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.
Hold an in class quiz with essentially the same problem but with different values. The students that actually worked through the problem should be able to do it again with the changes. Those who didn't understand and just put down what their peers got will struggle with a quiz. Bonus points if you can restructure the problem in a way to elucidate which specific aspects you think the students were skipping over with help from their peers. Feel free to have specific requirements assigned point values in the problem statement.
Don't call them into your office and put them on the spot. That will make this adversarial. Your job is to teach them how to solve problems and communicate their methods in a clear fashion. You should reevaluate your problem writing and grading policies if just looking up answers can earn a passing grade. If you give a quiz, be up front with them that you have concerns about some students skipping the work and copying answers. Reiterate that the point of the exam was to make sure they can solve problems, the correct answer is merely a byproduct.
I will add speculation that there is a difference between what your students think you expect from an answer and what your expectations actually are. Mismatches in expectations are immensely frustrating for both parties. So don't leave your students guessing. Give them specific examples of work of different quality and what aspects earn full points and what things might lead to point deductions. Some of the best professors I had would publish all the prior year exams with their solutions. That gave everyone the opportunity to mimic the workflow and match the level of detail expected. That also elliminates the concern of students finding the answers online or from prior year students for exams as the teacher will have had to avoid reused questions entirely.