How many squares on a checkerboard?

Ask a young person you know —of any age — “How many squares on a checkerboard?”

They may have learned the helpful rhyme, “Eight times eight fell on the floor. I picked it up, it was 64.” Which means they will quickly answer  . . . “64.”

If that happens, your response should be, “Good! But might there be an even better answer…a second right answer?”

They will say, “Huh?” And then you can point out how the entire checkerboard is a square!

Depending on their age, they will likely roll their eyes and say, “Okay, 65.”

That’s when you blow their little minds. Winsomely ask, “Are there any other squares?”  “Maybe squares that are two by two?”  “Squares that are three by three?”  “Four by four?” “Five by five?’  “Six by six?”  “Seven by seven?”

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

64 squares are 1×1.
49 squares are 2×2
36 squares are 3×3.
25 squares are 4×4.
16 squares are 5×5.
9 squares are 6×6.
4 squares are 7×7.
1 square is 8×8.

That’s a fun lesson for kids, right? But there’s an even bigger lesson for us grownups.

Too often, we settle for the first answer to many of our own questions. “What podcast should I listen to?” “What should I do this weekend?” “What career path should I follow?” “How can I better harvest my spiritual gifts?” “What’s the next season of my life going to be?” “Which donut should I grab?”

Clearly some questions are more important than others. Still, in most cases, while our first instinct might be perfectly fine, often there could very well be a “second right answer.”
Thinking ideas through — not jumping to conclusions or easy answers — is good practice for Christians of any age. In 2 Timothy 2:7, Paul writes,“Think about what I am saying. The Lord will help you understand all these things.”

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