(Q). In how many ways can two squares be choosen on a 8×8 chess board such that they have only one corner common?
Sol:-
Two squares may have one corner in common only when these squares are from adjacent columns.
Now there are total 7 adjacent columns in 8×8 chess board.
Now consider 1ˢᵗ column, marked with ✓ sign will have 1 diagonal square in common marked with ✓✓ sign & remaining other 6 squares marked with ✖ sign will have 2 diagonal squares in common marked with ✖✖ sign.
Thus from the first two columns we will get
2×1 + 6×2 = 14 pair of squares
therefore the total number of ways to chosing the squares = 14×7
↓
adjacent column
= 98 Answer