From one point of view, this may sound a little silly -- a proof is a proof, right? Once you've proved something, what else is there to say? But sometimes, rather than just saying "Okay, problem solved, so I just throw away my original intuition and never think of it again", we feel the need to "work on" that original intuition -- how do I come up with a new informal, imprecise, intuitive way of looking at things in order to try to convince my intuition that the correct answer is Q?

Here's an example that sort of qualifies for me.

**Spoiler:**

I wrestled with this for a little while and managed to change my intuition a bit. I can maybe post some remarks later about that, but I thought there was a chance that people here might want to wrestle with this one. And I hope you think the question in general is an interesting one -- what are some tricks for changing your intuition so it conforms with the facts? Can you think of other interesting examples from your own experience?