Talk:Mutually orthogonal Latin squares

More information on context and application would be helpful Calaf 02:03, 28 February 2007 (UTC)

Is it entirely necessary to have the entire list of 144 solutions? Skipperxc (talk) 18:33, 1 April 2009 (UTC)
 * I certainly don't think it is - and the article is 260k long! I think a link to the solutions would be more apt. --moof (talk) 08:50, 10 April 2009 (UTC)


 * I've informed the editor at User talk:Brhaspati. The size is just too big.  I'll suggest using the main 144 solutions, and cut out the other 7 x 144 transpostions, reflections, etc.  But even that might keep the article at too big a size.  Smallbones (talk) 13:10, 21 April 2009 (UTC)


 * I'm OK with pruning the list, but not with reducing them to the 144 solutions in the first column -- that would be neither complete (which is what it is now) nor instructive. An instructive reduction would be to reduce the 1152 to just 2 cases and show how the rest of the 1152 can be derived from them using permutations of suits and face values. I'll do this in a few hours. -- Brhaspati\talk/contribs 23:13, 21 April 2009 (UTC)

The two solutions are essentially the same by interchanging suits and faces. 2A02:908:FA28:A80:0:0:0:2 (talk) 20:30, 4 July 2016 (UTC)
 * Yes, it looks like what is meant by an 'equivalence class' here needs clarifying: the second "distinct" solution is obtainable from the first by reflecting across the principal diagonal and applying the permutation (JKQ)*(♦♥♣). Am I missing something here? Pirate pete (talk) —Preceding undated comment added 13:10, 9 May 2018 (UTC)

A related problem
If I have n2 things, I want to part them to n sets k times, and any two things are in different sets every times, what is the maximal value of k?

When n = 0 or n = 1, it is infinite.

When n = 2, I can part them like this:

{AB, CD}, {AC, BD}, {AD, BC}

Thus, the maximal value of k is 3.

When n = 3, I can part them like this:

{ABC, DEF, GHI}, {ADG, BEH, CFI}, {AEI, BFG, CDH}, {AFH, BDI, CEG}

Thus, the maximal value of k is 4.

When n = 4, I can part them like this:

{ABCD, EFGH, IJKL, MNOP}, {AEIM, BFJN, CGKO, DHLP}, {AFKP, BELO, CHIN, DGJM}, {AGLN, BHKM, CEJP, DFIO}, {AHJO, BGIP, CFLM, DEKN}

Thus, the maximal value of k is 5.

This is known when n ≥ 2, then k ≤ n+1. — Preceding unsigned comment added by 49.214.225.38 (talk) 15:07, 12 August 2016 (UTC)

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Merge proposal
I propose merging Thirty-six officers problem to this page. There is almost nothing in that stub that is not already here. --Bill Cherowitzo (talk) 20:30, 16 June 2020 (UTC)


 * Support A merge and redirect seems reasonable to me. There is a lot of overlap and this article provides better context for the problem. -- 09:37, 17 June 2020 (UTC)
 * No The Thirty-six officers problem has its own WP:RS and is more interesting to the lay person than an abstruse math problem in set theory notation. To the best of my knowledge Wikipedia is for lay people, not experts.  I'll bet 9 out of 10 people can't even venture a guess at what orthogonal means, and if you show them the defintion their eyes will glaze over and they would not be able to explain anything about it.  I don't remember learning it until some high level college calc. class or when we learned about Fourier transforms.  So again, let's please have some consideration for ordinary readers.
 * See also WP:READABLE,,  --David Tornheim (talk) 20:28, 19 June 2020 (UTC)
 * Comment: Its a merge, not a deletion and the redirect will be to the history section where the discussion is less technical. The use of the term "orthogonal" in Latin squares has nothing to do with the concept you may have picked up in a calculus class. It is quite simple, I've been able to describe it to a 5th grader without having his eyes glaze over.--Bill Cherowitzo (talk) 23:24, 19 June 2020 (UTC)
 * LOL. Yeah I sort of noticed that combinatorial orthogonality is something different. I haven't heard the term Combinatorics before even with a Masters in E.E. and having passed the content-matter tests in California so I could teach math 6-12.   Hopefully I have not mistakenly equated combinations (of probability & statistics combinations/permutations) with something that might be an entirely different field of study.
 * As for the merge, I'm not sure why it would be necessary or desirable. I do understand that a merge might be little more than cut & paste.  I just would hate lay readers to find it buried in an article filled with math jargon.
 * I hope you chime in at Teahouse --David Tornheim (talk) 00:32, 20 June 2020 (UTC)


