Counting Chips On a Circle

You are to place evenly 2n red and 2n green chips, for some integer n ≥ 1, on a circle. Prove that always there is a half circle with an equal amount of red and green chips.

(The applet below is to help you experiment with the problem. There are 4N small circles in a circular formation. Clicking on any of those changes its color from green to red and vice versa.)

Solution

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