Is it acceptable to leave hints as answers?

Question

Question: Is it acceptable to leave a hint as an answer?

For the purposes of this question, let me attempt to define a "hint":

A hint is a short, generally terse, comment which does not provide an answer to the question asked, but instead gives a running start on the problem which, if followed correctly, will lead to a solution. For example, if someone asks how to evaluate $$ \int_{0}^{1} x \mathrm{e}^{x^2}\,\mathrm{d}x, $$ a hint might consist of the answer "Try the change of variables $u = x^2$." A proper hint (rather than an off-the-cuff suggestion for what one might try next) should ultimately lead to a complete solution. (Hat tip to quid for articulating this fairly well).

I am asking this question in order to seek some kind of consensus. There has been discussion in the past, but I don't see a clear consensus (and maybe there isn't one!), the earlier discussions seem rather out of date, and the questions seem to be more about leaving hints-as-answer vs hints-as-comments. So as not to muddy the issue, I want to focus very narrowly on whether or not it should be okay to leave a hint as an answer.

To summarize my impression of earlier discussions:

• An early discussion of hints-as-answer seems to land on the side of "Yes, this is okay." However, I think that the underlying assumption of the discussion here is that it is always okay to leave a hint, and the question is where is the right place to do so (comment vs answer). I also note that at least one answer makes reference to the now burninated homework tag. This suggests that some new discussion might be productive.
• More recently, it was suggested in this topic that we make a change in the culture of MSE to focus more on hint giving. This proposal seems to have been received negatively, but that doesn't really address whether or not providing hints-as-answers should be okay.
• Answers to this question suggest that it is acceptable to leave hints-as-answers, but it seems that this is suggested as a way to bypass the limitation that low reputation accounts cannot comment.
• Possibly relevant (there is some discussion, but not much): hints for homework questions (reloaded)
• Should there be a policy about hints.

Answer 1

Sometimes the question explicitly only asks for hints.

Rather more often, a hint will actually be more useful to the asker. This is often the case for "homework" questions (when they deserve to be answered at all).

With many exercise-type questions, nobody (including the problem setter) actually cares about the answer, but the point of the exercise is to give the student a chance to acquire familiarity with definitions and techniques by thinking about them themself. Giving a full answer would rob the asker of the chance to learn; but a hint pointing in a fruitful direction might save them from being stuck.

For example, I remember a question asking whether various cartesian products of closed and half-open intervals, equipped with the lexicographic ordering, have the supremum property. That sounds like a good exercise for getting some feel for how the definitions of least upper bounds and/or lexicographic orders work -- but I'm pretty sure that in reality nobody cares whether those particular sets have least upper bounds. Giving a complete answer would have killed the value of the question without contributing anything useful to anyone.

Here is another example, posted during this discussion. Humanity is not made even a tiny bit richer by having the particular equation the answer concluded with posted on this site; and the asker has been deprived of any chance to practice things for himself. Posting just a hint that such-and-such two vectors need to be perpendicular would have been much better for everyone.

Answer 2

Apparently there is considerable divergence regarding what a hint is. So, here is what I expect from the content of an answer-post, whether it is prefaced "hint" or not is maybe not crucial. (Obviously there are questions to which this does not fully apply or for which it does not make sense at all, say a reference request, it is for your typical question that asks about a mathematical problem without particular restrictions on the answer.)

1. An answer-post comes with the (implicit) promise what is described or suggested actually works. If it says "Try to do {this}." Then doing {this} should actually work. An answer post is not for hopeful recommendations what might work.

2. Related to this, the answerer actually should be able to give a complete and detailed answer. (If somebody believes they have a good suggestion that could work, but are not sure about it, they can leave it as a comment.)

3. The post should contain something that directly allows some progress, and is described in an unambiguous way. In particular, answer-posts in the form of rhetorical questions should be avoided. It is annoying for everybody involved when those get flagged up as Not An Answer and then get "if you have a new answer" comments from review. (Yes, it is sometimes more the flaggers fault, but it can be tricky sometimes, and we want to make life easy for everybody.) The very same information can usually be conveyed in a form that does not lead to that confusion. Moreover, rhetorical questions especially in writing are not really an efficient way to get somebody to think about the problem. Often they'll rather think about what the asker likely expects.

To avoid confusion, this is my personal opinion quickly stashed down, I am not in the habit of removing content that goes against these preferences.

That said, as this discussions shows "hints" means all kinds of things. Independent of the actual content of the answer post somebody creates, I would kindly like to invite everybody when they write "HINT:" at the start of the post to pause and think what they actually want to convey by this and if this could not be conveyed more directly.

Some things that seems to be common use cases:

• "Hint" because it is an outline of the method but does not carry out or finish routine calculations or spell out all details. In my opinion, that's not really a hint but an outline of a solution and should be described as such if at all (actually mostly no actual explanation is needed, usually people get what is intended).

• "Hint" because it only does one or a few of similar problems. That's a partial answer not a hint.

