Hi everyone. I've a question that i wondered since the high school. Let's take two identical particles (same mass) that collide frontally. Assume it's an elastic collision. We have to conservate both the momentum and kinetic energy: v_1 + v_2 = v'_1 + v'_1 v^2_1 + v^2_2 = v'^2_1 + v'^2_1 (where primes denotes the velocities after the collision). Now I do know the solution: the velocities are swapped among the two particles and here comes my question: since the one I wrote is a symmetric system, why should I not accept the solution where the two velocity are not swapped?