Researchers at the University of California Santa Barbara have conducted a study which suggests that undemanding mind wandering enhances the ability to be creative in solving previously encountered problems. Per the article:

The researchers presented 145 undergraduate students with two 'unusual uses' tasks that gave them two minutes to list as many uses as possible for everyday objects such as toothpicks, clothes hangers and bricks. After the two minutes were over, participants were given a 12-minute break, during which they rested, undertook a demanding memory activity that required their full attention or engaged in an undemanding reaction-time activity known to elicit mind-wandering. A fourth group of students had no break. All participants were then given four unusual-uses tasks, including the two that they had completed earlier. Those students who had done the undemanding activity performed an average of 41% better at the repeated tasks the second time they tried them. By contrast, students in the other three groups showed no improvement. The work will be published shortly in Psychological Science¹.

http://www.nature.com/news/why-great-ideas-come-when-you-aren-t-try...