At my college there was a class where one of the teacher assistants got ahold of the answer key and handed it out to class mates. The memorized the key, not the answers, but the actual “A,B,A,C,C…” of the key. We told the professor, so he just rearranged the answers. So every student that cheated got a perfect 0. This had the effect of them failing the assignment on their own, and also telling you who the cheaters were.
Sanity checks like this can be defeated by having all of the options (ABCD...) be similar enough and plausible to anyone who didn't actually study the material.