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I've encountered several posts in the past that explicitly ask for a hint for their stated problem. It's not uncommon for these questions to gather full solutions for their problem, sometimes in their first answer. Sometimes, the asker is quite emphatic, including the request in bold, or prominently in their title. Sometimes, it's less clear cut, where the request for a hint is less exclusive, and more an indication that they'll accept whatever help they can get.

On the end of that spectrum, there are the askers who have no context to add to their question, and hope that asking for a hint will get them help here, despite not meeting community standards. This is a separate issue, so let's ignore such cases, for the purpose of discussion. Others have raised this issue, here for example. Or better yet, here.

I want to know is, what does the meta community think about answering a question with a full solution, when a hint was requested. Is it an answer to the question? If not, should we be flagging these answers as "not an answer"? Should we be down-voting them? Deleting them? Or perhaps we simply leave a comment below the answer, asking the author to modify or delete their answer? Assume, for the purpose of discussion, that these answers are otherwise high quality.

Also consider, does it matter how emphatically the asker requests a hint? Perhaps we should take some of the more drastic measures from the previous paragraph only when the asker specifies they want only hints, but not in other cases.

There is a discussion from 6 years ago that pertains strongly to this one. Quid gives an answer that answers the core question here, but given it was made so long ago and received a total of 7 votes, it would be good to get a more definitive and current ruling.

Another relevant discussion from 8 years ago rules more convincingly that full solutions can be provided to older questions answered just with hints. Does this still apply to questions asking explicitly for hints?

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    $\begingroup$ There is skill involved in providing hints : that's almost always why I end up actually avoiding questions explicitly asking for hints, or end up divulging very little via a comment (or using spoilers, which I see to be useful). I'm actually quite happy if there is someone great at providing hints on-site. What I would love is feedback on how good the average answerer here is at providing good hints, but it's all subjective, so right now, merely with my gut : if someone says hint-only , I will respect that : BUT if there's a duplicate with a complete answer, then I will close the question. $\endgroup$
    – Sarvesh Ravichandran Iyer
    Commented Nov 11, 2021 at 2:30
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    $\begingroup$ I think I resonate with this answer of Asaf : your hint is meant to tailor itself to OP's requirements because when you write an answer, you want to write it for a general audience and you consider the OP a representative of it. Therefore, by all means , the context required to provide a good hint answer either is to be given by the OP or to be inferred by an outstanding mind reader (which I've seen happen but I don't think everyone is!) $\endgroup$
    – Sarvesh Ravichandran Iyer
    Commented Nov 11, 2021 at 2:38
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    $\begingroup$ @Teresa I also thought Asaf's answer was good. I have to say, while I support my proposal below, I'm not 100% convinced by it yet, and I sympathise greatly with Asaf's 5th point in his answer. I believe, generally speaking, that our first duty, as answerers, is to the askers themselves, and the needs of future readers are of secondary (but not zero) concern (though there are exceptions to this rule of thumb). $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 2:46
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    $\begingroup$ If somebody out there believes strongly in a more neutral option between Xander and myself (e.g. hints or full solutions should be accepted by the community, no matter what the asker wants), please make a proposal like Xander's or mine. $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 2:58
