I'm stuck on the following question:

Three small smooth identical spheres each of mass 1kg move on a straight line on a smooth horizontal floor. Initially B lies between A and C. Spheres A and B are projected directly towards each other with speeds 3m/s and 2m/s respectively and sphere C is projected directly away from sphere A with speed 2m/s. The coefficient of restitution between any two spheres is e. Show that B will only collide with C if e>3/5.

I've come up with 4 equations by considering the momentum and coefficient of resitution but I have five unknowns, the speed of A and B after 1s collision, speed of B and C after second collision and e. Have I missed something from the question? Help would be greatly appreciated.