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IMO 2000 - Shortlisted Problems Question 4

IMO Shortlist · IMO 2000 - Shortlisted Problems

Question 4

C4 (CZE). Let $n$ and $k$ be positive integers such that $n/2\lt k\le2n/3$. Find the least number $m$ for which it is possible to place $m$ pawns on $m$ squares of an $n\times n$ chessboard so that no column or row contains a block of $k$ adjacent unoccupied squares.