If you subscribe to the New York Times online, they had an interesting article yesterday about scientists who are trying to understand the "Aha!" moment of creativity. What the scientists have found is that humor helps put the brain in the right frame of mind to achieve insight in solving word problems (as opposed to the trial-and-error method). Apparently humor makes it easier for the brain to spot the less-obvious connections that may be necessary to solve a puzzle. Doing crossword or Sudoku puzzles also helps open up the brain. Subconscious clues may also help people solve problems. Although analysis and insight may both be required to solve a problem, they are different states of the brain. If we know how to switch ourselves from one state to another, we may become more creative and better problem-solvers.
I think we writers need to keep these points in mind not just for ourselves, but for our characters, since we often toss tough tasks their way and expect them to muddle through. Knowing how to achieve insight will help us resolve our tangled plot points, which are often problems our characters have to face too. Sometimes it's not enough for them to resolve the problem; we have to show how they figured it out and how creative they were. The more we know about creativity and problem-solving, the better we'll be at helping characters solve their problems and showing how they do so in a realistic way. Perhaps that wise-cracking sidekick is more helpful than he or she knows.
Finally, to help you with your creative thinking today, here's some Whose Line Is It Anyway? humor. I've posted it before, but it's been a while: