Talk:Lights Out (game)

Mathematical proof by matrix analysis
Let $$\mathcal{L}$$ be the set of all 5×5 matrices over the two-element field {0,1}. Then any board setup in Lights Out can be represented by a matrix in $$\mathcal{L}$$, where 1 corresponds to a light that is on and 0 to one that is off.

However, if we regard the elements of $$\mathcal{L}$$ as simply matrices over {0,1}, then we can add them according to the rules of matrix addition. And we know from matrix theory that $$\mathcal{L}$$ is an Abelian group under matrix addition.

If $$m,n\in\{1,2,3,4,5\}$$, let P(m,n) denote the matrix whose (i,j)th entry is 1 if (i,j) = (m,n) or (m±1,n) or (m,n±1), and 0 otherwise. Then for a board setup L, pressing the (m,n)th light corresponds to adding the matrix P(m,n) to L.

This analysis proves the two statements stated in the main article. The first statement is proved by the fact that matrix addition is commutative and associative, while the second statement stems from the fact that $$\forall\,L\in\mathcal{L}, L+L=\mathbf{0}$$, the zero matrix (board with all lights off).

Jane Fairfax 13:38, 12 May 2007 (UTC)

strategy missing something
using the strategy, what happens when you're left with a light at D or E (single light at the last row in pos E for example)? gujamin 16:52, 24 August 2007 (UTC)
 * If that were to happen, it would mean that the position you started with was insoluble. Spacepotato 21:47, 18 October 2007 (UTC)

Error in illustration?
In the illustration, the upper-left square of the board appears to change erroneously in the last step. Am I missing something? —Preceding unsigned comment added by BHSPitMonkey (talk • contribs) 01:26, 16 January 2009 (UTC)
 * No, it was a mistake. It's been fixed now. Spacepotato (talk) 01:44, 16 January 2009 (UTC)

Strategy section seems incorrect - w/ Response
The table for 3 x 3 grid is:

3x3 === A -> -BC B -> ABC C -> AB-

So, the strategy becomes:


 * 1) If A is the first light that is on in the bottom row, then press B in the top row and bring down the lights to the bottom row.
 * 2) If B is the first light that is on in the bottom row, then press A in the top row and bring down the lights to the bottom row.

Now, if you play with this starting configuration where 1 indicates ON and 0 indicates OFF, then this strategy doesn't lead to a solution.

ABC === 101 101 011

Next, I do as the article says: "The most common method to solve this puzzle is to start by wiping all the lights except in the bottom, or last, row. This is done by pressing lights that are directly below lights that are turned on to cancel them out until only lights in the last row remain." and I get this:

ABC === 000 000 110

Now, since the first light that is on in the bottom row is A, I press B on the top row and start wiping again. I get this:

ABC === 000 000 001

Now, how do we proceed? The first light that is on in the bottom row is C, but we do not have a rule for C. I think something is wrong with the strategy section or it requires more clarification of the strategy.

It looks to me that this question is answered by the article (at least it was at some point in time, by the deleted strategy section): "Some calculation must be done to figure out what combination of top row lights must be pressed in order to blank out the bottom row. (This is an example of the decomposition in linear algebra of a vector into basis vectors.)"

So, to blank out 001, you would press B & C on the top row, then wipe all the way down. This is because B -> ABC + C -> AB- -- BC -> --C (mod 2)

Of course, you could have avoided this step by noticing from the beginning that pressing C results in AB-, which is exactly the original pattern you had after the first wipe to the bottom. I believe you were misled by the simplification which applies only to the 5x5 case. I suppose an edit would make this more obvious, but I'm not about to jump into the middle of the edit war mentioned below. Cxseven (talk) 07:49, 28 November 2010 (UTC)


 * Well, I clarified the strategy section and added several references as you can see here, but User:Sottolacqua promptly deleted the entire section again. This should be considered vandalism. Cxseven (talk) 07:49, 28 November 2010 (UTC)

Photography of game device
I could take and upload a photograph of a Lights Out game if potential copyright that I do not know about does not forbid it? Zeyra (talk) 16:02, 1 March 2010 (UTC)

Large sections deleted
The fact that a large section of helpful information about Lights Out has been deleted as "original research" is mindless enforcement of a rule, ie. Doing the Wrong Thing. More experienced editors of mathematical articles seem to have come to an understanding that they will allow unsourced proofs which are easy to verify and hard to cite (which might be because the proof is so trivial as to be traditionally considered an "exercise for the reader.") I have also seen simplifications of proofs allowed for the same reason.

