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Students A and B in my physics class turned in identical solutions to certain homework problems on two problem sets in a row. My policy is not to give credit in situations like this. The similarities are far too extensive and idiosyncratic to be explainable if the students had really done their work independently. Normally this kind of thing is not a big deal, because the assignments are only worth token amounts of credit. The students get the message and change their behavior.

But this particular case is becoming more of a big deal because A acts very upset and claims he did the work totally independently. I asked B what happened, and B said he found a solution online and copied it down. This seems plausible: A and B both copied the same online solution.

How could I determine/prove whether this is what happened? I have heard that there are web sites that students can use to access materials like these. Is there a small enough number of such sites that I could check each one to see if this work originated from materials provided there? To gain access to these sites, would I have to upload materials that they wanted, which could be onerous or unethical? If this was an English paper, I could google for the plagiarized text or use a service such as turnitin. There are also tools for use with computer code. But AFAIK there is no way to do this with mathematical material.

Please do not post comments or answers about whether it is a good idea to count homework in students' grades, or whether I can really tell that two students' work is too similar to be explainable if the work was independent. These could be worthwhile things to discuss, but they are not the subject of this question.

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    Have you tried to plug in your assignment questions, or the solutions themselves into search engines? You'd be surprised at what is available on the internet. – Srihari Yamanoor Sep 21 '16 at 5:34
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    @SrihariYamanoor: Good suggestion. Googling on the text of one of the questions doesn't turn up anything relevant. The solutions the students turned in are basically just equations with no surrounding explanatory text. – Ben Crowell Sep 21 '16 at 5:45
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    Did B refuse to disclose where they found the solution? – Massimo Ortolano Sep 21 '16 at 7:23
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    Have you asked student A to explain how it's possible that student B turned in an identical assignment, if student A really did all the work? Maybe student A did post his solution online for whatever reason and would be willing to tell you where (with a way to prove that they were the one to post it online, before the day they were supposed to turn in the assignment)... – user9646 Sep 21 '16 at 8:18
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    Most likely, you have enough leverage with B to just extort the source from him (the "academic honesty rules" are usually pretty strict and if you invoke them at full swing just literally following the procedures in the written university regulations, he may lose a lot more than a few points. On the other hand, he doesn't have much to lose by spilling out the source to you at this point). So, if you are really interested, just fry him and you'll get the answer. On the other hand, I would not pursue the issue beyond giving both A and B zero score and letting them have a headache over it. – fedja Sep 21 '16 at 12:32
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Disclaimer: The answer below is based on my experience, but I'm not in the US.

I'll try to address this question:

Is there a small enough number of such sites that I could check each one to see if this work originated from materials provided there?

Along the years, I have seen students searching for solutions online in at least three different places: newsgroups (Usenet is agonizing, but not definitely dead), forums, specific repositories and -- last but not the least -- Stack Exchange.

Exercises are usually reported in the form of plain text, text with LaTeX equations, an attached PDF file, or a picture taken with the smartphone (sometimes the picture is taken after having printed the PDF file. Gosh).

Moreover, exercises might not be reported in the original language: a student knowing a second language might ask for help on a foreigner forum, translating the exercise (I saw it happening).

From the above points, I think that the general answer to your quoted question is no, and trying to identify an online source might be a hopeless task. Of course, strokes of luck can happen and at a local level there might exist communities of users of a specific college or university.

Therefore, I strongly support alternative strategies, like that suggested by Patricia Shanahan in her answer.

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From a comment:

The solutions the students turned in are basically just equations with no surrounding explanatory text.

Ask student A to produce the explanatory text for the equations in the common answer. If A indeed worked out the answer independently, A should be able to explain the reasoning leading to each equation. If A just copied down a solution that only contained the equations, that is less likely.

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Disclaimer: I don't know how to do this within the framework of usual university rules.

Assuming you are not strictly bound by these rules:

If the students provided their solutions electronically (PDF/PS) or printed, ask them for the source code (TeX / Word / ...) for that solutions. Feed the search engines with that code.

If the students provided only handwritten material, you can still test them by asking them orally to reproduce the solution in your presence. Then you would know who copied and who genuinely solved it himself/herself.

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