# That Creepy Extra Area Under the Stairs

**Discrete Mathematics**Level 3

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 \(p\) and positive integers \(i<p\), \(j\) and \(k\) and generalize this solution to the number of paths with an area congruent to \(i\) mod \(p\) on a \(jp\) by \(kp\) grid.