2000 IMO 第 4 题

C4 (CZE) Let $n$ and $k$ be positive integers such that $n / 2<k \leq 2 n / 3$. 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.

C4 (CZE) 令$n$ 和$k$ 为正整数，使得$n / 2<k \leq 2 n / 3$。找到可以在 $n \times n$ 棋盘的 $m$ 个方格上放置 $m$ 个棋子的最少数量 $m$，这样任何列或行都不会包含 $k$ 个相邻的未占用方格。