Daily Math Puzzle 2026/10/20

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English

Let \(n\) be an integer with \(n\geq 2\). Some cells of a \(2n\times 2n\) grid are to be colored black. Every row and every column must contain at least one black cell, and every \(2\times 2\) square of adjacent cells must contain either one or three black cells. What is the minimum possible number of black cells?

日本語

\(n\) を \(2\) 以上の整数とする． \(2n\times 2n\) の方眼のいくつかのマスを黒く塗る． どの行にもどの列にも黒いマスが少なくとも \(1\) 個あり，縦横 \(2\) マスずつのどの正方形にも黒いマスが \(1\) 個または \(3\) 個あるようにしたい． 黒く塗るマスの個数の最小値を求めよ．

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