• "Hint" because it stops at some point. That's a partial answer not a hint. That's alright. It's good though to say that it is incomplete though. This is not always clear to everybody.

• "Hint" because it gives the crucial idea but does not say much in addition. This one is an actual "hint" in my book. Still I'd say on the one hand it can often be useful to say a bit more (which then shifts it into the former category), or at least to say how specifically it applies. I cannot help but feel that some "hints" are mainly popular with those that don't need them actually, but find them nice and are happy that they understood them.

• "Hint" because it give some relevant piece of information that when interpreted correctly is helpful. Again, that's a hint in my book. It's risky though since it might just not help at all, too. Personally, I'd avoid to write answer posts only comprised of this. But, alright, that's an actual hint. I'd still recommend to give at least some complementary information.

• "Hint" because somebody was a bit too lazy or too busy to write an answer proper and want some fallback. Just don't.

• "Hint" because somebody answers a question they know they should not answer and wants some fallback. Just don't.

• "Hint" because somebody was actually not sure about the answer. But, hey, why not throw it out there and let it validate or correct by commentators. Again, just don't.

Answer 3

Sometimes it is obvious that a question-asker is a student struggling with a homework question. In this case, I argue that a hint not only can, but should be posted as an answer:

1. It is pedagogically beneficial for the student to work out the problem as much as possible on their own; a hint that clears up an error or misconception on the part of the student, or points a key idea the student needs to apply to solve the problem, is exactly what the student needs. The student can always comment and ask for more help if needed.

2. Posting a full answer, that the student copy-pastes into their solution without understanding, is pedagogically damaging. Posting a hint as an answer discourages others from spoiling a full solution.

3. Posting the hint as an answer removes the question from the Unanswered queue, which is important for keeping the queue clutter-free.

Answer 4

You can post your hint, someone else might post an answer, and you'll see which is accepted, or which one gets more upvotes. It's not really up to us to decide whether a hint is acceptable, it's up to the people looking at and asking the question.

I guess it's also up to the mods; you pointed out there's been a discussion about whether there should be a policy against it.

Answer 5

tl;dr

If it answers the question or adds to the answer, yes. If it skips to answer the question and just gives a hint: no

argument

This is from the official, overruling Stack Exchange help center (emphasis mine):

Answer the question

Read the question carefully. What, specifically, is the question asking for? Make sure your answer provides that – or a viable alternative. The answer can be “don’t do that”, but it should also include “try this instead”. Any answer that gets the asker going in the right direction is helpful, but do try to mention any limitations, assumptions or simplifications in your answer. Brevity is acceptable, but fuller explanations are better.

Let's look at some examples:

• Question A is "I have trouble finding which theorem to use in this case. I want to solve X, I have this [insert of where OP is]. Where to go now?"
• Question B is "I want to solve X. I have this, but the answer does seem wrong. Where did I go wrong?"
• Question C is "I have this problem. I have no idea how to solve it. How does one solve it?"

let's look at what the questions ask for:

• Question A asks for a hint. Only a hint to the right direction. Providing a Hint-answer is acceptable, as it is providing what the question is asking for.
• Question B asks to judge the answer, pick it apart and point out where the solution went wrong. As long as the answer tells where the error is (and best what to do instead) anything additionally might be acceptable.
• Question C does not ask for a hint but a solution. So it is not an answer to just give a hint, providing a hint should not be acceptable. In case of a Textbox Question, though, a full answer detailing all the steps and giving all the intermediate steps should be neither. It's better to outline the steps with enough information to allow someone working themselves through the problem to solve it.

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As amWhy pointed out, a lot of type C questions seem to be what physics.SE would ban as "homework questions" or, as they phrased it bare PSQ's (problem statement "questions" that read like an exercise copied (often literally copied) from a textbook or problem set, or a test). A hint to such is (after the guidelines) not acceptable. Yet a full answer does not help the student in the same way as a collection of hints as they won't learn from getting their problems solved for them. (roughly quoted form amWhy).

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And before someone says "we are different from the communities at large", please check https://math.stackexchange.com/help/how-to-answer which has the identical text.

Answer 6

Hints can come off as hostile to the asker and are often not very useful unless you already have a good idea on how to solve the problem. While we shouldn't be giving the answers to homework questions we should be giving answers that explain how to solve the class of that problem.

Answer 7

One problem with a hint is, when the asker is getting it, but you are not.

Think of an interesting question. Now someone leaves a hint, the asker can solve his problem and then accepts the answer with the hint. This will prevent most people from adding actual answers.

Now you googled the problem and found the question and cannot get the hint, but would like to have the solution.

Leaving hints is nice for forum discussions, where you can help one by leading him to the solution, but it is help for one person and not creating an Q&A item.
On Stackexchange, we try to create a knowledge base, not a list of exercises with hints how to solve them.

And even when you think leading people to understand the problem better is better than just providing an answer, sometimes people (often not the asker himself, but anonymous readers) just want the answer to use it without understanding all details.