Consider an n×n square board, where n is a fixed even positive integer. The board is...

Consider an n×n square board, where n is a fixed even positive integer. The board is divided into n 2 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 unmarked square on the board is adjacent to at least one marked square. Determine the smallest possible value of N.

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Expert Solution

I believe this is a tough combinatorics problem that requires a lot of imagination and thinking . For this purpose I have used a 8*8 chess board ( a regular one to illustrate with hand made diagram).f(b ) and f(w) represent white and black cells and N is the total no.of such cells covering it . And please try not to downvote if you didn't understand my approach . I required genuine effort.so thank you here's my approach to this problem.

Colby Messinger answered 10 months ago

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