A variant of rubber-duck debugging: Ask the question and hit Send. Invariably, no matter how long I've thought about it, the obvious answer will occur to me minutes (or seconds) after I've embarrassed myself my asking. (is there a term for this?)
Similar to remembering you forgot your keys the moment you step outside and shut the door. My theory is that stop deliberately struggling to think and your brain is suddenly free to start processing things subconsciously, which can generate solutions to complex problems.