I have taken notice of the value of quiet time to ponder and do nothing. It took years to notice this something that I was doing all the time, but now I take advantage of it to solve complex problems. While working on large data structures, or complex digital/analog circuits, if I come across a tough obstacle, I set it aside for later. ... Then I go for a walk, or just sit and find a book to read, or tinker with something else. In a few hours the solutions to the tough complex problem come pouring in. I usually write them down on paper as quickly as possible so as not to forget.
Thus, I have learned how to find solutions to some tough engineering problems with zero effort, I just let the subconscious do all the work. I apply this every now and then.
this approach has largely worked for me when faced with something im stuck on. the harder i think about it the less gets solved. however if i time out and think on nothing - ie look out the window and watch the leaves or birds or landscape - when all that deliberate thought "noise" in my head is removed by putting my brain in neutral.. usually *pop* a solution or at least a better approach pops in my head.
it like a signal to noise ratio. i have to remove the noise (my spinning thoughts about the problem) and suddenly the signal (a solution) is clear.
hard to explain, easy to do once you know. but to anyone watching you stare out the window you look like youre goofing off or something.