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    $\begingroup$ In my experience, this often goes like this: Hints are left in the comments (where they belong). The OP then responds with something along the lines of "Got it!" or requests further hints until they reach clarity. At that point, I'd say it was appropriate to either post a full solution or (better, where applicable) to encourage the OP to post a full solution. So there's a middle ground...regard such questions as works in progress, the end goal being a full solution reached collaboratively with the OP or the deletion of the question. $\endgroup$
    – lulu
    Commented Nov 11, 2021 at 12:26
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    $\begingroup$ @quid Perhaps we ought to describe the motivation as “unknown”, rather than “dubious”; I don’t think we get anywhere good by assuming negative intentions of our askers. Note that I mentioned as many "good" cases as I did "bad". $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 18:33
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    $\begingroup$ I won't quibble over the word. Indeed sometimes it is simply unknown but that's not all there is to it. Indeed you wrote it yourself "there are the askers who have no context to add to their question, and hope that asking for a hint will get them help here, despite not meeting community standards". Isn't that a negative intention, trying to get around the guidelines? $\endgroup$
    – quid
    Commented Nov 11, 2021 at 18:48
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    $\begingroup$ Personally I even did no mostly think of that. There are also those that try to do their homework, get stuck, and then ask only for a hint because they do not want a full solution for their HW. That's not so much a negative intention but it is a practice that I consider as dubious regarding its merits, or misguided, ill-advised whatever you prefer. $\endgroup$
    – quid
    Commented Nov 11, 2021 at 18:52
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    $\begingroup$ @quid I see, thank you for clarifying. Yes, indeed asking for a hint for the purpose of circumventing community standards is a negative intention. The purpose of my second paragraph is to acknowledge then dismiss this (and point to where it has been discussed), because it is a separate issue. I wanted to focus specifically on cases where this is not the case, and I think there is great merit in both asking for and giving good quality hints. $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 18:58
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    $\begingroup$ We shouldn't discourage full solutions. It is possible that some users may not understand the hint fully to arrive at an answer and then they may seek for more clarification or a full solution. On the other hand hints are preferable if someone is trying to learn some new stuff. IMHO a full answer is better in the long run compared to a hint. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 14, 2021 at 2:20
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    $\begingroup$ I think the more contentious issue is whether (or not) to allow hint answers at all. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 14, 2021 at 2:27
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    $\begingroup$ I think we should avoid too crafty hints (which are beyond the reach of typical average student). My own favorite is hint combined with spoilers to make a great answer. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 14, 2021 at 2:30
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    $\begingroup$ @ParamanandSingh Hints are indeed a delicate art. The more I discuss this, the more I'm coming around to Leslie Townes' answer: this is too subjective to have a solid policy on. I would encourage, as both Leslie and user1729 would, answerers to pay attention to and try to honour the requests of the asker. $\endgroup$
    – Theo Bendit
    Commented Nov 14, 2021 at 2:35
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    $\begingroup$ Here is another point which people think but may not express explicitly. Some smart hints can be very short and garner a lot of upvotes. Some people frown upon getting such high rep with litte effort. I don't mind it because there aways an option to downvote if you don't like such answers. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 14, 2021 at 5:28
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    $\begingroup$ Also in many of my answers I have tried to honor the requests of askers by providing highly tailored solutions. And then if I wish I also include a more general version with more details to cater to a wider audience. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 14, 2021 at 5:30

