January 7, 2013

# How many squares do you see?

If you enjoyed the Facebook math problem about PEMDAS, I’m sure you will love this second math problem about counting squares which I also got from Facebook.

**Problem**

**How many squares do you see?**

Answers given in Facebook include 24, 25, 26, 27, 38, 34, 36, 40, 42.

**Solution**

Here’s how you can systematically count the squares.

# of 4 by 4 squares = 1

# of 3 by 3 squares = 4

# of 2 by 2 squares = 9

# of 1 by 1 squares = 16 + 2 (in the middle)

# of 1/2 by 1/2 squares = 8

**Answer: 40**

**Extending the problem:**

Suppose you have a 100 by 100 square grid. How many distinct squares are formed?

Challenge: How many squares with whole number area can you form with 4×4 grid? Click the link for some hints.

One Comment

I got 43.. For real.. Count again