Question

In the given figure, if the centres of all the circles are joined by horizontal and vertical lines, then determine the number of squares that can be thus formed? 

• A. 13
• B. 42
• C. 37
• D. 44
• E. 56

Hint:

In a grid of points, squares can be of different sizes; count each size separately.

Answer 1

The Correct Option is D

Step 1: Understanding the Grid:
When centers of circles are joined by horizontal and vertical lines as shown in Q90.png, they form a grid of points.
Count the number of squares (of all sizes) that can be formed in this grid.

Step 2: Formula for Counting Squares:
For an \(m \times n\) grid of points, number of squares = \(\sum_{k=1}^{\min(m-1, n-1)} (m-k)(n-k)\).
Based on the figure, determine \(m\) and \(n\). Then calculate.