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I am looking through unanswered questions (specifically in combinatorics, but this is irrelevant) and I want to ask advice on how to proceed.

Apart from questions that I can simply answer or where I can upvote a correct answer that got no votes at all, I found the following type of questions:

  1. Hard questions

    Obviously, some of the hard questions are interesting questions that should just wait around, but many of them are of the type "anyone can construct a diophantine equation that is impossible to solve" (and no one wants to answer that there is no nice way to solve them because you never can know). Should anything be done about them?

    I want to note that especially in combinatorics there are many elementary-looking questions that even get lots of upvotes for "looking nice" where I am rapidly convinced that there is no nice elementary answer, but proving it would be next to impossible.

  2. Vague questions

    There are questions that might have been interesting questions, but it was too hard to determine the intentions of the OP and after several months, the OP will certainly not return to clarify and no one will be able to answer this kind of question or profit from it. It cannot be closed by several votes after several months, either, because there is no activity.

    Should I flag it for closing by the mods? For deletion?

    I am not talking about borderline cases here, but about questions where I genuinely think that they will benefit no one. Also, no reputation is involved, as, by definition I am looking at questions without upvoted answers and the clear-cut cases I am talking about have at most 0 votes.

  3. Questions that have actually been answered in the comments and float around as unanswered questions because no one wrote an answer.

    Very annoying, and there is nothing I can do about this alone, as I cannot move a comment to an answer and upvote it.

Why am I opening this thread? I think that this forum would benefit from having primarily precise and answerable questions in the unanswered questions section to improve the chance of newcomers to answer interesting unanswered questions.

Edited to add a concrete example: https://math.stackexchange.com/questions/31330/do-you-have-some-interesting-q-hypergeometric-identities

This questions asks about "interesting q-hypergeometric identities" which is not a well-crafted question at all. In addition, the author offers people email contact. I don't see any possibility for this question to have a good answer, and there is no point for me to give it a lonely close vote at this time.

So, should I flag it? Add a close vote and post a link in a new meta thread "please help me to close the following questions or give a good reason against closure"?

I can think of no reason to let this type of questions open, but I am of course open to any reason I have overlooked. (And I, in fact, do know interesting q-hypergeometric identites, that is, interesting to me, in a certain context.)

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    $\begingroup$ The 3rd point was discussed here meta.math.stackexchange.com/questions/1148/… - but Henning has already covered this in his answer. $\endgroup$ – Martin Sleziak Oct 30 '11 at 17:21
  • $\begingroup$ @MartinSleziak Well, I can hardly accept the answers on other people's questions. $\endgroup$ – Phira Oct 30 '11 at 17:41
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For case (3) you should just write an answer yourself, summarizing the solution from the comments -- or even just pointing to it, if it is more than a few days old. This will bump the question and hopefully attract someone else to upvote the answer.

Some may see this as a way to troll for easy points. Personally I don't mind; getting resolved questions shown as answered is a service to the community that does deserve some reward. But it you're worried about such impressions you could mark your answer as CW (which could here be taken to stand for Credit Waived).

(...or not. It turns out that marking the answer as CW means that the OP will not get +2 rep for accepting it, and there's no need to penalize the OP for the fact that someone originally wrote the helpful answer as a comment.)

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    $\begingroup$ "Credit Waived" - I like this interpretation... :) I think I'll use this take from now on. $\endgroup$ – J. M. is a poor mathematician Oct 30 '11 at 16:54
  • $\begingroup$ Credit Waived is indeed clever :) What can you do with points, anyway? $\endgroup$ – user13838 Oct 30 '11 at 19:11
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    $\begingroup$ This is probably obvious, but you should explicitly mention that your answer is related to the comments and mention the commenter with the key idea. $\endgroup$ – Noah Snyder Oct 10 '12 at 9:43
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In Tex.SE (of which I am a huge fan) moderators and users have regular sessions of "Answering the Unanswered questions" about once a month and it works quite nicely. Same might happen here but admittedly the $\TeX$ is easier to test the answers rather than solving tough and often specific problems.

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    $\begingroup$ I like this idea. $\endgroup$ – Phira Oct 30 '11 at 20:12
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Case 2 is partially addressed in Moderator Clean-up of Abandoned Poor-Quality Questions , where the consensus seems to be that moderators shouldn't unilaterally close those questions. For questions that are old and truly vague, and which does not have any answers, a better way is to vote it down (preferably also leaving a comment as to how to improve the question). Completely unanswered, old, and negatively voted questions will be automatically purged from the system from time to time.

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In Case (1), which are probably the least annoying of the three, I tend to take the following approaches:

  • Give a description of why (I think) the problem is unlikely to have an easy solution. E.g. (a) show that it contains another hard problem, (b) show that "nearby" problems are difficult (e.g. NP-complete, #P-complete), (c) show that natural ways of approaching the problem are unlikely to work.

"If we attempt to solve this problem using Method X, then blah blah blah."

or

"The problem you pose is equivalent to finding a Widgit. Searching for Widgits has been studied extensively by Prof. Blah's research group, but there is still not a complete solution. See: Blah et al., blah blah blah, J. Blah (2010) pp. 1-$\infty$ for a survey of this topic."

  • Give a partial answer. I especially like this approach, since it sets the standard for subsequent answerers (and this is exactly how research works).

"This problem seems hard. We can prove it in the case of X, where blah blah blah. But this method doesn't extend to the whole problem due to blah blah blah."

  • Show that it follows from a (reasonable) conjecture.

"Assuming Conjecture X, we can prove your claim as follows by blah blah blah."

  • Give a computational/algorithmic answer.

"Here's some code that checks that your conjecture is true for $N$ up to a gazillion. It has been optimised in the following ways: blah blah blah."

  • Acknowledge I'm not learned enough to provide an answer to the question.

This is, more or less, what I'd do if I was asked the question face-to-face.

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If there's an unanswered question you think should be closed one option is to vote to close and leave a comment encouraging others to vote to close but also make some little edit to the question, as that will bump it up to the front page. Maybe that will get it enough attention to get it closed.

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  • $\begingroup$ Instead of polluting the front page with a question that doesn't deserve to be open in the first place, it would in my opinion be much better to open a meta thread about the specific question. That's more than enough to alert five people with enough reputation to the question. $\endgroup$ – Alex B. Oct 31 '11 at 6:15
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    $\begingroup$ If all people with more than 10k reputation once a week took a look at the moderator tools and quickly went through the list of questions that received close votes in the last week then I think there would be no need for bumping. $\endgroup$ – t.b. Oct 31 '11 at 8:10
  • $\begingroup$ @t.b., sounds good, but it wouldn't catch the questions that got a close vote or two many weeks ago. $\endgroup$ – Gerry Myerson Oct 31 '11 at 11:57
  • $\begingroup$ @t.b. Done, Maaasterr. (With an exception, which is that I find bizarre the suggestion to close 75750.) $\endgroup$ – Did Oct 31 '11 at 13:46
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Temporary list of old questions I am trying to close (for the non-10k-users):

https://math.stackexchange.com/questions/49623/combination-with-repetition-problem-possible-solutions (OP asked about a difficulty reading a book, answer in comments, probably not worth an answer)

Solution to rarity-generalized coupon-collector's problem? (close as duplicate, a comment links to an answer in another thread)

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