Question

How many rectangles does a chess board has?

• A. $1^3+2^3+3^3+......+8^3$
• B. $1^3+2^3+3^3+......+7^3$
• C. $1^3+2^3+3^3+......+9^3$
• D. $1^3+2^3+3^3+......+{10}^3$

Answer 1

The correct option is A $1^3+2^3+3^3+......+8^3$


The chess board is an $8\times 8$ square.
We know that $n\times n$ square has $1^3+2^3+3^3+.....+n^3$ rectangles
Similarly, $8\times 8$ square grid has $1^3+2^3+3^3+......+8^3$ rectangles.