Heavy hadrons interacting via pion exchange can form bound states (hadronic molecules), analogous to conventional nuclei. A large number of possible states is controlled by the same interaction potential, and although the binding energy in a given channel depends sensitively on the details of the potential, the overall pattern of binding does not. In particular, bound states arise only for a restricted set of spin and flavour quantum numbers, leading to sharp predictions for experiment. In comparison with other models for exotic states, which typically predict a proliferation of states with all possible quantum numbers, this renders the molecular hypothesis uniquely falsifiable. The implications for $P_c(4450)$ and other exotic states are discussed.