 * It's been two weeks since I proposed this merge and I really didn't think it would be controversial, and still don't. I've gone ahead with the merge., have a peek and tell me if you think I have done anything wrong.--Bill Cherowitzo (talk) 20:45, 30 June 2020 (UTC)

RfC on mutually orthogonal Latin squares
Withdrawn by proposer

This section is in woefully bad condition and I will be rewriting it, but there are two issues that I'd like to bring up for discussion. First of all, the page title. The main subject here (although you can't tell by looking at the page at this point) is mutually orthogonal Latin squares (MOLS) and Graeco-Latin squares are just a special case. This special case does have an interesting history, but the name is rather passé except possibly in some application areas. When I'm finished revising the page, I'll ask for a title change if other editors agree. The second point (and more ticklish one) has to do with the big bright example of a compounded MOLS 5 that has been on the page in one form or another since March 2009. I like the example, it is correct and well crafted ... but it is also completely WP:OR. Other editors must have felt the same as I do, it is just too good to toss. I will be rewriting the section so that this example is not as prominent (it makes for a poor introduction to the topic) and I can explain what it is in more traditional terms. I would like to see some consensus to keep the diagram even though it is OR.--Bill Cherowitzo (talk) 18:33, 19 June 2020 (UTC)


 * Changing the topic to MOLS seems like a reasonable change given the content of the article. For the eye-watering textbox MOLS example, it depends on what you mean by OR. If it is the results of a simple algorithm, one could justify this as a routine, albeit high level calculation. It looks like the example use the facts that for p prime and $$t \in Z_p$$ and nonzero, a Latin square can be constructed as $$L_t(i,j) = ti+j$$ with $$i,j \in Z_p$$, and $$L_u$$ is MO with $$L_t$$ if $$t \ne u$$.. That is, this looks like a textbook exercise, and not quite out of the blue. -- 19:14, 19 June 2020 (UTC)


 * ??? -- what is the question you want us to answer? Are you familiar with the essay Writing_requests_for_comment? Starting off with This section is in woefully bad condition doesn't sound very neutral. I would suggest killing this RfC and trying to better follow WP:RfC and WP:WRFC. As with many math articles, I think it is fine to be precise in definitions, but I believe we should make articles accessible to ordinary people who are not math experts. If there is some decision somewhere saying we shouldn't care if lay people are baffled by our math and other highly technical articles, please point me there.  As the encyclopedia anyone can edit, I would hope it was one that anyone (with a sixth grade education) could read too... article on readability
 * See also WP:READABLE,,  --David Tornheim (talk) 20:52, 19 June 2020 (UTC)
 * I apologize for presenting a poor RfC and have withdrawn it as requested. This was my first attempt at this and I did not read all the appropriate background. The rest of your remarks concerning readability seem to be coming out of left field and have nothing to do with the issues I raised. Readability of math articles is one of my primary concerns and is the reason I am concerned with this section ... it is impenetrable by anyone not already familiar with the topic.--Bill Cherowitzo (talk) 23:05, 19 June 2020 (UTC)
 * Thanks. I wondered if this was your first. No hard feelings.  Completely forgiveable.
 * I'm glad we agree about the importance of WP:READABLE. Sorry if my comments on that come out of left field.
 * I hope you participate at the lively discussion at: Teahouse
 * --David Tornheim (talk) 00:38, 20 June 2020 (UTC)

Medieval reference
Donald Knuth found exmamples of orthogonal latin squares used by a 14th-century Maghreb mysticist. See []. AmirOnWiki (talk) 18:47, 4 January 2021 (UTC)

For which N does there exist an N×N Graeco-Latin square?
This is an obvious question whose answer may be already contained in the article.

But it is not at all clear how to extract this information without reading and fully understanding the entire article.

Suggestion: I hope someone knowledgeable about this subject can add a section containing what is known about the obvious question:

For which N does there exist an N×N Graeco-Latin square?

2601:200:C000:1A0:C17A:92A9:4C4E:C680 (talk) 13:27, 31 March 2021 (UTC)


 * For all n > 2 except n = 6. See Euler's conjecture and disproof. —Dexxor (talk) 19:28, 31 March 2021 (UTC)