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  4. Number of squares that can be formed in 8 × 8 chessboard, so that each square is surrounded by four squares of same dimension -

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Q. Number of squares that can be formed in $8 \times 8$ chessboard, so that each square is surrounded by four squares of same dimension -

Permutations and Combinations

Solution:

Case - I : Square of $1 × 1$ dimension $= 6 × 6 = 36$
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Case - II : Square of $2 × 2$ dimension $= 3 × 3 = 9$
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No other possibility is their
Hence total squares $= 36 + 9 = 45$