How many squares of any size on this chessboard do not contain a rook?
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Hint
There are no squares of size 5x5.
Answer
There are 125 squares without a rook.
Reasoning
There are 61 squares of size 1x1.
There are 39 squares of size 2x2.
There are 20 squares of size 3x3.
There are 5 squares of size 4x4.
Giving a total of 61 + 39 + 20 + 5 = 125 squares.
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