From Béla Bollobás: four types of problems to work on

[Qingmin Liu]

A “dream”: a big problem that you would love to
solve, but you cannot reasonably expect to solve.

Some very worthwhile problems that you feel
you should have a good chance of solving, given
enough time, effort, and luck.

From time to time, work on problems that should
be below your dignity and that you can be confident
of doing rather quickly, so that time spent
on them will not jeopardize your success with the
proper problems.

On an even lower level, it is always fun to do
problems that are not really research problems
(although they may have been some years ago) but
are beautiful enough to spend time on: doing them
will give you pleasure and will sharpen your ability
to be inventive.