IMO 2006 Shortlist C6
A holey triangle is an upward equilateral triangle of side length n with n upward unit triangular holes cut out. A diamo...
Category: Combinatorics
Problem
A holey triangle is an upward equilateral triangle of side length n with n upward unit triangular holes cut out. A diamond is a 60◦ −120◦ unit rhombus. Prove that a holey triangle T can be tiled with diamonds if and only if the following condition holds: Every upward equilateral triangle of side length k in T contains at most k holes, for 1 ≤ k ≤ n. (Colombia)