Just PM me the answer to the following questions to prove that you're smart enough. I already know the answers obviously, and I may ask for proof.

40th International Mathematical Olympiad
Bucharest
Day I
July 16, 1999

3. Consider an n x n square board, where n is a fixed even positive integer. The
board is divided into n² unit 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.

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