Combinatorics · Colouring argument · Parity classes · Pigeonhole · Kings on a chessboard · Independent sets · Counting contradiction
On \(41\) squares of a chessboard - the ordinary \(8 \times 8\) board - a king is placed, one king on each of those squares. Prove that among these kings one can find three pairwise disjoint sets, each containing at least \(5\) kings no two of which attack each other.
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Serbian National Competition (Drzavno takmicenje) 2013, high school grade I, category A, problem 4. Organized by the Mathematical Society of Serbia (DMS). Source