Lattice paths
Starting in the top left corner of a 2×2 grid, and only being able to move to the right and down, there are exactly 6 routes to the bottom right corner.
How many such routes are there through a 20×20 grid?
This program takes like 20 minutes to complete. There has to be some other mathematics I am not aware of that will work better for this. I'll have to invesitgate.