Question 12
(HUN 3) At $n$ distinct points of a circular race course there are $n$ cars ready to start. Each car moves at a constant speed and covers the circle in an hour. On hearing the initial signal, each of them selects a direction and starts moving immediately. If two cars meet, both of them change directions and go on without loss of speed.
Show that at a certain moment each car will be at its starting point.
Show that at a certain moment each car will be at its starting point.