The Kac ring consists of N equidistant points in a circle. Some of these points are marked. The number of marked points is M, where 0 < 2 M < N . Each point represents a site occupied by a ball, which is black or white. After a unit of time, each ball moves to a neighboring point counterclockwise. Whenever a ball leaves a marked site, it switches color from black to white and vice versa. (If, however, the starting point is not marked, the ball completes its move without changing color.)