So How Many Squares Are There, Really, In This Image?

by on December 14, 2012

in bruce's thoughts

A while back I saw this picture puzzle where they ask how many squares are in this picture?  I have what I think is the answer for how many squares are in the picture.

squares 00a

I gave it a go and put in my spin on the answer.  What I found amazing was how many different answers folks were putting out there!  So I started thinking how I can explain how I came up with my answer.

My answer is below… in case you don’t want to be spoiled.  But how did I come up with my answer?

Well, let me demonstrate with different diagrams that highlight the squares I saw.  (Let me “show my work,” as my math teachers used to say.)

1:  First, let’s not forget the most obvious of answers, the square itself.

squares 01

3: Here, I found three more squares, making a total of four so far.

squares 03a

4:  Now here’s four to add to that tally, making it eight.

squares 04a

6:  Six more squares, making it fourteen

squares 06

18: And here are eighteen more squares to add to that fourteen tally…

squares 18

Add those up and I got 32!

Update!  I forgot the small squares at the center of it all…  eight of them , which now adds up to 40 squares.

squares 08 small

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So the total number of squares in this bad boy is 40!

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