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Recently I posted a question about tiling dominoes in a 3x10 area. The community arbitrarily decided my puzzle is off-topic because it's "too mathy". Yet, questions like

are received perfectly well, even though most are combinatorial or computational in nature. I believe I've been on Stack Exchange long enough to know why this is happening. Sadly it is because I have only accumulated 700 rep on this SE while all those other questions are asked by 10k+ rep users. When I was low-rep on PPCG and SO I was treated the same way, but now that I have 10k+ rep they apply a different standard. The other reason is the "bandwagon effect" where one user who decides he doesn't think a puzzle is puzzle-enough puts in a close-vote and others follow along without thinking about the standard.

The tour page says "no textbook math problems". If my question appears in some combinatorics textbook, then the GCD question is even more cut-and-dry application of the Dirichlet Hyperbola method. The Keys and Locks puzzle is an application of a theorem in a graph theory textbook. The visiting all strings by swapping is a textbook application of graph theory. Is my question too easy? Should I just pick a question from a harder textbook? How about any of the later questions from Stanley's Enumerative Combinatorics just because they're hard? Peter Taylor points out in xnor's criteria on what is a puzzle or not that at least half of his examples are textbook problems. If the criteria is there has to be a "trick", well my question does have a nice trick and it's not brute-forcing every possibility.

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    $\begingroup$ Hi qwr, what's the best-case scenario you're looking to happen here? $\endgroup$
    – Jafe
    Commented May 30 at 7:29
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    $\begingroup$ @Jafe In the perfect world, there would be a consistent criteria as to what counts as a mathematical puzzle. Given the community has been debating this for years and so this is likely impossible, I would like the community to be lenient/inclusive on closing questions that may seem easy mathematically but still require some reasoning (my tiling puzzle is doable for people without a combinatorics background) and let upvotes/downvotes decide what people want. $\endgroup$
    – qwr
    Commented May 30 at 16:02

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It could be that some of the questions you list above ought to be closed. It might just be that no one happened to notice them when they were posted, and they've endured until now. Or it could be that they have some ethereal "quality" to them that makes them seem more appropriate for this site (I haven't reviewed them all, so I can't really say).

The fact is that nobody is perfect, and there are probably some questions closed that shouldn't be, and some left open that ought to be closed. The community is moderated by volunteers, and it's very hard to have cut-and-dry criteria for everything, so it's always at least a bit of a judgement call.

That being said, those users with 10K+ reputation here have been around for quite a while, and likely have a much better idea of the "feel" of the community, and what questions "fit", as opposed to someone who has only been here a short time. So it makes sense that even if you (being relatively new) can't see the difference, there might be a difference between the mathematical puzzle posted by the 10K+ rep user and the one posted by the 700 rep user.

I know it can be very frustrating to have your post closed, especially if you've spent a lot of time on it, but that doesn't need to be the end of it. You can always try reformulating the problem, add a story to it, put another twist on it, come up with a way to make more intriguing, and then flag it for re-opening.

People here have spent a lot of time and have had a lot of discussions about how to make sure this site continues to have great questions that keep people interested, and many of the high-rep users here are committed to trying to keep that happening. Please don't take it personally if your question is closed; take it as a way to learn more about the ethos of the site, and how to make your questions fit.

Happy puzzling!

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  • $\begingroup$ Thank you for your response. I've been thinking about my puzzle (and variants) for a long time and I was miffed it was considered unworthy because I think the puzzle has an appealing simplicity along with neat solution to it. $\endgroup$
    – qwr
    Commented May 30 at 16:07
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Your post here does not have an explicit question, but I assume it's something along the lines of: "Why the inconsistency?"

The line between "math problem" and "math puzzle" can be pretty fuzzy, and somewhat open to interpretation. I'm not going to make a judgement about whether your question should have been closed or not - but I can give a few likely reasons why it was.

It's not about difficulty, but about standardness, in a sense. I think anyone who's taken a combinatorics class has seen the 2-row version of this; the 3-row version is a similar enough idea that I'd fully expect it to be a homework question. (And it's not helped by the phrasing, which feels ripped straight from a textbook.)

Your question doesn't need brute force, true! But it doesn't have a 'trick' that makes it instantly gettable. Compare Waiting For The Gravy, which has a surprising trick that makes the solution much simpler. The 'trick' here, to the extent that it exists, doesn't really give an "aha moment", since there's still some somewhat-tedious work to do afterwards.

You also mention Keys and Locks Puzzle as your first example. I'd say that is very non-textbook. Sure, once you know Hall's Marriage Theorem is important, it might be fairly trivial to apply... but realizing that it's a graph theory problem is definitely non-obvious! You could say it's underlyingly a math problem, but its well-disguised-ness helps elevate it.

One other thing that doesn't help the appearance is the 'nature' of the result. This is a minor point, but I think something that makes a problem feel more puzzly is having the final answer be memorable. Compare the mutilated chessboard problem, another tiling question: on first glance, tiling the chessboard-with-two-opposing-corners-cut-off seems like an easy task, and people wouldn't be surprised to see that there are thousands or even millions of ways of doing it. So having the actual result be that it's not possible will definitely raise some eyebrows. By comparison, people skimming your question will not be surprised to see an answer of "571" (and will probably promptly forget it a few minutes after). The answer is not intimately tied to the solution process - it's just the number that happens to be spit out at the end.

In general, I'd say that these questions are all relevant in determining whether something comes off more as a problem or a puzzle:

  • Is the problem something I wouldn't expect to see in a math textbook?
  • Is the solution method surprising?
  • Is the result surprising?
  • Are the problem and solution accessible to the layperson?
  • Are the problem and solution interesting to the layperson?

Answering 'no' to one of these isn't an automatic disqualification, but the more 'no' answers there are, the closer to the "math problem" end of the scale you are.

(And of course, there's always the factors of "site standards evolving over time" and "which reviewers happen to look at the question".)

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