathematical reliable source, there is this paper on the subject,

• Velleman, D, "Rubik's Tesseract", Mathematics Magazine, Vol. 65, No. 1 (Feb., 1992), pp. 27-36, Mathematical Association of America.

For notability, there are three different books by Clifford Pickover which cover the topic;

• Pickover, C, Surfing Through Hyperspace, pp120-122, Oxford University Press, 1999.
• Pickover, C, Alien IQ Test, Chapter 24, Dover Publications, 2001.
• Pickover, C, The Zen of Magic Squares, Circles, and Stars, pp130-133, Princeton University Press, 2001.

There are also a reasonable amount of search-engine hits for the subject, including this one Computer Cubists by David Singmaster, an established notable authority on solutions to the Rubik's cube. Singmaster refers to the Kamach and Keane paper used as a source for this article, thus conferring at least some degree of second-hand reliability for K&K.

SpinningSpark 22:14, 19 June 2008 (UTC)

The "3x3 2D square"

I don't think it's an actual analog of the Rubik's Cube, just a similar puzzle. A Rubik's n-Cube's hypersurfaces (the rotatable sides) rotate in one dimension less than the puzzle itself. For example, the 3-dimensional Rubik's Cube's sides rotate 2-dimensionally. The Rubik's 4-cube's (I like to call it that anyway) sides rotate 3-dimensionally. In the same way, the Rubik's Square's sides must rotate 1-dimensionally, except there's no 1D rotation. Objects in 3D can rotate 2 ways - using an axis/line (1D) or a point (0D) - objects in 2D can rotate 1 way - using a point (0D) - and so following that pattern, objects in 1D can rotate 0 ways. I realize this is a wiki and thus I should probably edit this myself, but I think I should get input before completely rewriting an entire section. --cuckooman (talk) 05:57, 28 June 2008 (UTC)

Never mind, I didn't completely read it and didn't notice the end of the section that said that it isn't a true analog of it. :X --cuckooman (talk) 05:58, 28 June 2008 (UTC)

120-cell Combinations

I have undone this edit claiming the exact number of achievable combinations for the 120-cell puzzle because it disagrees with the reference and is not itself referenced. The exact number is given in the reference but not stated in the article. Of course, if this can be referenced the information can be re-instated. SpinningSpark 00:22, 31 August 2008 (UTC)

2D puzzle constructability

For the purpose of transparency, I reproduce below a discussion that has taken place on user talk pages, suitably refactored to put the comments in chronological order. SpinningSpark 15:33, 17 April 2009 (UTC)

I'm really not following your argument in your edit summary here that 2D electron gases somehow have a bearing on whether or not the puzzle can be physically constructed. Would you care to explain? In any case the sources are in agreement that it is not constructable so there is no reason the article should not say this. SpinningSpark 08:30, 5 April 2009 (UTC)

1)it's possible to construct a system whereby something (such as an electron gas or light) behaves to all intents and purposes as either a two or one dimensional structure by confining it such that freedom of motion in 1 or 2 of those dimensions is restricted. thus it is possible to actually physically make a low dimensional structure making an edge/face/etc...

2) if you're applying the same rules for the 2d version as for the 3d to n-d versions, you must be able to reflect opposite edges. this makes solution possible. (as here http://www.superliminal.com/cube/mc2d.html): eg -

for a 2x2 2d version:

12-----21-----12 (imagine each number is a different colour!)

34-->-34->--34 (effectively the 2d analogue of 4 90deg rotations clockwise/anticlockwise on the 3d puzzle)

by the rules, it is only the 1-d case that cannot be unscrambled ie:

12345 -> 51234 -> etc.. the numbers could only rotate round, with no way to change their order.

even physically it would be possible - imagine some sort of colour inverter in the centre that inverted a colour moving through it to the opposite side. possible to make in in 2d and would permit rotation as above. strictly a true 2d rubik's cube made of 1d plastic edges would not work - since motion would have to be constrained in 1d for the reflection the two opposite edges being reflected/swapped would collide.

