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This question comes in two parts.

  1. If I am a lecturer in a field (say, Data Mining) and quite stuck in my research, am I allowed to make exam questions (for undergraduate & graduate students) related to my research hoping that some answers may give me ideas?
  2. If I am allowed to do that and supposing that I did, what could I do if a student actually answers my question with a method (s)he is currently working on in his/her own research but has not published yet (which I don't have the means to know of)?

Should I give an announcement or some kind of encouragement to the students who actually give such an answer to finish their research as fast as they can so that I can cite their papers to avoid potential copyright infringements and plagiarism?

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I think you can do it in a homework exercise, but only as a bonus question that is not part of the ordinarily graded questions. Adding it to an exam is not fair, for reasons mentioned in other answers. But rather than using it to find a breakthrough in your own research, use it to find hidden geniuses among the students. Make it very clear that those questions are completely optional and harder than the main homework questions; you may or may not state that they are actually open problems.

There are historical examples of students who solved open problems in homework exercises. For example, George Dantzig:

An event in Dantzig's life became the origin of a famous story in 1939 while he was a graduate student at UC Berkeley. Near the beginning of a class for which Dantzig was late, professor Jerzy Neyman wrote two examples of famously unsolved statistics problems on the blackboard. When Dantzig arrived, he assumed that the two problems were a homework assignment and wrote them down. According to Dantzig, the problems "seemed to be a little harder than usual", but a few days later he handed in completed solutions for the two problems, still believing that they were an assignment that was overdue.

Six weeks later, Dantzig received a visit from an excited professor Neyman, who was eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics.

Of course, when you do against all odds find a hidden genius this way, you can offer to supervise him or her in writing a publication, which should land you co-authorship on the paper.

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    That's the only example I've personally ever heard.
    – user18072
    Commented Dec 18, 2016 at 0:09
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    Why the downvote?
    – gerrit
    Commented Dec 18, 2016 at 18:34
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    Why would this merit the asker getting co-authorship? I realise this is common in some disciplines, but it doesn't make the practice any more ethical.
    – cfr
    Commented Dec 19, 2016 at 4:03
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    @cfr Two parts: (1) asking/formulating the right question (a.k.a. the research idea), and (2) supervision in writing things up for publication. Both are, in my opinion, sufficiently significant contributions to warrant co-authorship. See also my comment on CaptainEmacs answer.
    – gerrit
    Commented Dec 19, 2016 at 10:21
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    I think it depends a great deal on the details. In general, I'd say (2) is not. If it is really supervision, as opposed to actually doing some of the writing etc. (1) is a different matter and will depend on a lot of further factors, including whether the idea is an original one or not.
    – cfr
    Commented Dec 19, 2016 at 11:44
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I find the whole idea as proposed in the first point quite underhanded. Just announce that you are looking for ideas on how to solve a specific problem and that you'd be happy to provide support for developing it to a thesis and/or publication to any students who got a promising idea. That way you create a win-win situation and avoid all potential ethical issues.

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    Underhanded and probably foolish. At least in my field, it seems exceedingly unlikely that a student under time pressure in an exam will arrive at a solution to a problem that a competent researcher has been stuck on for any significant amount of time.
    – xLeitix
    Commented Dec 16, 2016 at 8:58
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    @xLeitix I agree it is unlikely, but sometimes we underestimate the value of the different perspective.
    – BioGeo
    Commented Dec 16, 2016 at 10:13
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    @xLeitix Just one of those days : snopes.com/college/homework/unsolvable.asp
    – Amit Tomar
    Commented Dec 16, 2016 at 12:13
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    @AmitTomar Yeah, but there's a big difference between an actual exam and something that a student mistook for a homework.
    – David Richerby
    Commented Dec 16, 2016 at 19:51
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    @xLeitix, Foolish if you're depending on it. I knew an astrophysics professor who would give a final exam consisting of ten major unresolved problems (without telling the students this); he'd grade the exam on how the students approached the questions. Every few years, someone would come up with something promising enough to collaborate on a paper.
    – Mark
    Commented Dec 16, 2016 at 21:51
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Even ignoring the elephant in the room (that I am unsure why you expect your students to have a reasonable shot to very quickly solve an issue that has apparently been stumping you for some time), this sounds like a pretty bad idea:

