Start in the lower left corner of a 5x10 unit grid. You may only move to the right and upward along the edges to get to the top right corner. The area of a path between the corners is the amount of area beneath the line in square units. For example:
On a 5x10 grid, how many different paths from the lower left corner to the upper right corner have an area congruent to 1 mod 5?
Bonus: Choose any prime and positive integers , and and generalize this solution to the number of paths with an area congruent to mod on a by grid.