Wow - a blast from the past. My personal belief is that having "an analytical approach to problem solving" is an inate ability. Just like some people have a natural ability for art, or music, or languages, so is the ability to logically approach problems. This can be improved by a good education in science and mathematics - not for the subject matter that is taught, but in the approach to problems. As well, look at some of the books on design theory - Knuth's books are a good (but very academic) start - and structured analysis.
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