Question 172
Given a set $S$ of 200 points in the plane: 100 points are the vertices of a convex polygon $A$, and the 100 other points are in the interior of the polygon. Moreover, no 3 of the points are collinear. A triangulation is a way to partition the polygon $A$ into triangles by drawing edges between some pairs of points of $S$ such that no two edges intersect in their interiors, and each point of $S$ is a vertex of at least one triangle.
1. Prove that the number of edges does not depend on the triangulation.
2. Show that for any triangulation, one can colour each triangle with 1 of 3 given colours such that any 2 adjacent triangles have different colours.
1. Prove that the number of edges does not depend on the triangulation.
2. Show that for any triangulation, one can colour each triangle with 1 of 3 given colours such that any 2 adjacent triangles have different colours.