Number of ways of selecting pair of black squares in chessboard such that they have exactly one common corner is equal to:
Answers
Number of ways of selecting pair of black squares in chessboard such that they have exactly one common corner is equal to 49
Given:
8x8 Chessboard
To find:
Number of ways of selecting pair of black squares in chessboard such that they have exactly one common corner
Solution:
Considering a 8x8 chessboard, i.e., we have 8 rows and 8 columns in the chessboard, we have to select all pair of black squares in this chessboard configuration such that they have exactly one common corner.
Considering rows 1 and 2, one such pair of black squares where we have exactly one common corner is (1,2) and (2,1). Similarly other pairs in rows 1 and 2 are:
(1,2) and (2,3)
(1,4) and (2,3)
(1,4) and (2,5)
(1,6) and (2,5)
(1,6) and (2,7)
(1,8) and (2,7)
So, for rows 1 and 2, we have 7 such possible pairs.
Similarly, we have 7 such pairs each for rows
rows 2 and 3
rows 3 and 4
rows 4 and 5
rows 5 and 6
rows 6 and 7
rows 7 and 8
So, for each of 7 pair of rows, we can have 7 such pairs of black squares.
Hence, a total of 7 x 7 = 49 pair of black squares.
Therefore,
Number of ways of selecting pair of black squares in chessboard such that they have exactly one common corner is equal to 49
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