The most unexpected answer to a counting puzzle

Solution: Even prettier solution: Help fund future projects: An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: New to this channel? It's all about teaching math visually. Take a look and see if there's anything you'd like to learn. NY Times blog post about this problem: The original paper by Gregory Galperin: ~lebed/Galperin. Playing pool with Evidently, Numberphile also described this problem (I had not known): You'll notice that video has an added factor of 16 throughout, which is not here. That's because they're only counting the collisions between blocks (well, balls in their case), and they're only counting to the point where