KURSCHAK 2004 Problem 3
We have placed some red and blue points along a circle. The following operations are permitted:
(a) we may add a red point somewhere and switch the color of its neighbors,
(b) we may take off a red point from somewhere and switch the color of its neighbors (if there are at least points on the circle and there is a red one too).
Initially, there are two blue points on the circle. Using a number of these operations, can we reach a state with exactly two red point?
Dataset text AI-MO AoPS. Quoted with source.
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