I need to calculate the resultant velocities of 3 circles/masses/particles if they was to collide at the **exact** same time. I understand that this is theoretically impossible (or incredibly unlikely) to happen, but that's beyond the point.

Here is an example of what I mean

![Circle collision](https://i.stack.imgur.com/06YKC.png)

The blue line represents the velocity of the blue ball, the blue ball's X coordinate is exactly between the other two balls. The collisions are elastic.

I have asked my mathematics teachers about this problem and all of them said that it was impossible, since when you use conservation of momentum formula's you have too many unknowns. That being said, is there something that would give an accurate approximation?

Preferably, the radius' and mass's and velocities are variable, but I would be happy if they was kept constant if it means there is a formula (With the exception of the blue circles velocity).

Thank you.