There are n≥3 particles on a circle situated at the vertices of a regular n-gon. All these particles move on the circle with the same constant speed. One of the particles moves in the clockwise direction while all others move in the anti-clockwise direction. When particles collide, that is, they are all at the same point, they all reverse the direction of their motion and continue with the same speed as before.Let s be the smallest number of collisions after which all particles return to their original positions. Find s.Proposed by N.V. Tejaswi combinatoricsphysicsindia