The "Cadmium conundrum" has been a longstanding problem regarding the structure of low-lying states of Cadmium isotopes with A=110-116, where selected E2 transitions do not correspond to the known spherical paradigm as previously believed. In this lecture I will present the "Cadmium conundrum" and a suggested solution in the form of partial dynamical symmetry (PDS). The latter allows us to form a unique mixing between selected spherical states (phonons) instead of the more traditional approach of configuration mixing, which is insufficient in this case. An analysis within the framework of the interacting boson model with configuration mixing (IBM-CM) of energies and E2 transitions will be given for the Cadmium isotopes with A=110-116, demonstrating the relevance of PDS and the reproduction of the problematic E2 transitions, for the first time.