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I am an student at an elite math/sci college, and am planning on majoring in math and theoretical physics.

However, my high school preparation is a bit different than most. I went to a pretty mediocre highschool, and coasted through the super-easy math classes there. I fell in love with real math later on (I spend about 4 hours a day reading random math books), but I have never really been exposed to good problem-solving. However, I have read both volumes of Apostol, and Axler's Linear Algebra. So I feel pretty confident in my abilities to learn higher-level math.

However, whenever I try to do AMC-level problems, I get a few algebra ones, but can never figure out the trickier geometry ones! I feel that everyone else (that is good at math at my school) got a superb education in geometry and elementary math. Also, most successful mathematicians (and physicists) seem to have done fairly well on math competitions.

For those too lazy to read: I want to study higher math but never got good at elementary math problem solving (esp geometry). Are such skills necessary for success in math? Am I too far behind to do well in the Putnam? Is there something that I can do to remedy my lack of skills in this area?

Thanks in advance!

Broccoli