I still remember a number theory exam I had in college. There were three possible answers, and the question was to find which one met the criteria for the question. I naturally assumed the teacher wanted us to do the math for all three, so started with the final one. Which was, in fact, correct. So I didn't bother to prove the other two were incorrect. She marked me down for not proving the other two weren't correct, by saying, "I might have lied. There might have been more than one right answer." So I started questioning EVERYTHING about math problems. :-)