Hi: I am taking a problem solving class in which we are presented competition math, this class is designed for people writing in the putnam I believe but I am not writing, I just think is pretty fun to solve problems. Anyway, I'm usually only able to solve maybe half of them, then 3/4 takes me all day to think about, and the rest is just impossible to me. I have notice that while these problems require very elegant proof or tactic, sometimes require ideas that I have never thought of( not really new ideas that I haven't learned as in the textbook, but very simple things i never thought of using, but as soon as I was presented to the solution I can agree with it/understand it). that being said, how in the world do people know how to solve these problems so quickly? sometimes to me the solution to these problems are so inconceivable that you have to literally have tried everything possible to find the solution, even for the ones I solved. my strategy is usually just try random things that are at least a bit relevant to the problem , then proceed to assume it will work and prove it does, if i fail, I will move on, and sometimes come back. For those of you good problem solver out there(problems, not exercise), how do you do it? there must be a logical tactic/strategy, or a way of thinking that people use in order to solve these problems. I really don't believe in "you just can't do it"