Solution to the Facebook Square Puzzle

Last week, we posted a square puzzle on our Facebook page. The image was originally posted by Artify It and spread over George Takei’s wall where I spotted it and shared it with our Facebook friends. In the comments that ensued, we got answers ranging from 16 to 50+ as to how many squares are contained in this drawing. I promised I would post the solution that I came up with and so, here it is. Now, keep in mind that my solution may not be the most correct solution. If anyone can demonstrate a way to find more squares than I found, then I will include that information in an update. That said, let’s get cracking on the solution I came up with.

First, the original puzzle in its monochromatic glory:

As you can see, it’s a fairly standard 4×4 grid with two squares added. So, let’s get the simplest counts out of the way first:

Counting the large outer square and the two internal squares gives us three squares.

Now we count all of the small internal squares and find sixteen of them. That brings our total of squares found to nineteen.

After that, we count the squares inside the inner squares and find a total of eight of them. 8 + 19 = 27 squares.

Now things get a little tricky. We have to find all of the 2×2 squares. The corner ones are the easiest to spot for most people, giving us four. But, there are five more of these 2×2 squares, bringing the total to nine.

See the two in the center column? They’re mirrored by two more in the horizontal center row.

The last 2×2 square is dead-set in the center.

So, nine 2×2 squares added to our total brings us to 36 squares. That’s where many people stop. Indeed, that’s where I stopped the first time. However, there are still more squares to be found — these measuring 3×3!

Finding four of these 3×3 squares brings our total to 40 squares.

Now, after doing a bit of research on this puzzle, I have found that there are, supposedly, 42 squares. I have wracked my brains and strained my eyes looking for the last two squares. If anyone can present a solution to these two missing squares, I will buy that person a round of drink of their choice as well as giving them props and kudos for finding them!

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