IMC 2006, problem 1, day 2
Source: Easy
July 25, 2006
inductionIMCcollege contests
Problem Statement
Let be a convex polygon.
(a) Show that if has vertices, then can be triangulated such that each vertex is in an odd number of triangles.
(b) Show that if the number of vertices is not divisible with 3, then can be triangulated such that exactly 2 vertices have an even number of triangles.