set of 27 triangles can be divided into two parts of the same total area
Source: TOT 336 1992 Spring A S4 - Tournament of Towns
June 9, 2024
combinatoricsgeometrycombinatorial geometryareas
Problem Statement
Three triangles , , are given such that their centres of gravity (intersection points of their medians) lie on a straight line, but no three of the vertices of the triangles lie on a straight line. Consider the set of triangles (where , , take the values , , independently). Prove that this set of triangles can be divided into two parts of the same total area.(A. Andjans, Riga)