tau-theta paradox (1950s):

While two distinct types of kaons, tau & theta (today tau is a completely different particle) decay, tau decays in three particles, whereas the theta decays into two. The tau & theta differ only in parity; and at the time, it was thought that parity was conserved strictly, and that particles differing in parity only must behave exactly the similar. As the two decay differently, a paradox ensued. The paradox was determined while experiments carried out according to F. Yang & T.D. Lee's theoretical calculations indeed mentioned that parity is not conserved within weak interactions.