It sounds like you just rested your brain. I have read about studies that show an increase in aleartness and abiltiy to solve problems quicker in people who have gotten a good nights sleep compared to those who were fatigued.

On the other hand I have read about a chemestry teacher who used to work out complex problems through lucid dreaming. She would become lucid, and write it down in her dream. If she began to lose lucidity she would spin, and then have to re-work the problem. You could probably try to do something like this, through lucidicy.

Good luck =)