I think this is an example of a general pattern of problem solving that also explains why you can sometimes magically solve problems the moment you try explaining the problem to somebody else: **You’re benefiting from having to start over again.**
In the time you distanced yourself from the problem, you “lost your place”, and basically end up having to re-trace your trail of though to where you got before. Usually, if we’re stuck on a problem and can’t find the mistake in our thinking, it’s when the mistake happened so far back that we already forgot about it. Forcing you to re-trace your steps makes you notice the mistake.
I find a good way to do this deliberately is by trying to formalize my chain of reasoning to see if I can “prove” why my problem is impossible to solve. (Of course, such a proof usually fails – but the point is that in trying to make the proof rigorous, I can figure out what the error was.)
It also works great for puzzle games!
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