If you can do very well in a math or physics contest (preferably a university level contest), say, scoring in the top 2%, then I would that you are bright enough to be able to earn a PhD. However, what if, say you are good enough to place in the top 25%, but not good enough to place in the top 2%? Do you still have a good chance of coming up with useful original research to earn a PhD some years down the road? I've been able to place in the top 2% (and top 10 in my city) in the high school math contests I wrote, though I never wrote the Putnam. But I had many high school friends who got A+'s in their high school math courses but could not get a passing mark on a regular high school math contest if their lives depended on it (they just could not use their knowledge in the clever way that the difficult contest problems required). I lost touch with them so I do not know if they ever were able to earn PhD's. But my guess is that they didn't (if they tried at all). If a university student wrote, say the Putnam math contest, and could not come in, say, the top 10% (and lack of knowledge cannot be blamed due to the nature of the contest), is he good enough at problem solving to be able to solve an open problem years later to earn a PhD? Or should he just forget the whole thing, admit that he is not super-smart, and just settle for a degree?