# Introductory Combinatorics problem

I am stuck on problem 39 in brualdi 's book Ch-1 4edition. It's: Take any set 2n of points in the plane with no three collinear and then arbitrarily color each point red or blue. Prove that it's always possible to pair up the red points with the blue points by drawing line segments connecting them so that no two of the line segments intersect. I do not want the solution . I just want to understand the problem.

• which part of the problem do you don't get it? – Siong Thye Goh Nov 4 '17 at 4:49
• Actually, I think you just give me the solution – user497826 Nov 4 '17 at 4:50
• Are you supposed to color $n$ points red and $n$ points blue? Otherwise how do you pair them up if all the points are colored red? The idea is you draw line segments from each red point to a different blue point. There are lots of ways to choose which red and blue points are connected. The idea is to show that at least one of them has no line segments that cross. For example, you might have four points in a square with two on one side red. If you draw the two diagonals they cross, but if you draw the two red-blue sides they do not. – Ross Millikan Nov 4 '17 at 5:12
• Yeah that's what I got as well. That's why I think maybe I am interpreting it incorrectly. I think I am going to give up on this problem – user497826 Nov 4 '17 at 5:18
• I think one has to assume half are red and half are blue. I believe I see a solution and can give you a hint if you like. – fredgoodman Nov 4 '17 at 5:45