How many squares are there in a 3x3 grid (i.e., a square divided into 9 equal smaller squares by two equally spaced horizontal and two equally spaced vertical lines)?

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1746520825/aptidude_questions/p4ryncqwodggbzk05hel.png)

Question

How many squares are there in a 3x3 grid (i.e., a square divided into 9 equal smaller squares by two equally spaced horizontal and two equally spaced vertical lines)?

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1746520825/aptidude_questions/p4ryncqwodggbzk05hel.png)

Accepted Answer

Let's count the number of squares in a 3x3 grid:

1. 1x1 squares: Each small square is a 1x1 square. There are 3 rows and 3 columns, so 3 × 3 = 9 such squares.
2. 2x2 squares: A 2x2 square can be formed by choosing any 2 consecutive rows and 2 consecutive columns. The number of ways to choose 2 consecutive rows is 2 (top two or bottom two), and similarly for columns. So, 2 × 2 = 4 such squares.
3. 3x3 square: The whole grid itself is a 3x3 square. There is only 1 such square.

Total number of squares = 9 (1x1) + 4 (2x2) + 1 (3x3) = 14.

Therefore, the correct answer is 14.

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