regular hexagon with its vertices on the circle is drawn on a circular billiard
Source: 41st Austrian Mathematical Olympiad National Competition (Final Round, part 2) 2nd June 2010 p3
September 5, 2019
hexagoncombinatoricstangentcombinatorial geometry
Problem Statement
On a circular billiard table a ball rebounds from the rails as if the rail was the tangent to the circle at the point of impact.
A regular hexagon with its vertices on the circle is drawn on a circular billiard table.
A (point-shaped) ball is placed somewhere on the circumference of the hexagon, but not on one of its edges.
Describe a periodical track of this ball with exactly four points at the rails.
With how many different directions of impact can the ball be brought onto such a track?