number of non-congruent Rectangles in a chess board

What is the number of non-congruent Rectangles in a chess board?

2 Answers

62
Lokesh Verma ·

This is a novel problem. Seeing it for the first time..

The answer is same as the number of sets {a,b} such that
0<9

This will be same as number of (a,b) such that 0< a <=b<9
8C2+8

Explanation:

8C2 is the number of ways to select a,b such that a not equal to b and has the other conditions 0<8
8 is the number of ways to select a,b such that a=b

Thus, the total is 8.7/2 + 8 = 28+8 = 36

11
Shailesh ·

good solution.. thanks :)

Your Answer

Close [X]