A Guarded Field
Dimitri places the maximum possible number of Rooks on a chessboard in such a way that there's no two Rooks that attack each other. How many squares are under attack?
Note: A Rook does not attack the square on which it is.
The answer is 9900.
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1 solution
Dimitri must place 1 Rook on each column on the first row in order to maximize the number of Rooks. When he has placed 100 Rooks, he leaves 1 on the first row, then, moves one to the second row, then, another to the third row, and continue with the process until he has placed the 100 Rooks on the 100 rows. As an explicit example, he can place the 100 Rooks on the big square diagonal.
The chessboard consists of 10000 squares, as each Rook is attacking its whole column (and row), all the squares are under attack except the squares on which the Rooks are stood. As 100 squares are being occupied by the Rooks, 9900 are under attack.