Ring of beads

Here’s a great puzzle I heard at a conference in Leicester the other week.

On a circle of wire are a number of (point) beads moving at the same constant speed; for simplicity’s sake let’s suppose that they would complete one complete circuit in a second. Since they are not all necessarily moving in the same direction, they may collide – we assume that any such collision is completely elastic, that is, they are still moving at the same speed after the collision, just in opposite directions. Suppose all the beads are different colours.

Given any starting position for the beads, will they return to precisely this position in some finite time?

Answer to follow soon.

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