posted for the image link

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Alternative statement: "Find the smallest possible value for a positive integer $k$ with the following property: You can remove $k$ cells from a $n\times n$ board such that from the remaining cells there are not 4 cells that can be filled with a |-- tile" ( like the tile from your statement) This alternative statement was gave at a junior TST in Romania in 2004 (If I remember correctly) P.S: It is pretty simple if you color the board like a chessboard.