best aid to problem solving

All the important things in life have to be sidled up to sideways on, crab fashion...head on very rarely works.

If a problem seems insoluble don't try and solve it.

Instead of trying to solve the problem refuse to. Instead work on defining it. The clearer the idea you have of the problem the more its solution will be blindingly obvious. The many 'problems' of the world that seem insoluble are probably in need of greater definition without any attempt at solution.