Sleep on it, but only if it is difficult: Effects of sleep on problem solving
springerlink.com
springerlink.com
It sounds like he was onto something with the waking mind being being prone to finding local maxima, but the background/sleeping mind being good for branching out and finding other solutions.
edit: Actually it looks like he cited scientific american talking about the sleeping brain finding relations between problems, I only remembered the bits about strengthening memory.
- some tasks require "lateral thinking". the example given is: what joins the words "lick", "sprinkle", "mine"? maybe lateral thinking is the wrong expression, but the idea is that the solution requires making connections from unrelated "semantic areas"
- people guess that the brain has a network-like approach where "activation" starts at nodes associated with the different concepts ("sprinkle", etc) and slowly spreads outwards, until, presumably, all three growing (glowing? ;o) areas meet at "salt".
- sleep helps for these tasks, but not for easier ones.