I gave my students a take home exam over spring break. (This is normal where I teach) One of the questions was particulary difficult. It came down to a factor of three in the solution. That factor inexplicably appeared with no justification on many of their exams. I intend to have the students I suspect of cheating come to my office to solve the problem on the board. What would you do?
Edit: I gave them the Tuesday before spring break until the Thursday after. I didn’t want it to be right before or right after.
When I say normal I mean giving take home exams.
First of all, school or uni?
As many others have said, don’t give a take home exam during a break, however ‘normal’ it is considered in your community.
Second, have clear guidelines on what is allowed and what is cheating. We never had take-home exams in school, and in uni every take-home exam was open book, open internet and open discussion. In the absence of any statement to the contrary, your students would also be justified in assuming so.
Asking someone to repeat the answer is fine, but it doesn’t really prove anything - they might have simply forgotten all the formulae over their break.
The best option at this point would be to cancel that question and conduct future tests during class hours, under your supervision.