Math Puzzle


It is time for a real challenge now. Can you solve the following mathematical brain teaser?

You have 100 blue and 100 red points in the plane. Prove that you can connect all points in pairs of different colors, so that no two segments intersect.

Connect the points in pairs of different colors so that the total length of all segments is minimal. Now, if any two segments intersect, you can swap the two pairs among these four points and get smaller total length.