A pawn is put on each of $2n$ arbitrary selected cells of an $n\times n$ board ($n>1$). Prove that there are four cells that are marked with pawns and whose centers form a parallelogram.
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Tags: combinatorics
A pawn is put on each of $2n$ arbitrary selected cells of an $n\times n$ board ($n>1$). Prove that there are four cells that are marked with pawns and whose centers form a parallelogram.