max no of triangles, equilateral triangles inside equilateral
Source: Mathematics Regional Olympiad of Mexico Center Zone 2009 P3
November 10, 2021
combinatorial geometrycombinatorics
Problem Statement
An equilateral triangle has sides of length , a positive integer. Divide the triangle into equilateral triangles of length , drawing parallel lines (at distance ) to all sides of the triangle. A path is a continuous path, starting at the triangle with vertex and always crossing from one small triangle to another on the side that both triangles share, in such a way that it never passes through a small triangle twice. Find the maximum number of triangles that can be visited.