7 Answers 7

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One thing I've done myself a few times, and I've also seen used in some other answers, is to just give an initial solution start, as a form of a hint, and then have most or all of rest of the full solution behind a spoiler tag.

There are many cases where this doesn't work particularly well. However, where it is more applicable, I believe this idea can be used as a reasonable compromise between the OP only wanting a hint, but still also providing a full solution to everybody else (including the OP if they can't solve the problem on their own, or if they just wish to check on what the answerer wrote).

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    $\begingroup$ One could also give progressive structured hints via full blown solutions using multiple cascading hidden sections, but I'm not sure how well SE supports such. A richer platform would not only provide extensive support for such, but would also allow such proofs to be dynamically specialized to the readers context (e.g. using ideals for abstract algebra students but more elementary equivalents for beginner number theory courses). But that's a pipe dream for SE. $\endgroup$
    – Bill Dubuque
    Commented Nov 11, 2021 at 1:39
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    $\begingroup$ I distantly remember experimenting with spoiler tags, and running into some problem with how they interact with MathJax. I couldn't make this concern more vague if I tried, but I remember that there were, at some point, technical issues with using spoiler tags here on MSE. $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 2:06
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    $\begingroup$ @TheoBendit I've not yet encountered any particular issues with how spoiler tags interact with MathJax specifically. In general, the main limitation I've found is they don't handle manually entered end of line characters (e.g., by clicking Enter/Return in Windows). Within MathJax display equations, I often use separate lines to make it easier to read & maintain, but just remove these if within a spoiler. In general, when I want to have text start on a new line, including having blank lines, I use the supported <br> HTML tag. There might be better ways, but this works well enough for me. $\endgroup$
    – John Omielan
    Commented Nov 11, 2021 at 2:13
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    $\begingroup$ Since this answer is getting plenty of up-votes (and I myself up-voted it too), I just want to remind people that this doesn't answer the question of what to do about other people posting full solutions when a hint is requested. On a personal note, while the suggestion could be helpful, there are also many times when I feel like a more abstract hint is helpful than a solution with "holes" (hidden in spoiler blocks, or just left out of the answer entirely). $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 9:22
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    $\begingroup$ Spoilers are needless, really, because everyone, even those wanting only hints, is going to feel the compulsion to read whatever the answerer feels is the bottom-line. And to me, you are just providing a full answer, with a pretense of only hinting. $\endgroup$
    – amWhy
    Commented Nov 12, 2021 at 15:18
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My thinking is that even if an asker is relatively clear about wanting only hints, the line between "hint" and "solution" is often sufficiently imprecise that it is difficult to adopt any default strategy to answers that do not seem fully responsive to a question --- or even some answers that appear to be explicitly violative of an explicit, boldfaced, (whatevered) request for only X and not Y.

One rarely knows quite exactly what an asker is going for - whether a hint expressly intended to be such will push them over the line, vs. whether a solution somewhat worked out will be acknowledged as such, etc. It strikes me all as a bit like being asked about some aspect of a movie without providing "spoilers." A lot of that stuff really exists only in the eye of the beholder, and I wouldn't want to take a good faith answerer to task for behaving in some way that doesn't match my own view of what they ought to have done.

But personally I do hesitate to upvote an answer that proceeds directly opposite to what an asker is looking for. Most questions I see do not provide enough detail for me to regard this issue as being raised. If an answer does provide a full answer, and not only a full answer but a full answer clearly within the asker's express realm of understanding (it's possible to answer questions with reference to theories that the asker might not be familiar with, which I do not regard as "spoiling" the question), and an answer does such after being explicitly told not to provide such (and all of these are huge "ifs"), I might not upvote, and I'd prefer that such answers not be posted.

All of this strikes me as some version of quid's answer on that old post. Even if old it is good advice.

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    $\begingroup$ +1 Excellent points, thanks for answering. Even if your answer is a version of an older one, it is good to know that the sentiment does survive today. To repeat a previous comment of mine, I didn't envision my suggestion as being a rigid rule, so I would expect people to treat the muddy cases with common sense. But, I would be fine with leaving the whole thing to common sense, so long as we don't go down Xander's route (i.e. discourage askers from specifying that they want hints). $\endgroup$
    – Theo Bendit
    Commented Nov 14, 2021 at 2:12
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A proposal of my own (upvote to agree, downvote to disagree):

If an asker specifies that they want only a hint (this does not apply to askers that do not specify that they want hints exclusively), then answers that provide a full solution should not be posted until the asker has either

  • Accepted an answer,
  • Indicated that they have solved the problem somewhere in the comments, or
  • Apparently abandoned the question.

Any full solution posted beforehand should be down-voted and/or a comment should be left to say it is not a proper answer.

