Question 96
A convex 2009-gon is partitioned into triangles by non-intersecting diagonals. One of these diagonals is colored green. The following operation is allowed: for two triangles $ABC$ and $BCD$ of the partition with a common side $BC$ we may replace the diagonal $BC$ by the diagonal $AD$, where, if the replaced diagonal was green, it loses its color and the diagonal that replaces it becomes green. Prove that any previously chosen diagonal of the 2009-gon can be colored green by applying the allowed operation a finite number of times.