T is a given triangle with vertices P1,P2,P3. Consider an arbitrary subdivision of T into finitely many subtriangles such that no vertex of a subtriangle lies strictly between two vertices of another subtriangle. To each vertex V of the subtriangles there is assigned a number n(V) according to the following rules:
(i) If V = Pi, then n(V)=i.
(ii) If V lies on the side PiPj of T, then n(V)=i or j.
(iii) If V lies inside the triangle T, then n(V) is any of the numbers 1,2,3.
Prove that there exists at least one subtriangle whose vertices are numbered 1,2,3. combinatorics unsolvedcombinatorics