Back in the day, I was a big fan of the X Files. Although I'm a very logical person, I admired Agent Maulder's problem solving technique. I couldn't quite put my finger on it, but somehow, starting with an outrageous working theory, adding new input and following where it leads seemed to me to be an efficient way to solve complex problems or mysteries.
I think I've worked out why. Most of the time, when faced with a problem or mystery we have a set of possible solutions or working theories in mind. If something doesn't fit in with it; a pattern, a clue, a statement; the brain has a tendency to ignore it because it is deemed insignificant. It doesn't fit in to any of the possible solutions, therefore it must simply be a random event or object. By keeping even the most outrageous possibilities open (aliens, monsters, mega-conspiracies), you are tricking your brain into allowing you to acknowledge and store data and patterns it otherwise would have disposed of. This can be crucial when a potential solution that you hadn't previously thought of comes to mind and suddenly, everything fits.