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?
This. It’s a case of poor assessment design on the part of @wuphysics87.
In creating assessment you need to know what you are asking them to do, how you want them to do it, what you are measuring and how. The format you choose needs to accurately reflect those things.