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Is it possible to color each point on a circle either red, yellow, or blue in such a way that no three points of the same color or totally different colors from the vertices of an isosceles triangle?

I think we must be able to find at least one of such an isosceles triangle. My guess is to use pigeonhole principle. What should I do?

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Hint: Consider any regular pentagon on the circle. Then any triple of vertices forms an isosceles triangle.

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