I'm often asked how I think about a new problem, like what come to mind. A couple of thoughts come to mind when I first get a problem to solve. A. Comparison. Is this problem similar to problems I know how to solve? If yes, work to convert or transform the problem to one familiar. B. Simplify. If I simplify the problem some way, can I then solve it? If yes, then solve the simpler problem and try to work up to the actual problem. C. Eliminate. Learn how to eliminate solving ideas that will fail. Otherwise, you can get bogged down on a false trail. (Geniuses excel at this.) D. Read. If nothing rings a bell, I look at references about or related the problem and work from there. Hope for A or B. Yet, at any time reading up on materials can stimulate thinking. All in all, lots of problem solving experience is most important.
Random thoughts and used ideas