n cars around a circular race course
Source: Switzerland - Swiss TST 2000 p10
February 19, 2020
combinatorics
Problem Statement
At distinct points of a circular race course there are 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.