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The propagation of solitary waves in nonlinear diatomic lattices is a well explored and an interesting topic of research. Solitary waves are spatially localized disturbances that propagate unattenuated through the medium resulting in the medium reaching a stationary state in the trail of the propagating pulse. Recent studies have indicated that such waves are supported by essentially nonlinear granular lattice (ref. Fig. 1a) and Toda lattice. Interestingly, in these systems, the solitary waves are realized at a spectrum of the mass ratio (epsilon<=1, the only system parameter governing the system dynamics) corresponding to the considered interaction potential and the dynamics exhibit time scale separation. In contrast to the solitary waves, solitons are localized solutions that emerge intact upon collision with other solitons. The objective of this study is to explore soliton propagation in the dimer binary collision (BC) model (ref. Fig. 1b) in the limit of hard spheres. Interestingly, the considered dimer BC model supports soliton propagation at a discrete spectrum of mass ratios similar to those observed in granular and Toda dimers (Table 1). In fact, in Table 1, the index ‘i’ indicates the number of interactions a light bead has with its neighboring heavy beads and an increase in ‘i’ leads to a decrease in the value of ε which support soliton/solitary wave propagation. Furthermore, we report a qualitative and one-to-one correspondence (ref. Table 1 and Fig. 2) between the spectrum of mass ratio supporting solitary waves/solitons corresponding to the dimer BC model and those corresponding to the granular and Toda dimer chains.