I'm stuck on yet another mechanics question

Three perfectly elastic particles A, B and C with masses 3kg, 2kg and 1kg respectively lie at rest in a straight line on a smooth horizontal table with B between A and C. Particle A is projected directly towards B with speed 5m/s and after A has collided with B, B collides with C. Find the speed of each particle after the second impact.

I considered the coefficient of resitution between A and B, and between B and C, as well as conservation of momentum before and after the two impacts, and came up with 5 unknown and only 4 equations:

Let v be the speed of A after 1st impact, w be the speed of B after 1st imacpt, x be the speed of B after the 2nd impact and y be the speed of C after the 2nd impact:

15=3v+2w (1)

coefficient of restitution between A and B e=(w-v)/5 (2)

2w-2x+y (3)

coefficient of resitution between B and c e=(y-x)/w (4)

I need a bit more information to continue or have I missed something in the question? Any help would be greatly appreciated.