Besides that, however, I don't believe this is original research. What happened to leaving [citation needed] tags on text which seems true but does not yet have an "authoritative reference" (if a simple proof is not authority enough)? Cxseven (talk) 05:07, 28 November 2010 (UTC)

Investigating further, this seemed very similar to deletions of large amounts of material on the Long John Silver's page back in 2008 for "unsourced content". I am happy to see that that the user, Mythdon, was blocked indefinitely for a series of such incidents. The deleter involved in this Lights Out article, Sottolacqua, appears to be making the same mistakes. Archives of the Mythdon saga such as this and this are educating on what Wikipedians generally consider to be constructive edits -- and this wiping is not one of them.

I am a newbie to Wikipedia internals so will just have to trust that this will work out well on its own, for now. Cxseven (talk) 05:07, 28 November 2010 (UTC)
 * The info that was resourced and removed by me was again removed because of the narrative format and poor sources. Simply linking to the theories of mathematics based on the original research added still means its original research.  Sottolacqua  (talk) 07:46, 28 November 2010 (UTC)
 * Not sure what you mean by "theories of mathematics based on the original research", since it is hardly original research. In fact, the citations suggest the "bottom row method" is a trivially verified solution known to puzzle enthusiasts for years. To insist on referring to it as "original research" as if its veracity or acceptance are in question makes me wonder if you read any of the citations. (As to how you worded your criticism, the links showed how this method follows from well-established properties of linear algebra ("theories of mathematics"?), not the other way around.)
 * Finally, it is counterproductive to immediately delete half of the article when an effort is made to make exactly the improvements you require. If you demand peer reviewed or printed sources, many which I have not had the time to inspect are listed on JAAP's Mathematics of Lights Out page, which you have deleted as a reference. There is no urgent need to delete half of the article rather than add tags or actually assist in improving the article. Cxseven (talk) 08:42, 28 November 2010 (UTC)


 * The format of the material I most recently removed is not congruent with WP:MOS. It's written in a narrative unnecessary complex format. Additionally, some of the sources added are not from reliable, third-party sources. One of them is from an individual's "puzzle page" website . One of the two references listed in the Strategy section is again from the same puzzle page; the other is from a similar personal website . The Beyond 5x5 section is simply original synthesis and research. The Solutions to the Fiver Puzzle is also WP:OR and completely unsourced by a verifiable acceptable resource. The Variations and generalizations section is an unreferenced bulleted list of random modifications.


 * All of this information does not belong in this article.  Sottolacqua  (talk) 16:44, 28 November 2010 (UTC)


 * Originally you complained about "text written in first-person-plural point of view". I did not find any such problem, but fixed several uses of the second person voice. As for the supposed "narrative" aspect, be more specific as to how the article violates your specifications here in view of the fact that the strategy section described an algorithmic procedure consistent with the style of other Wikipedia articles.


 * You removed most of the article, parts which had been worked on by multiple contributors over the course of years. What existed could be stylistically improved, but was not controversial or difficult to verify (by taking 30 seconds to test it, for one). If such content requires more authoritative sources (which is doubtful, as the standard of proof appears consistent with articles such as God's Algorithm (Rubik's Cube)), you have not improved the article by deleting all of this material, but instead antagonized those who have worked on it and prevented new visitors from enlisting.


 * Please stop deleting most of the article for minor deficiencies. Cxseven (talk) 19:44, 28 November 2010 (UTC)


 * In summary, it would be helpful for you to gain experience with the norms of mathematical and computer science articles rather than look for whole sections of articles to delete that violate (what you perceive as) the letter of the law. Cxseven (talk) 19:51, 28 November 2010 (UTC)


 * I am not removing content based upon minor deficiencies. These are large sections of unverified unsourced original research. Regardless of the number of editors who have contributed or the length of time information has been included, strategies and novel syntheses used to solve puzzles—which have not appeared in reliable sources—merely linked from other personal websites/non-verified sources are still considered original research.


 * God's algorithm contains clearly-defined, acceptable sources for the information contained within the article from reliable third-party sources, including the BBC. The "sources" previously linked in this article contain links to two "puzzle fan" pages.


 * Earlier versions that include the pronoun "we" use the first person plural point of view; second-person POV would include usage of pronouns such as "you", which was not mentioned by me previously. The grey-bordered code that makes text appear as Unicode/non-standard font characters does not fit with WP:MOS as it makes the article difficult to follow. The article rambles on and on and on with regard to strategy and hypothetical uses of X by Y grids and is not concise.


