Question: Suppose that n red dots and n blue dots are drawn in the plane (for some integer n) with no 3 dots in a line.

Suppose that n red dots and n blue dots are drawn in the plane (for some integer n) with no 3 dots in a line. Prove that there *is* a way to connect each red dot to a different blue dot, which minimizes the total length of the line segments? Maybe this seems obvious, but let me remind you that not every set has a minimum element. If I said "okay, now let x be the smallest real number greater than 2", well, that x doesn't exist.

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