SIMON-MARAIS 2017 B3
- Paper B
Each point in the plane with integer coordinates is coloured red or blue such that the following two properties hold.
- For any two red points, the line segment joining them does not contain any blue points.
- For any two blue points that are distance 2 apart, the midpoint of the line segment joining them is blue.
Prove that if three red points are the vertices of a triangle, then the interior of the triangle does not contain any blue points.
Official text Simon Marais Mathematics Competition 2017 official paper, page 2. Quoted with source.
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