> he had spent the entire weekend trying and failing to prove it. I, on the other hand, had put all my energy into finding a counterexample and had one within an hour.

For a more extreme (although somewhat inverted) version of this, see Zeeman. He spent years trying to find a knotted sphere in a 5D space. Then realised this was impossible and got a proof for it in a few hours. [1]

[1] https://ima.org.uk/28009/sir-erik-christopher-zeeman-the-mat...

Trying and failing to prove something tells you quite a lot about what a counterexample would look like.