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    $\begingroup$ It's worth noting that I did not recommend deleting the answer. If the answer would have been valuable afterwards, if anyone else finds the question, then I'd say it should remain. But, in the short term, down-voting is a deterrent, and also helps hint answers rise to the top. $\endgroup$
    – Theo Bendit
    Commented Nov 10, 2021 at 23:46
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    $\begingroup$ I do not completely agree with a downvote,there might be a few questions which might make it difficult to answer with a hint and even if given it can be counted as a full solution A comment should be enough in my opinion . $\endgroup$
    – Albus Dumbledore
    Commented Nov 11, 2021 at 8:08
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    $\begingroup$ Good point @AlbusDumbledore, but remember that this is for questions that request for a hint and not a full solution. If the asker's request is unreasonable, then treat it like any other question containing unreasonable requests: raise the issue in the comments, possibly close the question, etc. $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 8:17
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    $\begingroup$ @AlbusDumbledore In such cases, the answer should at least acknowledge that the OP requested a hint, e.g. write "The question asks for a hint, but it is a simple one-step calculation....". $\endgroup$
    – user1729
    Commented Nov 11, 2021 at 9:50
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    $\begingroup$ @user1729 Yes I agree with that $\endgroup$
    – Albus Dumbledore
    Commented Nov 11, 2021 at 9:52
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    $\begingroup$ @user1729 For the record, so do I. The above proposal is intended to be, like most policy, not some unbreakable rule that should be adhered to at all times by the letter, but a guideline for handling the situation where someone posts a full solution against the asker's wishes. Common sense should absolutely be exercised (generally, not just on this issue). $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 9:57
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    $\begingroup$ @TheoBendit I understand and agree with your comment :-) I do wonder though if the answers we are discussing are often due to people did not read the question properly. (I've done this many times: read title, skim question, post answer, realise question should have been read more carefully...rewrite/delete answer.) $\endgroup$
    – user1729
    Commented Nov 11, 2021 at 10:15
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    $\begingroup$ @user1729 That is is a major source of them, yes. But, I also think that a large source of them come from laziness. It's often easier to write out the clear-cut solution in your head than to craft just the right hint to nudge them over the line without doing everything for them. I've been guilty of both problems in my time. There's a similar, and more common issue, with solution-verification questions. It's very often easier to post an alternate solution than actually pick through the asker's attempt. I would personally prefer if this were handled similarly to what's proposed above. $\endgroup$
    – Theo Bendit
    Commented Nov 11, 2021 at 10:20
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Discussing hints in general rather than in the precise scenario in Theo's question.

If I check out my own old answers labelled as hints, the collection of material leaves a lot to be desired. Some are generously upvoted pithy one-liners, which is fine I suppose. Many started out as hints, but evolved into what could be called "roadmaps". Those may make for good multistep exercises, but they do the discovering for the reader, and might be better avoided. Yet others are objectively failures (imagine the gif with Captain Picard facepalming here).

Many answerers label what (to me at least) look like complete answers as "hints" to thwart criticism for doing others homework. This is not good. But there is a beam and mote -problem here. Because what is "complete" depends on who is reading it. Undoubtedly some of my hints are seen as complete solutions by others. Conceding that a good hint is very difficult to come up with.

The first few times this theme was discussed in meta, many teacher types emphasized the educational role of a good hint. I think that many (if not most) of us agree that working on a good hint is a great way to learn, ideally leading to a socratic dialogue between the student and the teacher. But, we (or at least most of us) also agree that this platform is not really at all designed to serve that end well.

Still, some of us have an overwhelming desire to teach here (rather than simply post answers showing that we can solve the questions). I have not thought about the following nearly enough to see whether it holds water at all. Just tossing this suggestion for you all to criticize.

We can allow a hint answer, if the answerer makes a commitment to spend a sufficient amount of time on that page. Willing to answer requests for clarifications by socratically adding more hints.

  • This would discourage half-assed hints from users already on the way to their next low hanging fruit.
  • The process should converge to a full answer (in the interest of site hygiene).
  • Ideally the full answer should be prepared by the student, so that the dialogue remains there for future readers to see. But the teacher may want to (need to) step up to the plate at some point.

An obvious downside is that the teacher may misestimate the time needed to guide an asker to the finish line. So some kind of exit strategies should also be discussed. Anyway, if the end result is a somewhat satisfactory answer, this could be ok.

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    $\begingroup$ A problem is that the final form of a hint is not something that the teacher can decide in advance. Many of us think we are good at this (objectively many of us are good, but not great, if only because the next generation of students may need a hint different from one that worked back in the day). It is all too easy to fall in love with what you yourself think is a perfect hint. $\endgroup$
    – Jyrki Lahtonen
    Commented Nov 17, 2021 at 16:19
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    $\begingroup$ I think the idea is fine, but I don't know get how this can be enforced in terms of reviews? How long do we wait so that asker and answerer collaborate and reach a final full solution? Some of my answers actually started as comments and upon request from asker were developed into full answers. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 18, 2021 at 7:21
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The asker has the option to mark whichever answer helps them the most as "the answer" and/or ignore the less helpful answers or comments.

