What are some interesting mathematical things you have learned while grading (or marking, if you prefer) student work? For example, clever proofs that students came up with; nice counterexamples or insights; interesting new questions inspired while grading; even just something you looked up to find out if a student's work was valid. Answers can be things that students wrote, or inspired by something a student wrote, or just something we learned during the grading process in some way.

It is final exams time here, so if anyone can help cast a more positive light on the grading experience, it would be most welcome.

Please refrain from snarky answers about things we learned about our students and their state of knowledge. Please stick to mathematical things. On the other hand, puns about graded rings, marked points, etc., are allowed.