There are 100 red dots and 100 blue dots on the plane (a lot of planar riddles lately). The dots are arranged such that no three are on the same line.

A pairing of the red dots and the blue dots is a one-to-one function that assigns one blue dot to each red dot.

A valid pairing is a pairing such that when paired dots are connected with a straight line segment, no line intersections occur. This is depicted here:

Prove that there exists a valid pairing.

I do not really like the solution I found for this riddle. If you find an elegant one, please post it.

Thanks to Nadav Sherman for giving me this one.

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