1. The problem statement, all variables and given/known data there are N points on a paper. any three of points are not colinear. you draw lines from each point to all other points.lines can be drawn with three colors; red,yellow or blue. there will be obtained some triangles having colored edges. purpose is not to get a triangle, edges of which are drawn with the same color. what can be the value N at maximum? 2. Relevant equations the number of triagles from N given points : N*(N-1)/2 3. The attempt at a solution I can not get any mathematical expression for solution. I did try with considering all combinations for two color condition and I got N=5 maximum. for three color my trial was getting complicatd and I could not go on any more. But for N=10 I am sure it is possible to get all triangles satisfying the condition.