A sophisticated solution to a complex problem is fun to find. Its even fun when someone else finds the solution and thoroughly writes it down.
Despite the thrill of recognition for tackling a big complex problem, I find it's more practical to seek the simple problem lurking in and around the big problem. Not all tricky problems are complex. Some are presented in a complex way, some are complex because of restrictions that are easily worked around, and some are complex because of an adjoining social problem. Find the simple problem, or the social problem, and solve that instead. It often works for me.
My favorite kind of solution is one where the solver has taken a problem with a big surface area, found the core of the problem that is 80% of what people care about having solved, and then solved that tiny subproblem. If you want to see masters of this approach, check out the works of Blake Mizerany and Ryan Smith.
