How many squares do you see? Hint: There are way more than meets the eye!
Sometimes, the simplest tasks can turn out to be the most complicated. While that’s a frustrating fact of life in general, it does make for some fun brainteasers! Take this “how many squares” puzzle, for example. It challenges you to do something that seems laughably simple: Count the number of squares.
This square-counting puzzle might seem a whole lot easier than tricky math riddles and logic puzzles, but it gets tougher as you count each square. Remember, you’ll need to account for squares that overlap each other, squares within squares, big squares and little squares as well.
Think you’re up for the challenge? Read on to see if you can correctly identify the number of squares hidden within this “how many squares” puzzle.
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How many squares are there in this square-counting puzzle?
Take a long, hard look at the image above—then get counting. If you’ve given the “how many squares” puzzle your best shot, you’re ready to know the correct answer. Drumroll, please!
All told, there are 40 squares hiding in plain sight here. Didn’t find that many? Keep reading to see exactly how we arrived at that number.
What’s the trick to solving the “how many squares” puzzle?
Before we reveal the trick to correctly counting the number of squares in this visual brainteaser, let’s revisit one quick geometry lesson from school. A square is a shape with four sides of equal length. So a four-sided shape with different-sized sides (like all the rectangles within the puzzle) does not count.
Now for the solution to the “how many squares” puzzle: While the big square comprises 16 of the medium-sized squares, you can make squares with combos of four and nine medium-sized squares. Take a look below to see them highlighted, or give it another try before peeking at the answer.
FAQs
What is the formula for counting the number of squares in any given grid size?
When counting squares in a grid, don’t stop at the smallest boxes; the bigger ones are hiding too. The rule is simple: In an n × n grid—where n is the number of squares both horizontally and vertically—add up the squares from 1² to
- 4 x 4 grid: Add 1² + 2² + 3² + 4
Now, you’re thinking, how does this apply to the “how many squares” puzzle above? That’s a 4 x 4 grid … with a twist. Here’s how to determine the total number of squares in the puzzle:
- Start with the formula above, which tells you that the grid contains 30 squares.
- Look at the bonus squares in the puzzle: the 2 squares in the center.
- Count the 4 individual squares in each of the bonus squares.
- Add it all together: 30 + 2 + 4 + 4 = 40.
How do square-counting puzzles differ from rectangle-counting puzzles?
For starters, they focus on different shapes! Just as triangle-counting puzzles deal with triangles, square puzzles ask you to count only squares, and rectangle puzzles ask you to count only rectangles. But they differ in more subtle ways too.
Square-counting puzzles are all about perfect symmetry. With these, you’re looking only for shapes with four equal sides and four right angles.
Rectangle-counting puzzles, on the other hand, open the playing field to all four-sided figures with right angles, whether or not the sides match in length. That means every square is technically a rectangle, but not every rectangle makes the cut as a square. In short, square puzzles test your precision, while rectangle puzzles push you to think bigger.
Additional reporting by Brooke Nelson Alexander.
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