Gerry Myerson's integral and Joe Silverman's geometry problem fall into the category of problems that seem uninteresting at first because they can be answered by a straightforward calculation that is not expected to yield any insight after the answer is obtained.

Another potential category consists of problems that seem hopelessly difficult but that turn out to be tractable. As an example, I propose the question, "What are all the finite simple groups?" Superficially, this might seem (almost) as hopeless, and therefore as uninteresting, as the question, "What are all the finite groups?" Only when you know that there is a nice answer that can actually be proved does the question reveal itself to be extremely interesting.