Combinatorics · Colourings · Monochromatic configurations · Isosceles right triangles · Case analysis
The points of a plane \(\alpha\) are split between two nonempty sets \(A\) and \(B\): no point belongs to both, and every point belongs to one of them. Prove that some isosceles right triangle has all three of its vertices in one and the same set.
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Serbian Republic Competition (Republicko takmicenje) 2006, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source