Combinatorics · Lattice points · No three in line · Extremal combinatorics · Explicit constructions
Sixteen points of the integer lattice are marked, as in the picture: all points \((x,y)\) with \(x\) and \(y\) taken from \(\{1,2,3,4\}\). At most how many of these points can be coloured red so that no three red points lie on one and the same line?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2018, 1. letnik, category A, problem B3. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source