Stories about creative insight often involve some kind of "productive pause," or what psychologists call an incubation period.
Your memory is competitive. When you start thinking about a problem, certain ideas jump to the forefront. They leap to mind both because they are related to the description of the problem, and because they successfully tamp down competing memories. Once memory has been inhibited, it has a hard time reaching your awareness, even if the information from that memory might be crucial for solving a problem.
Sometimes, despite your best efforts, you can't come up with a good way to think about the problem. You are just stuck. In those times, the productive pause brings you into contact with lots of things in the world. And one of those chance encounters can lead to insight.
So, the next time you are stuck on a problem, take a break. Taking a productive pause!