100 triangles by lines // sides of equilateral triangle
Source: TOT 556 1997 Autumn J A6 - Tournament of Towns
September 11, 2024
geometrycombinatoricscombinatorial geometryEquilateral
Problem Statement
Lines parallel to the sides of an equilateral triangle are drawn so that they cut each of the sides into equal segments and the triangle into congruent triangles. Each of these triangles is called a “cell”. Also lines parallel to each of the sides of the original triangle are drawn through each of the vertices of the original triangle. The cells between any two adjacent parallel lines form a “stripe”. What is the maximum number of cells that can be chosen so that no two chosen cells belong to one stripe?(R Zhenodarov)