# 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?

I initially started to do the brute force calculation. From top-left to bottom-right step by step ( grid size * 2 ) but that is brutal on the PC even on step 20.

Then there is this solution starting from the back right-bottom to top-left each cell has two points to move backwards.

Solution: