Combinatorics · Colourings · Pigeonhole · Geometry in space · Ramsey type arguments · Triangle area
Every point of space is painted in one of three colours. Prove that one of the three colours can be chosen in such a way that for every positive real number \(r\) there exists a triangle of area \(r\) whose three vertices all carry the chosen colour.
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Serbian National Competition (Drzavno takmicenje) 2019, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source