Research shows you're twice as likely to solve a difficult problem by sleeping on it. And it's not necessarily because you are rested.
It's because you solve problems differently while sleeping, engaging other parts of the brain. After sleep, you're twice as likely to arrive at a "non-linear", creative answer. These findings are consistent with other research I discuss in my post: the muse comes quietly.
When I'm struggling with a really tough problem, I deliberately utilize my overnight problem solving machine (also known as sleep). It works. And I feel more rested, because I can remove the difficult problem from my to do list.
Often the good ideas like to be invited, not chased.