If you had started off with all the balls separated by a bit, you could analyse each collision in turn. When identical (ideal) balls strike each other, they 'exchange velocities' (mv=mv and using a coefficient of restitution of 1 implies their relative speed of parting is the same as the relative speed of approach) so, if balls 1 and 2 are moving, the first collision would be between balls 2 and 3. 3 would go off at the original speed of 2, leaving 2 stationary. Then 1 would strike 2 and 3 would strike 4, leaving 1 and 3 stationary with 2 and 4 moving. This would carry on to the end until, first ball n would leave, then ball n-1 - no ball ever goes faster than the original velocity.

The same thing will happen if the balls are touching, to start with.