How Many squares in this picture?

How many squares do you see in this picture? It’s been making the rounds on my Facebook friends list. The comments page below are not helpful with ten different answers being posted by hundreds of users.

FWIW, I count 36.

I got the same thing. Are there claims of more?

That’s my count, too.

I got 40.

(Actually on my first count, I got 42, but when I counted up the squares of each size, 2 of them disappeared, so I think I overcounted the first time.)

The breakdown:

1 4X4
4 3X3
11 2 X 2
24 1X1

Note that the size of the cells is not consistent.

I also got 40. 16 of the 1x1, plus 2 more of the 1x1s offset in the middle. 9 2x2. 4 3x3. 1 4x4. And then 8 of the tiny ones made by the offset 1x1s. 16 + 2 + 9 + 4 + 1 + 8 = 40.

I counted 41

On re-count, I got 40

I count 9 of the 2 by 2 squares. And 26 1 by 1. But I guess it’s how you count those ones in the middle. Now I count 40, as well. :confused:

How did you get 2x2 number?

And I’m off because I didn’t add right.

18 - 1x1
6 - .5x.5
9 - 2x2
4 - 3x3
1 - 4x4

So I get 38.

Call the length of the side of the whole square 8 units.

[SPOILER]Then I count the following number of squares of each dimension:

1 × 1: 8
2 × 2: 18
3 × 3: 0
4 × 4: 9
5 × 5: 0
6 × 6: 4
7 × 7: 0
8 × 8: 1

The total is 40.[/SPOILER]

Unless I messed up.

On my first count I got:

39, because I didn’t count the big one; then I did and got 40

I can’t add, or type things in correctly either. :smack:

8 - .5x.5

So it’s 40

Top left, top middle, top right, the smaller 2x2 contained within the top middle.
Middle left, dead centre, middle right.
Bottom left, bottom middle, bottom right, the smaller 2X2 contained within the bottom middle.

And the 1X1 are spoiler + 2(2X2) == 16 + 2(4) == 16 + 8 == 24[/spoiler]

Again, note, the size of the cells is not consistent.

I get the same as everyone else posting above. Took some careful elimination to ensure that I wasn’t double-counting on my way to




I got 39, then realized I forgot the whole shape, so 40.

def 40, but when i saw it on fb, the comments were rapid (something like 300k posts within an hour) and often very wrong.

When you have a perfect square of whatever number, you also have the perfect squares of all the other numbers counting up to it. Since this is four squared, you also have three, two and one squared.


Now you add the two squares in the middle, plus the eight subdivisions of those squares.


40 is the answer.

Going straight to the dope for my visual puzzles! We tackled it better than the facebook masses. Good call, me! :slight_smile: