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?

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    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)

    Viji_Pinarayi Expert Answered on 6th October 2022.
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