Many questions have been asked on this site regarding preparation for olympiads like the Putnam. I've read those questions and accordingly decided to start with Engel's "Problem Solving" but I have a few queries regarding how to practice the problems.
- Is Engel's book right for me? I think I have the knowledge of the material and that I just need lots of problems with clever solutions.
- How much time should I spend per problem? I am very bad at Putnam problems – I almost never get the solution – so is it better to: (1) spend just a little time on the problem, trying a basic approaches, and then looking at the solution, so that I can maximize my exposure to problem solving techniques in minimum time, or (2) spend a lot of time per problem and try as many possible approaches?
I feel that (2) is very discouraging beccause even after spending time I usually don't get the answer, and that I end up spending lots of time on just 1 problem.
So far, studying has been a frustrating experience for me. I lose energy and feel discouraged when I start solving a problem because I almost always fail to do so. I lose my concentration and give up eventually. After looking at the solution, however, it seems so obvious. Is this just a phase that I'll get past, or am I studying wrong?
Best Answer
Here are some things to keep in mind:
From your rough description, it sounds like you are just feeling the initial discouragement that lots of people feel when first starting against a challenge. My advice would be to pick a fixed duration to struggle with a problem. Feel free to break the rules and extend it if you're having a good time. If I were you, I might spend an hour or two or more on a problem before looking for a hint. It depends on the problem. I would definitely avoid looking for a full solution for as long as possible. When practicing for qualification exams, I definitely spent an hour on many problems. One qual itself took $8$ hours to finish, and we were only submitting $8$ solutions. We all took the full time :)
Actually, think about moving on to other problems before looking up the solution to the last one. Sometimes you will find yourself solving the problem later, maybe the next day. There is no rule that you have to solve and understand them sequentially. I know for sure that in every math test I took, I jumped around doing different problems, and often felt like I was finishing the test more efficiently that way. Problems that were initially puzzling usually resolved themselves by the time I got around to them.