Cantor's pairing function is a well-known bijection used in his proof that rational numbers are denumerable. We will have a brief survey on Cantor's pairing function and discuss open problems on this topic (just not to look too simple). During the talk, we will have some fun with a math puzzle regarding paring functions and, more importantly, a cat. We will also explore what happens if we generalize the puzzle: Cantor's cat will dance on a donut, a ball, and a Möbius strip.