How many squares of any size on this chessboard do not contain a rook?
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Hint
How many 2 x 2 squares are there?
Answer
There are 128 squares without a rook.
Reasoning
There are 62 squares of size 1 x 1.
There are 41 squares of size 2 x 2.
There are 18 squares of size 3 x 3.
There are 6 squares of size 4 x 4.
There is 1 square of size 5 x 5.
Giving a total of 62 + 41 + 18 + 6 + 1 = 128 squares.
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