First of all, you can study for those (although virtually all of us hit a ceiling because those problems are very hard). I used to study for those tests (althou

First of all, you can study for those (although virtually all of us hit a ceiling because those problems are very hard). I used to study for those tests (although technically not IMO since I never qualified for it) and did reasonably well, although my IQ is "only" about 150. If these tests were perfect IQ tests, I shouldn't have even placed in the top thousand... since there are 400-4000 Americans smarter than me per year, plus the international students. (However, my "math IQ" if such a thing could be measured would probably be around 165-170, and "verbal IQ" around 135-140.) Also, there are a couple of famous mathematicians (names don't come to mind) who are notorious for sucking at proofs. Their conjectures were very good and almost always right, but they relied on future mathematicians to prove their work (details, details). They would likely zero the Putnam.