How many squares of any size on this chessboard do not contain a rook?
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Hint
How many 1 x 1 squares are there?
Answer
There are 116 squares without a rook.
Reasoning
There are 61 squares of size 1 x 1.
There are 37 squares of size 2 x 2.
There are 15 squares of size 3 x 3.
There are 3 squares of size 4 x 4.
Giving a total of 61 + 37 + 15 + 3 = 116 squares.
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