How many squares of any size on this chessboard do not contain a rook?
Puzzle Copyright © Kevin Stone
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Hint
There are no larger squares than size 4 x 4.
Answer
There are 110 squares without a rook.
Reasoning
There are 60 squares of size 1 x 1.
There are 35 squares of size 2 x 2.
There are 12 squares of size 3 x 3.
There are 3 squares of size 4 x 4.
Giving a total of 60 + 35 + 12 + 3 = 110 squares.
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