Imagine that we are in a dark room with flat walls covered with mirrors. The room has several turns and side passages.If I light a match somewhere in the room,would you be able to see it on matter where you stand in the room,and no matter what the room shape or in which side passage you stand?We can equivalently pose the question in terms of a billiard ball bouncing around a pool table. Must there be a pool shot between any two points on a polygonal pool table?