A box divided into identical compartments \(\mathrm{A}\) and \(\mathrm{B}\) contains 25 distinguishable particles in \(\mathrm{A}\) and 20 distinguishable particles in B. There are nine energy units in the box, initially distributed only among the particles in B. The system is closed, but the energy units can move from one compartment to the other as the particles collide with the separating partition. If one energy unit is exchanged during each partition-particle collision, what is the smallest number of collisions between the particles in B and the partition that must occur before the system reaches equilibrium?