What I tend to do, is sit back and listen to some jazz, and think about the problem from an "outside perspective", like "how would an advanced space alien view the problem" ? :-)

It usually comes down to building a "mental blackbox", which processes information. Then I define what information is available as input, and what is the desired output. At that point, the question is formulated.

Then it just becomes a question of the "mechanics of the internal blackbox functioning".

Then I start slapping together snippets, setting up feedback loops, and whatever is needed to process some typical sample input to give the desired output. Then I start testing for the "edge cases" of "possible, but not probable input"; and make code modifications to handle them.

When I'm done, I have a big heap of spaghetti code. :-) But I understand it :-)

Then I like to sit back for awhile and let the spaghetti cool. As it cools, I seem to get "serindipidous inputs" from "the world in general" as to ways of improving the blackbox functioning. This is a great source of mystery to me. Sometimes I'll be listening to the radio, and a "word" will just "pop out" at me, triggering a new insight into how to make a code improvement. Sometimes, it will be in the "Newest Nodes" right here, where someone will ask a question, which immediately translates in my mind into a code improvement.

It could just be my "sub-concious genius" trying to get a message thru to the "concious-dummy at the controls", but too often it is hard to believe it's coincidence, and I often "look over my shoulders for cameras".

Well thats my "zen-psychic" method of problem solving. I know that the modern school system discourages this way of thinking, but in some weird way, it makes the programming FUN.