[Eromaveabeara]

While the symmetry is satisfying, why does the initial ball (or balls) not bounce back instead of imparting nearly all the momentum and energy to the last ball (or balls)?

The simple equations used for the conservation of kinetic energy and conservation of momentum can show this is a possible solution, but they cannot be used to predict the final velocities when there are three or more balls in a cradle, because they provide only two equations to find the three or more unknowns (velocities of the balls). They give an infinite number of possible solutions if the system of balls is not examined in more detail.
http://en.wikipedia.org/wiki/Newton%27s_cradle Nice.... infinite complexity