Question

What is the maximum number of squares that could be formed using four of the dots in the unit grid as vertices?

Answer 1

Given:

The unit grid image.

To find:

What is the maximum number of squares that could be formed using four of the dots in the unit grid as vertices?

Solution:

Steps to find the number of squares:

Draw vertical and horizontal lines to join the dots.

Now, we need to count  the number of squares formed by single units,

1 - 16 squares

Now, we need to count  the number of squares formed by four units,

4 - 9 squares

Now, we need to count  the number of squares formed by nine units,

9 - 4 squares

Now, we need to count  the number of squares formed by sixteen units,

16 - 1 square

Therefore, a total of 16 + 9 + 4 + 1 = 30 squares.