Question

Number of ways of selecting pair of black squares in chessboard such that they have exactly one common corner is equal to:

Answer 1

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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