 We usually assume that two different things can’t be in the same place at the same time: how could there be room? But certain puzzle cases challenge this assumption. These puzzles are of interest in their own right, but they feature in this article because, as with the problem of change, perdurantists have argued that believing in temporal parts is the best way to solve the puzzles. And, as with the problem of change, endurantists may reply that temporal parts don’t help, or that there is a perfectly good endurantist alternative, or both.