Given right hexagon. Each side is divided onto 1000 equal segments. All the points of division are connected with the segments, parallel to sides. Let us paint in turn the triples of unpainted nodes of obtained net, if they are vertices of the unilateral triangle, doesn't matter of what size an orientation. Suppose, we have managed to paint all the vertices except one. Prove that the unpainted node is not a hexagon vertex. Coloringhexagoncombinatorics