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Question: 2n dots are placed around the outside of the circle. n of them are colored...

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2n dots are placed around the outside of the circle. n of them are colored red and the remaining n are colored blue. Going around the circle clockwise, you keep a count of how many red and blue dots you have passed. If at all times the number of red dots you have passed is at least the number of blue dots, you consider it a successful trip around the circle. Using some form of induction, prove that no matter how the dots are colored red and blue, it is possible to have a successful trip around the circle if you start at the correct point.

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