whether it is possible to make the 2d rubik's 'cube' is moot, since the article discusses 4d, 5d, n-d puzzles which are unlikely to be possible to realise physically. hence, in terms of pure mathematics, applying the rules that the rest of them work on - yes it can be done. there are sufficient degrees of freedom to allow reflection of edges. how that reflection happens doesnt matter. whether it is possible to make, i believe so but i cant back it up with citations! it's quite an interesting problem in some ways.

i'm going to have to shoot you down on 'yahoo forums' not being a reliable enough source though, i'm afraid. also, since the article is currently titled 'N-dimensional sequential puzzles', rubik's cube rules need not apply :) Jw2035 (talk) 23:41, 6 April 2009 (UTC)

I am still really not getting the relevance of electron gases here. But I concede the point that in essence, it is possible to physically construct a 2D puzzle. The fifteen puzzle, in all essentials, is a 2D puzzle despite being constructed of 3D material. If that was the point you are making then we have no argument on that score.

You have pointed me to Superliminal's page on the 2D puzzle, with which I was already familiar. On that page it is stated regarding reflections that this probably doesn't make it a proper analog to the higher dimensional versions which is in contradiction to your claim that you must be able to reflect opposite edges in a 2D analog of the 3D cube. I think perhaps that you have also missed that one of the principles in the Yahoo forum discussion is Melinda Green of Superliminal, the creator of this puzzle and she is corresponding with David Vanderschel, the creator of the 3D Magic Cube software. They are quite clear that the puzzle is not constructible. Roice Nelson of Gravition3D (5D Magic Cube and Magic 120 Cell) also takes part in this forum and would be expected to pick up on this if it was in error but he has not. In fact, he pointed me to this thread after making the same point in a private correspondence regarding the true nature of the 2D analog of the 3D puzzle.

You make the point that forums are not generally considered reliable sources. However, there can be exceptions for recognised experts in the field and in this case we have the three principle authors of the software to which the article relates all taking part in the forum. If anyone can claim the title recognised experts it is this group. If you have more acceptable references then I will be happy to defer to them, but the fact is, you are offering none at all against the sources I give in the article. You offer only your own design (imagine some sort of colour inverter in the centre) which not only amounts to OR but is also vague on how this would be mechanically realised.

I propose to put back the disputed text. If you object to this, please start a thread on the article talk page. I hope I can convince you that you are mistaken, but if not I will happily participate in any process (WP:3O, WP:RfC, WP:MEDCAB) you choose to resolve this. SpinningSpark 00:39, 9 April 2009 (UTC)

Allowing reflections will make it no longer a Rubik's cube-like puzzle, but an extension, regardless of which dimension it is in. A 3D Rubik's cube that permits reflection is not constructible in 3-space, because rotation through a 4th dimension is necessary to physically realize such reflections (cf. August Ferdinand Möbius, who realized that to mirror-image a 3D shape, rotation through a 4th dimension is necessary). So physically building a 2D puzzle that allows reflections requires that the realization be in 3D. In fact, the middle layer of a Square One may be considered to be an example of such a reflection-allowed 2D puzzle (consider what happens to the coloring of the stickers in the middle layer when the puzzle is twisted). Of course, in this case, the puzzle is not very interesting, since there are only 2 permutations possible. But in principle, the middle layer of any of the higher-order generalizations of the Square One (such as the 4-layer "Super Square One") constitutes an example of a 2D puzzle with reflections. In general, an N-dimensional puzzle that allows reflections can only be built in (N+1)-space.—Tetracube (talk) 17:09, 17 April 2009 (UTC)

I think I can imagine a physical implementation of the 2D puzzle. At any stage it would be possible to choose one of the 4 sequences of 3 consecutive "squaries" (corresponding to the sides of the big square) and reverse its order. Although I do not know all the details of its construction, it seems eminently possible to me, and no more difficult than the design of the original Rubik's Cube.

For this reason I think the sentence

"A 2-D Rubik type puzzle can no more be physically constructed than a 4-D one can."

is greatly premature, and would need far more convincing evidence than just quoting the claim :::of impossibility from some source. Also: Referring to the illustration an an "implementation" :::is ridiculous. It is just a picture, not an implementation.50.205.142.50 (talk) 19:04, 19 March 2020 (UTC)

Regarding 2D analogs, reflections shouldn't count in general, but a proper twist of a 2D puzzle takes place within a 1D line which just coincidentally happens to look like a reflection, so the superliminal version should be fine. Also, that implementation is a Java Applet which is no longer supported by modern browsers, but the picture of the state graph should suffice as proof since it represents the entirety of the puzzle.

