I have a programmer friend who is spectacular at this sort of approach. When he and I worked together, I often would talk to him about problems I was having trouble solving. It never failed that Rick would make suggestions that were in a direction that had never occurred to me.

In most cases, he would not suggest anything obvious like looking at the problem backwards or sideways. He would come at the problem from a direction I would never have considered. (I wish I could think of an example right now.<shrug/>)

As a general rule, these suggestions would not solve the problem, but they would invariably change the way I saw the problem. A solution inevitably followed.

When in doubt, redefine the problem.