TITLE: How many squares actually ARE in this picture? Is this a trick question with no right answer?
QUESTION [35 upvotes]: This is one of those popular pictures on sites like Facebook. I always see a huge variation of answers such as $8, 9, 16, 17, 24, 28, 30, 40, 41, 52,$ etc., yet I've never seen a definitive answer on any website.

I counted $16$ whole squares ($4$ going down on left side, $4$ going down on right side, $8$ small squares in the centre). With this method the answer could also be $17$ if you want to count the entire shape as one big square.
I can also see the answer being $24$ if you count the smaller squares separately, as if they were floating above the main grid instead of intersecting with it.
Is there a right answer, or is it possible that there is no 'right' answer and it just depends on your counting method?

REPLY [7 votes]: To find total squares of $n \times n$ squares, the total no. of squares in it is given by:
$$n^2+(n-1)^2+(n-2)^2\ldots1^2$$
In the box above of $4 \times 4$, the total no. of squares are $$4^2+3^2+2^2+1^2=30$$
Additionally, there are $2$ small squares in the middle along with 4  even smaller squares each. They total to $10$ squares.
$\therefore$ The total squares is $ 30+10=40$