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First, let me say that I completely understand the idea of not posting full solutions, but instead "hints" (or outlines) to let the OP figure out the details by themselves. I tend to do that myself.

Now, I have seen quite a few times (maybe more frequently these past months, although I cannot say it for sure) supposed hints that were actually wrong. That is, either barely better than a comment suggesting a first step (and definitely not enough for the OP to figure out what to do after that); or, even worse, suggestions to go in a direction that would not work.

(The latter, I reckon, being a sign that the person answering is just there to harvest points quickly, and did not actually follow their own suggestion to see if it did go through).

Should there be an officially stated policy about these hints? (e.g., a mention like "only post such answers after checking that this indeed is a valid and fruitful approach to the question; and provides enough insight to continue the argument.")

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    $\begingroup$ When I have doubts that the hint leads to a correct complete proof, I ask the author to provide more details. Unfortunately gamification encourages half-baked answers (and, alas, they often get highly upvoted, esp. if the question ends up on the Hot Network Questions list) $\endgroup$ – Bill Dubuque Jan 18 '17 at 15:54
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    $\begingroup$ Too often, newer-ish (with respect to the age of this site), offer hints that explicitly answer the question, anyway, or offer "hints" that repeat what the asker has indicated they already know. Entitling an answer with Hint doesn't a good hint make. $\endgroup$ – Namaste Jan 18 '17 at 18:49
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    $\begingroup$ We should avoid introducing unenforceable policies. $\endgroup$ – quid Jan 18 '17 at 19:26
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    $\begingroup$ @quid Indeed -- that's one of my concerns. One the other hand, writing a general guideline somewhere would maybe prevent some of these, and (in the "worst" case) encourage the downvotes of the worst occurrences. $\endgroup$ – Clement C. Jan 18 '17 at 22:03
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    $\begingroup$ "That is, either barely better than a comment suggesting a first step" - I see very high-reputation users post these as answers all the time and when I mention it I get a bunch of self-righteous nonsense back about how I don't understand because I'm new. $\endgroup$ – The Count Jan 18 '17 at 22:22
  • $\begingroup$ @TheCount Yes, I agree with you. Often their answers are very short, and while moderating the site, I get the message that this answer has been flagged due to it's length and content. I still retain such answers, however sometimes such hints can be abstract, and not take into account the level that the user is (I once saw a calculus-based answer for a seventh standard kid's question). Sometimes this is the questioner's fault: they don't provide enough context to deduce their level. But I always ensure that my answers are complete, except for facts "trivial" at that level. $\endgroup$ – астон вілла олоф мэллбэрг Jan 18 '17 at 23:52
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    $\begingroup$ I wrote a mini-screed about hints a little while back. I still stand by it. meta.math.stackexchange.com/questions/22263/… $\endgroup$ – Ron Gordon Jan 19 '17 at 0:20
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    $\begingroup$ @ClementC. That could make more sense. Maybe there are some non-controversial and non-obvious remarks one could make on what a "hint" should fulfill. We could then title the thread "Hints for Hints" :-) $\endgroup$ – quid Jan 19 '17 at 1:04
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    $\begingroup$ A "hint" will be evaluated as an answer by people via upvotes/downvotes in the same way as a normal answer, so why a different policy? Besides, at least from my perspective, I've seen as many "complete" wrong (and I emphasize: blatantly wrong) answers as "hint" answers. And as many helpful "complete" answers as "hint" answers, in terms of proportion. I put quotations because, as I see things (and by the way the system works), the only distinction between answers are "helpful" and "unhelpful". $\endgroup$ – Aloizio Macedo Jan 19 '17 at 6:04
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    $\begingroup$ That's already policy. What is the downvote feature (or at least the comment feature) for if not for incorrect answers? $\endgroup$ – Jack M Jan 20 '17 at 15:47
  • $\begingroup$ I think hint is between answer and comment. $\endgroup$ – Takahiro Waki Jan 23 '17 at 13:03
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    $\begingroup$ FWIW, answers that only indicate how to start a problem are a natural consequence of questions that don't show even basic research effort. And a false start is still a start, and reflects the first thing an actual, knowledgeable person might to do tackle the problem. $\endgroup$ – user14972 Jan 24 '17 at 15:24
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    $\begingroup$ @Hurkyl Information on what 'an actual, knowledgeable person might to [sic] do [sic] tackle the problem' can be given in comments. It's not an answer. $\endgroup$ – quid Jan 24 '17 at 16:21
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    $\begingroup$ I think that, at least to some extent, the question whether hints are appropriate depends on whether low-effort homework/exercises (interpreted in a broad sense) is on topic. Since there does not seem to be a possibility of everybody agreeing on the former, I think it is clear no consensus can be reached here either. $\endgroup$ – Danu Jan 24 '17 at 22:09
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    $\begingroup$ I don't know what the word "Hint" means anymore. More often than not I see people start their answer with this word and then a complete answer follows. Full answers are good, but why add the word "Hint"? It's like a virus word. $\endgroup$ – Winther Jan 24 '17 at 23:15
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I agree that hints that lead the OP in the wrong direction or barely offer any help at all aren't valid answers, as are hints that simply restate information the OP has already stated. However, moderating every hint to check if they are valid is impossible, and we as a community should avoid at all costs putting in place policies that are impossible to enforce.

For one, this would put an unnecessary load on moderators, it's also unlikely anybody's going to read a hint and check for themselves if it works, because it's a waste of their time.

