I had a similar problem when I was 19 and working on a statistics problem. It was finals week and was very tired. Frustrated, I decided to take a nap, except my mind was "awake" during the nap if that makes any sense. Solved the problem in this state quite readily.

Unfortunately, I was unable to replicate that "mind awake, body asleep" effect since then. I suspect it is because I was never as tired as I was back then.