  • It does not sound ethical. Fundamentally, in an exam, you are expected to know the answer to the questions you ask. How are you going to evaluate different proposals? Does a student who writes a simplistic answer that won't work get more points than a student who recognises how difficult the issue is and consequently is unable to come up with a comprehensive solution (and writes nothing at all)?
  • It probably won't work. An exam is not a brainstorming exercise. Your students are under time pressure, and they will assume that there is a reasonably simple solution to the problem. They are not gonna throw crazy ideas that might just work at you, but instead they are going to waste a lot of precious exam time trying to find the "obvious" solution that you yourself have not yet found. An exam is not the right frame for creative problem solving.
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    +1 for "An exam is not the right frame for creative problem solving." If you want your students to give it a go, you can always add it as a bonus question to a homework sheet and/or discuss it in class.
    – Sumyrda - remember Monica
    Commented Dec 16, 2016 at 10:41
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    All things aside, the second part of this answer is the most important part. Students will waste exam time on your problem, potentially resulting in a lower grade because they rush the other questions when time runs out.
    – user63119
    Commented Dec 16, 2016 at 13:38
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    As an added anecdote - I had an undergrad exam which I almost failed as I started getting denominators divisible by 13 and thus 'impossible' on exam without calculator. I redo the whole exercise. After the exam it turned out that it was intended result so I was just wasting my time.
    – Maja Piechotka
    Commented Dec 16, 2016 at 20:08
  • I disagree that an exam is the wrong time for creative problem solving. At least in math many people can produce original work (but not research-level) during exam conditions just fine. Also if you only grade regurgitation proofs ou will only encourage this.
    – Jacob Murray Wakem
    Commented Dec 16, 2016 at 22:44
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    @Insulin69: Maybe they can, but maybe their attempt at producing original work will also end up taking way too much time. They will then want to know which approach they should have chosen to solve the problem within the available time. "Uh, no idea, I had hoped you tell me." is not an acceptable response by the examiner in that situation.
    – O. R. Mapper
    Commented Dec 17, 2016 at 0:06
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You will trap students who cannot leave a question until it is solved. Since dropping difficult question during exam time is a skill by capable examinees, you are going to shoot down some students with weaker self-management skills who otherwise would have passed.

Very nasty.

If you would like to implement the stealth approach, you could place that as a bonus question in coursework, to be solved only after everything else has been solved.

However, it is a complete taboo to even consider an actually successful proof by a student, not to be fully cited/quoted. Maybe you do not even deserve co-authorship (depending on how well developed/written the paper is at its submission). If you subject them to such a challenge, you would be nonetheless expected to coach the student towards publication even if you do not become co-author and just get an acknowledgement. That would be my take on the ethics of the case.

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    Whether or not one would deserve co-authorship would depend on the culture in the subfield. A juvenile maths genius does not necessarily know how to communicate the result in a publishable form, and it would seem not necessarily unethical that supervising someone in how to write their first paper makes one a co-author.
    – gerrit
    Commented Dec 16, 2016 at 19:53
  • @gerrit Absolutely. That's why I mentioned the well developed paper; Ramanujan's mentor Hardy clearly did deserve the co-authorship.
    – Captain Emacs
    Commented Dec 16, 2016 at 20:26
  • I'm very sorry about the question. It was very misleading. I've reworded it and added more explanation.
    – Widi Widiyanto
    Commented Dec 17, 2016 at 0:23
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    @WidiWidiyanto Lots of people spent time to answer your original question; all these answers have now been rendered obsolete. Please revert this question to the old form, and ask a new one, now reformulated with what you actually wanted to know. This way, the work of the community will not be wasted and perhaps there is someone who is interested in the question as originally asked.
    – Captain Emacs
    Commented Dec 17, 2016 at 1:16
  • @CaptainEmacs Thank you, for the suggestion. I'm really inexperienced with SE.
    – Widi Widiyanto
    Commented Dec 17, 2016 at 1:28
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At some point in the 80's an unsolved problem was given as an exam question to about 200 pupils during the preparation for the international mathematical olympiad. It was judged as a problem where a good idea could give a rather simple solution. More than 20 years later the problem was solved, and the solution required heavy machinery. On a lower level the same was done using bonus questions on homework sheets. I remember that one exercise in logic asked for a statement equivalent to P=NP, and one sheet in number theory for the Birch Swynnertion-Dyer conjecture. Needless to say, none of these were successful.

So what you propose has been done before, and it didn't work.

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  • That does not seem to be OP's situation.
    – user111388
    Commented Mar 3, 2023 at 9:11
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I second the recommendation of using it as a homework question, time and pressure is less than in an exam.

However, if you were still considering posing it as an exam question, I would make it a bonus question, and make it clear that you are giving points not based on whether or not the question is solved 'correctly', since that is likely improbable on an exam, but the students' approach to the problem.

Weighing the value of the question even as a bonus is tricky. Too low of a value won't motivate students enough to solve the problem, and too high of a value will place unnecessary anxiety on students to attempt the problem.

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The answer remains the student's IP. The exam setter would be plagarising if they used it without having the student's permission (and probably co-authorship).

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  • Permission isn't enough. Permission does not make use non-plagiarism. If it is plagiarised without permission, it is plagiarised with it. Plagiarism has nothing to do with IP.
    – cfr
    Commented Dec 19, 2016 at 4:07

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