Find the greatest possible integer n such that one can place n points in a plane with no three on a line, and color each of them either red, green, or yellow so that:
(i) inside each triangle with all vertices red there is a green point.
(ii) inside each triangle with all vertices green there is a yellow point.
(iii) inside each triangle with all vertices yellow there is a red point. combinatorial geometrycombinatorics unsolvedcombinatorics