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1999 IMO Problems/Problem 3

Revision as of 20:39, 6 October 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== Consider an <math>n \times n</math> square board, where <math>n</math> is a fixed even positive integer. The board is divided into <math>n^{2}</math> units squar...")
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Problem

Consider an $n \times n$ square board, where $n$ is a fixed even positive integer. The board is divided into $n^{2}$ units squares. We say that two different squares on the board are adjacent if they have a common side.

$N$ unit squares on the board are marked in such a way that every square (marked or unmarked) on the board is adjacent to at least one marked square.

Determine the smallest possible value of $N$.


Solution

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