If new particles are discovered at the LHC, it will be important to determine their spins in as model-independent a way as possible. We consider the case, commonly encountered in models of physics beyond the Standard Model, of a new scalar or fermion D decaying sequentially into other new particles C,B,A via the decay chain D → Cq, C → Blnear, B → Alfar, lnear and lfar being opposite-sign same-flavour charged leptons and A being invisible. We compute the observable 2- and 3-particle invariant mass distributions for all possible spin assignments of the new particles, and discuss their distinguishability using a quantitative measure known as the Kullback-Leibler distance.