MathDB

There are

n\ge 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

Problem Statement