We study a system of three identical bodies that can move freely on a horizontal track. Initially
one body moves and two are at rest. The moving body impacts with one of the resting bodies which
then impacts with the third and so on. The impacts are assumed to be characterised by a coefficient
of restitution. We investigate the total number of impacts, the final velocities of the bodies, and
the final energy of the system in terms of the initial velocity and the coefficient of restitution.
The problem, which originates from mechanics textbooks, can be analysed as a discrete dynamical
system with three degrees of freedom. The full solution is more subtle that one might expect.