Classes like this were funny. I often found that people who just knew the answer immediately had a lot of difficulty doing proofs, and the people good at doing proofs usually didn't arrive at the solution very quickly or seem to have an intuitive understanding of the problem at first.
That’s interesting. In your context what is “knowing the answer”? To me it seems like they “knew” a given statement was true but they didn’t know how to prove it which makes me wonder how they knew.
The teacher may start off a class with a question like "what is the most efficient way to satisfy this problem given these constraints?" Some people would know the answer immediately but couldn't do a proof for it hardly at all. Others could find a proof in class almost every time, but necer really saw the answer to the problem until they'd sat on it for a while and chewed over it.
Can't really give an example question, it's been well over a decade (closer to two) since I took it.
Some people are just wired differently.