The 15 puzzle is a game that tasks the player with sliding 15 numbered squares around a 4 by 4 rectangle to reach a target configuration. Because there is only one unoccupied square in the rectangle, this puzzle can be incredibly challenging if not impossible, though it becomes significantly easier if we make the rectangle a little bit bigger. One can interpret this fact as a homological stability result. In this talk, we generalize this idea by considering the ordered configuration space of n open unit squares in the w by h rectangle. We exhibit conditions on w, h, k, and n that ensure that the k-th homology of this space is isomorphic to the k-th homology of the ordered configuration of n points in the plane. This talk is based on joint work with Jesus Gonzalez and Matthew Kahle.