Square Deal

Part of being on Facebook is tolerating the “memes” that every single one of your friends feels compelled to post. It happens in waves: One group does the original posting, then there’s a week of silence, and then suddenly the same exact joke — or pithy statement, or picture of a puppy — comes back with a vengeance as the next group of friends jumps belatedly on board.

We’re on round three, at least, of the puzzle shown below, which I think may have been posted by every single radio station in the country, and always with the same weird caption: “We count 24 squares in the image below. How many do you see?” What then follows in the comments is a bewildering debate as people claim they see any number of squares from 20 to 100.

Let’s clear this up, shall we? There are 40 squares. Forty. Let’s count ’em together!

We’ll start by ignoring the two squares in the center. Just focus on the largest square for a moment. This square is 4×4. That is to say there is 1 4×4 square.

Within that 4×4 square are 4 3×3 squares:

Also within that 4×4 square are 9 2×2 squares.

And finally, there are also 16 1×1 squares.

16 + 9 + 4 + 1 = 30

Now consider the two squares we previously decided to ignore. Each one encompasses five squares: Itself, and the four smaller squares within it. That’s ten more squares, bringing us to a grand total of 40.

There, that takes care of that! Glad to be of service.

By the way, how many stars are there in the image below?

One thought on “Square Deal

  1. I always thought it would be fun to include, as the answer to the squares puzzle, the ability to bring out the number 4, or 9, or 16, etc., by tracing the numbers as if from a digital clock out of the lines forming the squares. But that quickly devolves into hundreds of squares, especially if “1” is considered a square.

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