help with m2 collision

A uniform sphere A of mass m is moving with speed u on a smooth horizontal table when it collides directly with another uniform sphere B of mass 2m which is at rest on the table. The spheres are of equal radius and the coefficient of restitution between them is e. The direction of motion of A is unchanged by the collision.

(a) Find the speeds of A and B immediately after the collision.
(b) Find the range of possible values of e.

After being struck by A, the sphere B collides directly with another sphere C of mass 4m and of the same size as B. The sphere C is at rest on the table immediately before being struck by B. The coefficient of restitution between B and C is also e.

(c) Show that, after B has struck C, there will be a further collision between A and B.

i need help with part (c)

for part (a) i got
Va=u/3 (1-2e)
Vb=u/3(e+1)

for part (b) i got e < 0.5

What have you tried already for part c?

i worked out the velocity of b after the second collision. Vb2= u/3(e+1).1/3.(1-2e)

Basically you just need to show that either A and B are travelling towards each other, or that if they are travelling in the same direction that the one further back has a higher velocity so will eventually catch up