<p>How do you guys prep for the AMC and similar math competitions? I have the AoPS books (Vol 1-2) and read the sections/do practice problems, but my main issue is every time I do the problems, I end up looking to the answer key on how to solve a majority of them. I know this can't be exactly beneficial, but I'm not sure how to improve this. Should I read and absorb the concepts in each section on a deeper level, or what? I feel like I am unable to apply the concepts I learn for different varieties of problems. </p>
<p>Ex. I learn Euclid's Algorithm, and it seems simple enough. But I get a problem that asks you to prove the fraction (12n+1)/(30n+2) is irreducible for all positive integers n, and I have no idea how to approach it until I see the entire solution for the problem.</p>
<p>How do I progress to the point where I can perceive the solution to a problem on my own?</p>