Posting solutions to older hint-only questions should not be policed either, because it adds to the knowledge accumulated on the forum.

As long as people are helping each other to study math on a math forum, I don't see why their communication needs to be policed.

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  • $\begingroup$ The thought behind the idea of active "policing" was threefold, in decreasing order of importance: 1. The asker wants only a hint, which suggest to me that they want to reserve some part of the process for themselves, and a complete solution could rob them of this opportunity. 2. Giving good hints is hard, and I wanted to discourage laziness on the part of answerers who find it quicker just to dump a full answer. 3. Giving askers what they ask for and no more could teach some problematic askers, non-judgementally, that asking for hints will not net their poor question full worked solutions. $\endgroup$
    – Theo Bendit
    Commented Dec 6, 2021 at 3:49
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If the question explicitly asks for a hint, then how is the question of a complete solution even a discussion?

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    $\begingroup$ You question could easily be answered by looking at the answers provided here, and in the linked threads in the question above. There is a lot of context here which might help you to understand why this question is being asked. $\endgroup$
    – Xander Henderson Mod
    Commented Nov 18, 2021 at 15:28
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    $\begingroup$ it was more rhetorical, saying "any attempted justification of doing the opposite of what the OP asks for is over-analysis" $\endgroup$
    – tomos
    Commented Nov 18, 2021 at 15:56
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    $\begingroup$ This presumes that the goal of Math SE is to give askers exactly what they ask for. It is not. The goal is to create a repository of questions and answers which are useful to a wide range of people. So someone giving a complete answer to a "I want a hint" question is maybe not giving the original asker exactly what they want, but they are providing a service to future askers. The alternative is to ask every question twice: once with hints only, and once for complete answers. This would not be sustainable. $\endgroup$
    – Xander Henderson Mod
    Commented Nov 19, 2021 at 0:46
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    $\begingroup$ @tomos I think we regularly do the opposite of what OPs ask for. Take for instance the situation where an OP asks us for help in proving a false statement: hopefully we show that their statement is false! Another example could be when someone copy/pastes a question from a textbook and asks for a solution - it is very common that we close their question instead of answering it. $\endgroup$
    – KReiser
    Commented Nov 19, 2021 at 0:47
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    $\begingroup$ @KReiser: nice examples of opposing the request of asker! $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 20, 2021 at 2:54
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I believe that the goal of Math SE is to provide a repository of questions and answers which is of lasting value. I believe that any answer to a question should be a complete answer to that question, and that an asker's request for a hint-only is antithetical to producing a searchable database of questions and their associated answers. Thus (in my opinion, moderator hat off):

  1. Full solutions are preferable.
  2. If one is making other edits to a question, the request for "only a hint" should be edited out of questions (this is similar to how salutations and "thank yous" should be handled).
  3. "Hint" answers which don't actually answer the underlying mathematical question should be deleted or converted to comments. (Note that there is a class of "hints" which actually do completely answer a question, but I think that these are generally uncommon—crafting a good hint is hard.)

(And, as a reminder to folk who may not be familiar with meta: upvote to agree, downvote to disagree.)

