Programmers often discover solutions while explaining a problem to someone else, even to people with no programming knowledge. Describing the code, and comparing to what it actually does, exposes inconsistencies. Explaining a subject also forces the programmer to look at it from new perspectives and can provide a deeper understanding.
Also going for a walk, driving, or the other morning I woke up spontaneously about 2 hours early and come up with a solution.
Prolonged and energetic walks jolt my brain so well that I have a standing task of maybe finding a way of recording audio clips right from the lock screen of my phone. Unfortunately, I know for certain that this will result in a pile of said clips collecting on the phone, as sorting them into notes isn’t a priority once I’m back home.