Squares in Chess Board
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In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there? 
126
62 squares of one unit each (excluding the two containing the pieces) +
41 Squares of 2 x 2 sides each +
18 Squares of 3 x 3 sides each +
4 Squares of 4 x 4 sides each +
1 Square of 5 x 5 (lower left corner)
Total: 62 + 41 + 18 + 4 + 1 = 126
Larger squares (6+ unit sides) are can’t be considered because any such square will contain at least one piece. There are 9 squares of 6 x 6, 4 squares of 7 x 7 and one 8 x 8 square (which is the entire board)
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