How many squares on a checkerboard?
Asking your kids how many squares are on a checkerboard creates a great chance to teach them the rhyme “Eight times eight fell on the floor. I picked it up, it was 64.”
But, of course, if they say, “64,” you’ll want to suggest there may be an even better answer. When you point out how the entire checkerboard is a square, they may roll their eyes. Or they may say, “Okay, 65.”
Then 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 your kids, right? But there’s an even bigger lesson for us grownups.
With any brainteaser, the goal is never to make our kids feel stupid. The goal is to empower them to see how they can approach a challenging question from different angles. Explain that the answer “64” is not wrong. It’s just that sometimes we should look beyond our first thought. If we look at a problem or question from a few different angles, we may discover an even better answer.
Thinking ideas through — not jumping to conclusions — 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.”
The above is a partial excerpt from Chapter 75 of the book, Quick Tips for Busy Families.