My suggestion would be that if you see an invalid hint, downvote it. If the hint clearly doesn't provide any useful information, flag it as "not an answer", and if it is blatantly wrong, flag it as custom and explain the scenario leave a comment and mark it as not an answer.

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    $\begingroup$ The way I understand it, correctness of answer should be decided by the community not moderators: Is it in the Moderator's Job Description to patrol for correctness?. So I am not sure whether custom flag is a good way to go. NAA flag is a bit different, because it puts a question into low quality review queue: What happens when I flag a posted answer as “not an answer”? In any case, it would be good to know what moderators think about your proposal. $\endgroup$ – Martin Sleziak Jan 23 '17 at 6:32
  • $\begingroup$ @MartinSleziak the problem I see with the NAA flag in that situation is that you can't leave a message, so it's hard for the reviewers to know why it's flagged, especially if it seems believable. $\endgroup$ – Travis Jan 23 '17 at 22:56
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    $\begingroup$ For NAA flag, you can sill leave a comment. Some reviewers might look at it. My main point is that custom flag does not put it into review but must be handled by moderators. (I hope that some of the moderators will comment on this, since they handle the flags and their opinion on what should and should not be flagged matters the most. I have even asked about this in Math Mods' Office, but no response so far.) $\endgroup$ – Martin Sleziak Jan 24 '17 at 6:47
  • $\begingroup$ Another possibility how to get attention of other users to answer which you consider worth deleting would be mentioning it in this chat room which was created explicitly for stuff related to closing, reopening, deleting, undeleting, etc. However, it will probably not work - hardly anybody visits that room nowadays. But it used to have periods of bigger activity, maybe it will become active again in the future $\endgroup$ – Martin Sleziak Jan 24 '17 at 6:49
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Sometimes the question itself asks for a hint, and anything more than a hint is not an answer. I see full answers given in such cases, and I think that is bad too. Where I see a full question where I think that a hint may be enough, I generally post in a comment, but I do that more now than I used to do. Occasionally I still post a hint as an answer to a full question, because I imagine that the person who asked the question will learn something by figuring the rest out for themselves. Perhaps that is wrong - but there are ways people can, and do, indicate that I have overstepped.

A couple of times I have given "hints" which I thought would help and on reflection lead nowhere. I learn a lot from that, but the discipline of the site is that I should delete or retract. Certainly such things have been both upvoted by people as careless as me, and called out and down voted by those who notice - that is painful, but I am grateful, because this site is - in the end - about good mathematics rather than large egos.

The overall tone of the site should be encouraging, but maybe there needs to more active feedback on poor quality contributions.

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    $\begingroup$ "this site is - in the end - about good mathematics rather than large egos." - this really should be emphasized more. $\endgroup$ – J. M. is a poor mathematician Jan 26 '17 at 6:02
  • $\begingroup$ +1 I try to leave my mistaken answers (and hints) up, noting the mistake, so others can learn not to make the same one. $\endgroup$ – Ethan Bolker Jan 29 '17 at 17:37
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The purpose of this website is not to be a collection of Questions and "Hints that may or may not lead to a complete answer, no one could be bothered to check, and in any case future readers will need to spend an indefinite amount of time trying to work the full answer from the hint because what constitutes a hint is variable from user to user". It is designed to be a collections of Questions and Answers.

My personal policy regarding hints is thus as follows:

  • If the hint is immediately obviously wrong, or if it's not obvious how to get to the full answer in a reasonable amount of time using the hint (and it's a part of math where I'm confident enough that I can tell whether it's the case), or if I feel like the hint-giver barely gave any thought to the question and posted something that they didn't even bother to check leads to an answer, I downvote and possibly vote to delete if I can;
  • If the "hint" is a full answer poorly disguised as a "hint", when I can be bothered I remove the useless word "hint" (typically written in bold and full caps for unbeknownst reasons) from the answer;
  • Otherwise, I encourage the answerer to flesh out their hint (again, when I can be bothered, which is not very often these days).

I believe that hints are actively harmful for the long-term usefulness of the site. It is infuriating, when I have a question I'd like the answer to and look it up here, to find that someone only answered with a "hint" that I'm not sure will lead to the answer, and since there's already an answer potential further answerers are discouraged / don't even bother to look at the question because there's already an "answer".

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    $\begingroup$ While I agree that hints may detract from additional answers, I strongly disagree that hints---in general---are harmful to the site, in the long or short term. Good hints usually worth just as much if not more than a complete answer. Bad hints are harmful, but no more than bad answers. $\endgroup$ – Asaf Karagila Jan 24 '17 at 10:55
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    $\begingroup$ @Asaf: Bad hints can be worse in that their broken nature can be harder to establish. Also, if there is a problem with an answer it can be pinned down and one can ask for clarification. For a hint, alas, some are of the opinion it's poor form to even ask for clarification, and replies will only be provided if it contributes to their personal enjoyment. $\endgroup$ – quid Jan 24 '17 at 14:50
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    $\begingroup$ I completely agree with Najib: very often hints are just vague and obvious allusions to topics trivially related to the question, but which show very little insight. I'm not even talking of the numerous hints consisting of completely false claims. I'd be quite curious to see a few examples of "hints worth more than complete answers" in algebraic geometry, commutative algebra, differential manifolds or algebraic topology, just to mention some of the fields in which I spend much time in order to contribute explicit and detailed answers, $\endgroup$ – Georges Elencwajg Mar 24 '17 at 19:56

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