In this article, Scott Smith presents an innocent problem (Problem 12 of the May 2001 Calendar from "Mathematics Teacher" ("MT" May 2001, vol. 94, no. 5, p. 384) that was transformed by several timely "what if?" questions into a rewarding investigation of some interesting mathematics. These investigations led to two conclusions: (1) Developing generalizations from patterns can be as rewarding to obtain as they are hard to discern; and (2) Sometimes the most productive question to pose is, "Can this result be generalized?". Although Smith did not prove the general case in his own investigation, he writes here that he thought it was still satisfying to uncover patterns and discover that these patterns were themselves considered by others in the mathematics community.