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    $\begingroup$ -1 Thank you for the answer, Xander. :) $\endgroup$
    – Theo Bendit
    Commented Nov 10, 2021 at 22:59
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    $\begingroup$ @TheoBendit Thank you for the question. I have thought in the past that we needed to have this discussion again, and come to some kind of consensus (as it seems that no such consensus currently exists). Maybe this time, some conclusion will be reached. $\endgroup$
    – Xander Henderson Mod
    Commented Nov 10, 2021 at 23:00
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    $\begingroup$ Though, I have to say I do agree with the third point. It is indeed hard to craft a good hint. Bad hints give away everything tricky, or give help with the wrong steps to the answer. The former should probably be a complete answer, if anything, and the latter should be a comment, if anything. $\endgroup$
    – Theo Bendit
    Commented Nov 10, 2021 at 23:03
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    $\begingroup$ Hints can be viewed as special cases of more general queries about the key ideas or conceptual essence of the matter. These important pedagogical matters are rarely addressed in textbooks (or lectures), so a strong argument can be made that this is one of the most important features provided by this platform. If we disallowed such then the site would be nothing more than a sterile reproduction of proofs that mostly already exist in textbooks. Thankfully the community has always decided that it should be much richer. $\endgroup$
    – Bill Dubuque
    Commented Nov 10, 2021 at 23:58
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    $\begingroup$ That said, no doubt there is much abuse of questions asking for hints - and I think that we can devise good solutions to some of those problems that don't require flushing the baby with the bath water. $\endgroup$
    – Bill Dubuque
    Commented Nov 11, 2021 at 0:02
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    $\begingroup$ We should edit out explicit requests for hints? I can't even.... $\endgroup$
    – Gerry Myerson
    Commented Nov 11, 2021 at 8:04
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    $\begingroup$ @BillDubuque I think Xander's point, going by the parenthetical remark in (3), is that most "hint answers" are not like this. (Sometimes I see "hints" which are no more than poor half-answers written by people too lazy to type up a full answer, which maybe is what Xander is talking about.) $\endgroup$
    – user1729
    Commented Nov 11, 2021 at 9:42
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    $\begingroup$ An additional concern that I have is that "please give me a hint" questions are another source of needless duplication on this site (ditto solution-verification questions). If a user asks for a hint, but the question has already been answered elsewhere (below a question which is not asking for hints), should the "please give me a hint" question be closed as a duplicate? $\endgroup$
    – Xander Henderson Mod
    Commented Nov 11, 2021 at 16:11
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    $\begingroup$ I should also clarify that I don't think that posts should be edited just to remove requests for hints, but that if one is making other edits, I would encourage them to remove the requests (in the same way that salutations and thanks ought to be removed when editing. I'll edit the answer to clarify. $\endgroup$
    – Xander Henderson Mod
    Commented Nov 11, 2021 at 19:15
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    $\begingroup$ I think there's a big difference between salutations and thanks, on the one hand, and requests for hints only. $\endgroup$
    – Gerry Myerson
    Commented Nov 11, 2021 at 22:45
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    $\begingroup$ Obviously, @GerryMyerson, we disagree. While hints are a useful pedagogical tool in the context of coaching students one-on-one, they are not a good fit as answers in an encyclopedia-style Q&A format. As the majority of "hint" answers are noise, and a complete answer is just as good (if not better than) a hint in this format, requests for hints are noise in the same way that salutations are noise. $\endgroup$
    – Xander Henderson Mod
    Commented Nov 11, 2021 at 23:33
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    $\begingroup$ I don't consider request for hints as noise. Sometimes the request may be genuine and the asker may really be trying hard to come up with their own solution and need a little help. Editing asker's post without their permission might offend them when their request is genuine. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 14, 2021 at 2:36
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    $\begingroup$ @XanderHenderson: I agree that hints are not a very good fit, more so when it may not be understood by some users. I gave comments (to the current meta question) in this regard. What I wish to say is that there is no need to edit the asker's question. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 14, 2021 at 15:23
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    $\begingroup$ @ParamanandSingh if a user get's offended when their post is edited, we can remind them that Editing is important for keeping questions and answers clear, relevant, and up-to-date. If you are not comfortable with the idea of your contributions being collaboratively edited by other trusted users, this may not be the site for you. $\endgroup$
    – Mike Pierce
    Commented Nov 15, 2021 at 22:20
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    $\begingroup$ @MikePierce: in general I prefer to avoid edits which change the intent of a post without permission of author. Improvements to fix typos or a little bit of grammar are fine. If there is a mathematical error, it is best to comment about that (and maybe you can downvote to add some weight to the comment). Your linked post also says that edits should not change the meaning. $\endgroup$
    – Paramanand Singh Mod
    Commented Nov 16, 2021 at 1:27

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