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How many squares of any size on this chessboard do not contain a rook?

Rooks On A7, C2, E4

Puzzle Copyright © Kevin Stone

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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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