"Sometimes, finding the problem is almost all of the work."
These are NP problems, where confirmation is easy but determination is hard.
The current work I'm doing is one of these. Once I'm able to prove my result, I can write a program that anyone can run and it will check it quickly. "So what's the fuss?", they will inevitably say. But it has so far taken me three weeks to prove this and I'm not finished yet.