An aticle on Ars Technca talks about how Gamers (Computer in this case) were used to solve amino acid problems using human recognition of 3D patterns.

Although this is a computer gaming related article, it brings up an interesting parallel to board gamers also.  Many board games often use spatial awareness, spatial relationships, numerical computations or combinations of all of these (and many more) complex visualization problems to make games.

Some boardgames are implementations of problems, that through visualization and planning can be "solved" by players; usually by a reward of victory points.   Games that I think of like this are Power Grid, Factory Manager, Puerto Rico (with experienced players, Caylus, etc.  Optimization of the problem is the goal of the game.

Can you think of other games that fall into this category?  Food for thought!