Given an m*n grid,
How many ways are there to go from upper left corner to the lower right one?
You can only move right and down, not up or left
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I think your answers in the test suite are for an (m+1)x(n+1) grid, as there are only two ways to reach the bottom right for a 2x2 grid. Check out http://www.mathworks.com/matlabcentral/cody/problems/1483-number-of-paths-on-a-grid for more details.
There are 6 ways of reaching the bottom right corner of a 2*2 grid. Are you considering m*n lines or m*n boxes?
I was considering m*n vertices, not boxes. If you have a 2x2 grid of boxes (3x3 vertices), then you're correct; there are six ways to reach the bottom. Just some miscommunication there.