In this discussion, participants analyze the collision of three spheres on a frictionless surface, focusing on the velocities after an elastic impact. They emphasize the need to conserve linear momentum and explore the implications of the inextensible cord connecting two spheres. The conversation highlights the complexity of setting up equations due to the multiple unknowns and the necessity of using both momentum and energy conservation principles. Participants also debate the correct treatment of the velocities along the string and the role of angular momentum in the analysis. Ultimately, they arrive at a solution for the velocities of the spheres post-collision, while considering the implications of different types of collisions.