I've seen a couple posts on the message board, and had a few emails from people who were concerned that they couldn't do all the problems in the AoPS books. Some of them even went as far as to conclude that they were bad at math as a result.

The problem here is that most students have been trained to expect perfection because their school classes are too easy. So, when they hit the AoPS books and can 'only' do 50-75% of the challenge problems, it freaks them out. If their regular school texts have challenge problems at all, these students can always do 100% of them, because the challenge problems there are not, well, challenging. But in the AoPS books, there are very hard problems, because if you can do every problem you see, then you aren't being challenged enough.

This is one of the great benefits of math contests - they get these high-flying students used to the idea that there are problems out there that are very hard. And maybe, just maybe, problems that many top students can't do. When you get to college, almost all the tests are like this. In most top schools, 80% is a guaranteed A, and maybe even the highest score in the class. That's because these schools are designed to train top-notch students, while most high schools and middle schools are not.

So, if you're constantly just breezing through books without a challenge, you need to find harder books. And if you have a book in which you can only solve 50% of the hard problems, don't panic. Be happy about it - you've finally found a book that's worth your time.