That runs into the scalability problem that I mentioned--someone (say, a Mechanical Turk user) can solve that problem once, and put it in a database. To avoid this, there needs to be a way to generate them cheaply, so you pretty much need a computer that can solve the problem in the first place.

Basically, my point is that there's no such thing as "uniquely human intelligence". There's lots of problems that fall into that category now, but with the continuing rise of computational power, it's getting harder and harder to find new problems of this sort without excluding a lot of real people.