 * As someone who claims to be "a newbie to Wikipedia internals", it would be helpful if you familiarize yourself with WP:MOS, WP:Sources and WP:OR since the information you wish to have re-added to the article does not meet criteria set in these guidelines.  Sottolacqua  (talk) 20:49, 28 November 2010 (UTC)


 * You deleted the section on the Mathematics of Lights Out, which was completely verified and sourced with statements such as "The order in which the lights are pressed does not matter." A source I'd added for this was MathWorld. Is MathWorld an unreliable source? Why did you delete this, along with everything else? Are you actually paying attention to what you're deleting?


 * What Wikipedia's policy on original research says is "all material added to articles must be attributable to a reliable published source, even if not actually attributed." As the references on Jaap's Puzzle Page suggest, there are numerous published solutions of the Lights Out puzzle. This all looks highly attributable to me, not to mention well-verified. You took it upon yourself (without checking) to decide that the material posted is unverified. It sounds like you found the article confusing (although it is rather simple linear algebra) and that this slanted your opinion on verifiability. Let me ask you this: do you regularly edit mathematical articles? Are you familiar with the fundamentals of linear algebra? Would you agree to let this disagreement be mediated by a neutral editor with experience in both?


 * As for the article on God's algorithm, it links to cube20.org, among others. While the Lights Out sources could be improved, several mathematical articles link to works on the web which summarize results of others. I do not take Jaap's puzzle page to be the gold standard of references, but it contains uncontroversial and well-cited material, which appears to fall well inside the generally accepted quality of reference for a mathematical article.


 * The fact that you crudely deleted such a large section of the article, including parts which were well-sourced (the Mathematics section), does not amplify the importance of your reason for doing so. That's rather putting the cart before the horse. For the other parts, what you have done epitomizes WP:Demolishing the house while it is still being built. Cxseven (talk) 03:15, 29 November 2010 (UTC)

The strategy section has been restored, with the long series of "beyond 5x5" tables eliminated. I agree that these were unnecessary. I have also researched some of the citations, such as Jaap Scherphuis's Mathematics of Lights Out page. It is cited by 3 scholarly articles. Jaap Scherphuis is probably the closest to what is considered an established expert in this field and the page is well sourced (both outward and inward). In the meanwhile I have put in a request to him to further improve our sources list, but feel this should be sufficient for now to allow the section to stand. Cxseven (talk) 08:03, 29 November 2010 (UTC)


 * Please stop adding Jaap's puzzle page as a citation; th is is not a valid source, as a puzzle collector is not an expert on a topic. Although he is mentioned as being a software engineer in this interview, his credentials are not listed. Also, you mentioned WP:SRS in your edit summary but this guideline does not exist. What does this refer to?  Sottolacqua  (talk) 12:30, 30 November 2010 (UTC)


 * I removed this link reference tagged as "Builiding a Better Cat" from 2002 as it does not relate to the article topic. Fiver at Maze Works is the exact same game as already listed from math.com. This article needs verifiable, acceptable sources and not merely links to online versions of the game.  Sottolacqua  (talk) 15:01, 30 November 2010 (UTC)

Existence of solution?
Surely, the most obvious question that can be asked (and, incidentally, the information I came here especially hoping to find) is: are all starting positions solvable? Perhaps this was answered in the deleted sections mentioned just above. If so, their removal is a sad loss, because surely the answer must be known and a good source could be found.

Currently, the article states "'Light chasing'" is a method similar to Gaussian elimination which always solves the puzzle", implying that a solution always exists, but further down, "If the 5x5 puzzle is unsolvable under legal game creation", implying that unsolvable positions exist. 2.25.120.117 (talk) 22:47, 7 December 2012 (UTC)

There are indeed unsolvable positions. If after doing the first round of light chasing, the bottom row is not one of those in the list of bottom row -> top row solutions, it was an invalid starting state and cannot be solved. 92.233.51.116 (talk) 15:58, 26 January 2014 (UTC)

Multiplication Puzzles for Apple II, 1985
There is a 1985 computer game by MECC for the Apple II called Multiplication Puzzles which includes a mode called "Lights Out" which is very much a variation of this game (mixed with an arithmetic quiz).

Reference:
 * video of the game
 * archive.org emulation

- Rainwarrior (talk) 08:13, 7 April 2018 (UTC)

There exists a solution for every N×N case?
How can it be that "There exists a solution for every N×N case"? The article gave two 5x5 cases which are insoluble.

Jmichael ll (talk) 21:29, 27 February 2022 (UTC)