Question

The number of ways of choosing $2$ squares $(1\times 1)$ from a chess board so that they have exactly one common corner is?

• A. $98$
• B. $112$
• C. $36$
• D. $72$

Answer 1

The correct option is A $98$

Let us consider the first and second row of the chess board in the diagram given above.
The red arrows mark the pairs of squares that share only one corner.
In the first and second row, there are $14$ ways of selecting two $(1\times 1)$ squares that have only one common corner.
Rows $2$ and $3$ will similarly have $14$ squares that have only one common corner.
We can pick $7$ such pairs of rows in a chess board viz., $(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),and(7,8)$.
Therefore, the number of ways of selecting two $(1\times 1)$ squares in a chess board that have only one common corner $=14\times 7=98$