IL-GILLIS 2016 Problem 4
In the beginning, there is a circle with three points on it. The points are colored (clockwise): Green, blue, red. Jonathan may perform the following actions, as many times as he wants, in any order:
- Choose two adjacent points with different colors, and add a point between them with one of the two colors only.
- Choose two adjacent points with the same color, and add a point between them with any of the three colors.
- Choose three adjacent points, at least two of them having the same color, and delete the middle point.
Can Jonathan reach a state where only three points remain on the circle, colored (clockwise): Blue, green, red?
Dataset text AI-MO AoPS. Quoted with source.
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