Regarding 4D analogs, claims that it is impossible are clearly wrong now that Melinda's 2x2x2x2 exists. Cutelyaware (talk) 00:03, 20 March 2020 (UTC)

This so called "4D" puzzle is actually a 3D puzzle which just happens to have the same transform group as a 4D puzzle. No, that doesn't count as an actual 4D puzzle. SpinningSpark 15:59, 20 March 2020 (UTC)

Sure it counts. Having the same transform group is the only requirement. It's why all of these software implementations are also valid. Similarly for the 2D cube. All that matters are the state changes. It doesn't matter if the implementation of a move produces the same result as a reflection, or physically moves through a higher dimension are just coincidences or mechanical details which are not germane to the underlying mathematical puzzle. Cutelyaware (talk) 00:15, 21 March 2020 (UTC)

"quoting the claim" (from a reliable source) is how Wikipedia works, so yes, that is all that is needed, and our own thoughts on the matter count for nothing. As Tetracube said above, any physical construction of this puzzle requires a move through a third dimension. For instance, pivoting the sides of the spuare at the centre of an edge can only get a reflection by rotating in the third dimension. Rotating in the plane brings the corners in with one edge pointing "outwards", not snugly in the corner. Even disassembling the puzzle into its component pieces and reassembling cannot produce a reflection without rotating two of the individual pieces in the third dimension. SpinningSpark 15:59, 20 March 2020 (UTC)

The image is not just an illustration, it is a screenshot taken directly from Melinda Green's software, so you are wrong on that too, it actually is an implementation. SpinningSpark 15:59, 20 March 2020 (UTC)

6⁵ MagicCube5D has been solved!

Perhaps the article should reflect this change. Furthermore, the bottom does not include the 6⁵ cube in the "never been solved" category, whereas the top does. See the Hall of Insanity. --116.14.26.124 (talk) 07:06, 13 July 2009 (UTC)

File:Magic Cube 2D.png

Combination map of Magic Cube 2D.

Uh, I think not. The combination map of the Magic Cube 2D, by the way, is the only image I've ever uploaded - too bad Wikipedia doesn't support .bmp format! Could there be a substitute for this image? Professor M. Fiendish, Esq. 06:23, 5 September 2009 (UTC)

Failed GAN

While this article has certainly improved from when it was first posted, it is not, at present, up to Wikipedia's Good Article standards for several reasons. Firstly, it is primarily a bunch of tables. Secondly, the tone in what text exists is much too informal contrasted with Wikipedia's standard. Thirdly, it is quite lacking in informative context for readers outside of the first couple sentences. If there isn't much more to say than what is currently in the article, is possible that this article would be better approached using list techniques, which is to say, organizing the tables of data more tightly and combining the prose together into one much tighter, less chatty lead.

So while I'm sure User:Spinningspark had the best of intentions at heart, I'm afraid I must fail this page. As a rule of thumb, before nominating a page for GA, you will want to make sure all the cleanup tags are off of it, then improve it by a substantial amount from there, then check it against the criteria list to see if you would pass it, and then consider nominating it. --erachima talk 09:43, 16 July 2010 (UTC)

Puzzle sizes available in the Superliminal MC4D program

The article claims that "The Superliminal MagicCube4D software is capable of rendering 4-cube puzzles in four sizes, namely 2⁴, the standard 3⁴, 4⁴, and 5⁴." But, by going to Puzzle -> Invent my own, you can enter any desired size in the format "{4,3,3}n" where {4,3,3} is the Schläfli symbol of a tesseract and n is the desired order. However, only orders up to 19 can be solved using the interface because the slices are made by holding a number key and making a twist, but there are only 9 number keys available. This allows to make 9 slices on each cell from the bottom, 9 from the top, and the middle layer can be usually left untouched to solve the puzzle. Programagor (talk) 14:09, 11 June 2016 (UTC)

Clearly the program has been updated since our article was written. SpinningSpark 16:42, 11 June 2016 (UTC)

I've updated it.Cutelyaware (talk) 10:24, 20 March 2017 (UTC)