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.
