How Many Squares are in This Image?

[AviatorTom]

Let's see how awake everyone is on this Friday, end of the week. In the US, it's the start of the Memorial Day holiday weekend, one of the worst travel days of the year, and the Indy 500, where cars zoom around a near oval at 200+ mph.

Question is... How many squares are in the image above?

BONUS: how many rectangles (other than squares) are in the image?

We'll reveal the correct answer in a few days (Monday).

Updates

1 y

There are 40 squares in the image: 8+(16+2)+9+4+1 (smallest to largest size squares)

There are 74 rectangles in the image: (12+4)+8+6+3+4=37 (horizontal, smallest to largest rectangles); same number vertical rectangles, total=37+37=74

Thanks to all who participated, and congrats to those who got the correct answer.

[Maybe_Maybe_not]

Several answers are correct here, because different perspectives can be used since the assignment isn't defining restrictions:

• 24, if counting the mid size squares then adding the mini squares, without treating intersecting squares as faulty
• 16, if counting mid and mini while subtracting the mid intersecting with the mini
• Infinite, if acknowledging microscopic and macroscopic scales (cheating but valid lol)
• 36, counted like this: 1 ultimate square containing all of them
  24 counting intuitively mid and mini, even intersecting
  2 containing the mini
  4 maxi contained in the main one, reading from top-left to bottom-right
  2 maxi, center raw, X axis
  2 maxi, center column, Y axis
  1 dead center
• ... ?
• ... ?

[Massageman]

I get 40. 8-18-9-4-1.

[Julie_TS]

Ok...

Squares, going with 35. Rectangles, going with 30.

That was a lot of counting, hoping I did it right, lol.

[Dongie]

You missed a lot.

[jennifer_bloom]

I could 40

[KostasKouvalis]

I got 26

I ain't doing the rectangles

I know it is, don't get me started. I had to spend 5 hours at Dallas Airport after closing hours because my plane got diverted, because some guy decided an airplane would be a good place to have a stroke. They could have at least diverted it to a state I haven't been to yet

[KostasKouvalis]

Thinking of it now, I may have miscounted, but how are there THAT many? The math doesn't tell me anything. Post a picture with them colored in.

[slatyb]

40 squares: 16 1x1 + 9 2x2 + 4 3x3 + 1 4x4 plus 5 for each of the detached squares.

[Gaylordslav]

your maths off.. (24) 1x1 (11) 2x2 (4) 3x3 (1) 4x4

[docster]

This is a tough one, but I came up with 44 squares. I'm not going to try for the rectangles otherwise it will keep me up tonight.

[Grond21]

I feel like this is the right answer, but I don't know where the last four squares are.

[Sunrising]

I give you my answer on Sunday when everyone has given you their answers.

[Sunrising]

nxn = n²+(n-1)²
+(n-2)²...1²
4²+3²+2²+1² =
+2 small squaresA + B =
Equals the answer someone has already given.

[Sunrising]

Using simple maths again for the bonus, there are 32 rectangles in the image.

[Sunrising]

40 Squares.

[fish5505_87]

24, I hate these things so much I love them!

[Grond21]

I got 40. Feels like I missed a few though.

[Kingofkings1992]

Why are you making me use my brain? God damn you

[Account]

There are 40.

[Account]

It took me a few moments though. I lost count at some point.

[purplepoppy]

I get 40

[OlderAndWiser]

I count 37

[OlderAndWiser]

Make that 41.

[FunkyMonkee]

I'd say 40.

[exitseven]

if we count squares and not rectangles it is 35

[douride2]

I may be wrong but I came away with 35.

[Wiredone]

I counted a total of 36 squares

[Panthero80]

I see 24 squares.

[lightbulb27]

i see 33

[SandandWaves]

18...

[MisterWack]

My guess: 25

[BCRanger10]

I count 41.

[Miristheiss]

I get 39

[Agape93]

24 squares

[DawnB]

I think 33?

[DancingQueen16]

I counted 24

[jamesgoldman]

I've up to 35

[LiamS95]

26 squares

[WonderingManII]

I think 25.

[Dongie]

39..

[Gaylordslav]

very close ! (1) is the image itself 4x4. (24) individual squares inside 4x4 + 8 mini squares. (11) 2x2 squares and ultimately (4) 3x3s expand the quadrants out 1x1

[Dongie]

Alright!

[Dongie]

35 rectangles.

[Gaylordslav]

Care to explain? At first glance i see 16

[Gaylordslav]

ok after counting i think 58 rectangles, 40 squares.

[Dongie]

They're all over it like the squares. Two squares together, you have 8 horizontal and then the same vertical. Then 4 squares horizontal and 4 vertical. Then double squares. And so on.

[Gaylordslav]

S= squares in rectangle. (24) 2S (16) 3S (8) 4S (6) 8S (4) 12S

[Dongie]

Shit it's more like 50.

[Dongie]

I made my last comment without seeing your last one.

[Gaylordslav]

30? ?

[Gaylordslav]

31* the image itself is square

[Gaylordslav]

36 actually. 1, 16, 9, 2, 8. Outer square, 16 in the 4x4, 9 in the top middle and bottom row, 2 squares holding the small 8 ones. 36

[Gaylordslav]

Its 40. Omg.

[Gaylordslav]

I didn't even see the 3x3s my eyes hurt

[Jeff51]

16 squars

[Anonymous]

24 I think.

[Anonymous]

27..