How Many Squares Do You See In This Image?

Recently I ran across this challenge on a Facebook post: How many squares do you see in this image?

Well... After studying it for a while, I came up with 40. Scroll through the images below to see if you agree.



Let's start with the easy ones.  There are 16 squares which make up the basic grid.

Then, expanding the corner squares to 2X2 yields 4 more squares.

The same 2X2 shape yields 4 more squares nestled between the corner squares.

Then, expanding the corner squares to 3X3 yields 4 more squares.

Now we add the internal squares.  There are 2 of them.

But wait!  There are 4 smaller squares inside each of those squares, for a total of 8 more squares!

Oh, yeah, there is 1 more internal square.

And, of course, there is the basic square shape itself.  That's 40!

this web page was developed by Herb Klug     updated Jane 2, 2018