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.
What were the rules for the exam? Were you clear what resources were acceptable and which weren’t?
Especially for a take home exam, establish a rule where you give points for showing work as well as for correct answers. It’s almost impossible to enforce a perfect honor policy for a take home exam, so you should have structured your grading to account for that.