math questions can be *subtle*!
It's not obvious from a question:
* whether it has a nice answer or not
* whether it is easy to solve or not
...and slightly different problems can have widely different solutions
Fermat and 3k+1 are notorious.
EG, plane/sphere embeddability of a graph
Kuratowski's theorem says that $\set{K_5, K_{3,3}}$ is an obstruction set,
but for instance no finite obstruction set for torus-embeddability is known!
I think that it's easy to show that a planar graph is 5-colorable,
but 4-colorable is *hard*
(iirc).