An awful lot of mathematicians, myself included, have had the experience of working very hard to find a proof, going to sleep still feeling clueless about the what the right approach is, and waking up knowing the solution.
I don’t know if I buy it. I’ll have to sleep on it and see what I think tomorrow. Funny how scientist are able to confirm common sense.
However, I've also found that when I get totally stuck on a hard puzzle and just put the book down, turn off the light and go to sleep, that the next day if I pick up that same puzzle, I will suddenly just whip out all the answers. It's kind of weird - I always wonder, how could I not see that solution last night...