Time to finish the month strong!
A robot is located at the upper-left corner of an m x n grid. The robot can only take one step at a time, moving either down or right. How many unique paths are there that take the robot to the bottom-right corner?
If you haven't seen it before, this is a pretty classic problem for learning Dynamic Programming. We can describe it as an elegant induction problem, and use that to write an elegant program.
Consider: for most grids, the robot has to move either right or down. If it moves right, it's now at the upper-left corner of an (m-1) x n grid. For moves downward, we reduce n by 1. Add those together, and you have a solution. For an easy base case, a 1 x 1 grid has 1 unique path.
If you code this naively, it might be too slow on its own. You can improve the base cases or exploit the symmetry, but I really like memoization: caching previously calculated results. You'll often be able to reuse solutions to subproblems, almost as if you're a hoity-toity functional programmer.