Quick. How many squares on a checkerboard?

Dear Friends:

Gotta love a good brain teaser. This one even comes with a life lesson for yourself or to share with a young person you know.

Ready? A question . . . how many squares are on a checkerboard? You know it’s eight by eight. And you may also remember the old rhyme “Eight times eight fell on the floor. I picked it up, it was 64.” So logic tells you the answer is “64.”

That’s not wrong. But the takeaway—and the lesson to remember—is that quite often your first answer can be improved upon. Give yourself an extra moment, dig a little deeper, and you’ll often find an even better answer.

Did you consider that the entire checkerboard is a square? Aha! That makes 65 squares.

But don’e stop there! How about squares that are two by two? Or three by three? Or four by four?

The actual total number of squares on a checkerboard is a whopping 204. And, I agree they are a little tricky to count because there are eight different sizes and they all overlap. Here’s the math:

64 squares are 1x1. 49 squares are 2x2. 36 squares are 3x3. 25 squares are 4x4. 16 squares are 5x5. 9 squares are 6x6. 4 squares are 7x7. And 1 square is 8x8.

With any brainteaser, the goal is not to make you feel stupid. It’s to get you thinking in new ways. So, can you apply this life hack to a challenge you are currently facing?

Here’s the point: The first solution that comes to mind may be a wonderful option. But it’s not the only option.

Here’s a mundane example: Next summer, when it’s time to mulch the flowerbeds, you could do what you always do. That is, buy 15 bags from Home Depot—which leaves your trunk trashed, your back a little sore, fingernails filthy, your trash can full of empty bags, and your yard looking the same as it has the last five years. But there are all kinds of other options. Maybe better options!

Have a pile of mulch delivered to your driveway. Pay a neighborhood kid $40 to do the work. Get free mulch or wood chips from the city. Buy decorative stones that don’t require annual replacing. Plant ground cover or low shrubs. Plow up the flowerbeds and plant vegetables. Put in a putting green around the flowerbeds. Astroturf. Spend all summer in an RV exploring America. Move to a condo. You get the idea.

Maybe you’re too set in your ways to learn new tricks. But—for sure—if you know a sharp 10 year old, text them right now and ask them, “How many squares on a checkerboard?”

Let me know how that text thread goes,

/jay

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