When/how do we get answers to our creative problems? Seldom by trying to think our way through, a method that seems to get more circular and frustrating the longer we keep at it.
I knew an electrical engineer who had developed a strict problem-solving regimen. He laid out the problem before he went to bed, then thought no more about it. The next morning, while shaving, he opened his mind to any ideas that might float up, no matter how irrational or unrelated to the problem they appeared to be.
A writer friend finds answers when he goes for a walk with the intention of staying in the present and opening all his senses to whatever flows in. The scent of honeysuckle and new-mown grass on one such walk provided the solution to an unfinished story he'd put away months ago, a story unrelated to either honeysuckle or grass.
In her Writing and Wellness newsletter (http://www.writingandwellness.com/), Colleen M. Story writes that she keeps a notebook by her bed for the answers that come in that dreamy, not-quite-conscious period between sleep and waking each morning.
My ah-ha moments often come in the shower. When I lived in an old house without a shower, I relied on ideas coming at the intersection of Rtes. 27 and 518, where there was no stoplight and where I sat in my car for a long time with my conscious mind only partially engaged.
In each of these anecdotes - and I have many, many more - either the problem-solvers are open to sensory experiences or their minds are in a semi-conscious state. In all of these anecdotes they were ready to accept solutions that they would have discarded as illogical if they had been "thinking" about the problem.