MathDB
ASU 413 All Soviet Union MO 1985 7 of 24 triangles in a hexagon

Source:

August 5, 2019
combinatoricscombinatorial geometryhexagon

Problem Statement

Given right hexagon. The lines parallel to all the sides are drawn from all the vertices and midpoints of the sides (consider only the interior, with respect to the hexagon, parts of those lines). Thus the hexagon is divided onto 2424 triangles, and the figure has 1919 nodes. 1919 different numbers are written in those nodes. Prove that at least 77 of 2424 triangles have the property: the numbers in its vertices increase (from the least to the greatest) counterclockwise.