{from, "Unsolved Math Problems" link, on the 'Web'}
Unsolved Problem 16:
Does every obtuse triangle admit a periodic orbit for the path of a billiard ball?
We assume that the billiard ball bounces off each side so that the angle of incidence equals the angle of reflection. If it hits a vertex, it rebounds along the reflection of its entry path in the angle bisector of the angle at that vertex. The orbit (or trajectory) is periodic, if after a finite number of reflections, it returns to its starting point.
Reference:
 
[Croft 1991]
Hallard T. Croft, Kenneth J. Falconer, and Richard K. Guy, Unsolved Problems in Geometry. Springer-Verlag. New York: 1991. Page 16.
 
{comment: Which goes to prove, that sometimes, being literate in
a given language does not necessarily lead to comprehension, Or
understanding!}