Just thought this was pretty interesting - from Slashdot:

An anonymous reader writes "CBC news reports that the effectiveness of 'sleeping on it' when faced with a difficult task may have more than just anecdotal roots. 66 students were trained to perform a calculation on an eight digit number using two simple rules which would take seven steps to complete. A different method existed to perform the same calculation 'almost instantly', but was not shown to the students. After eight hours, where half the students were allowed to sleep and the other half remained awake, 60% of the rested and 22% of the wakeful students discovered the more efficient method."