Tuesday, November 29th, 2011...9:39 am

X marks the spot

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This fall, I’ve been leading a seminar for the Charlotte Teachers Institute entitled, Math through Popular Culture. This Thursday will be our last session together. We will lead a Celebration of Mind event co-hosted by CTI, the Bernard Society of Mathematics at Davidson College, UNCC Math Department, the
Charlotte Teachers Circle, and HHMI Outreach at Davidson College. Throughout the evening, we will explore games, puzzles and magic as we celebrate and honor Martin Gardner, who touched millions of lives with his mathematical writing. This is one of worldwide Celebration of Mind events occurring on all 7 continents and a fitting way to complete our study of popular math.

To warm up our mathematical engines, I share a magic trick emailed just this morning among our seminar group. First, here’s the trick:

  • Think of a number 1-20
  • Double it in your head
  • Add 6
  • Divide by 2
  • Subtract original number

I bet I know your number! How? Let’s see (and create some space until I unveil the answer).

I don’t know the number you’ll pick so I’ll call is x. It’s the treasure of the problem and I must uncover it. So, x is marking the spot where I’m trying to use math to find a number.

Next, we double it so we get 2x.

Adding 6 yields 2x + 6.

Next, dividing by 2 gives us (2x + 6)/2 = x + 3.

Finally, we subtract the original number! Ack, I don’t know the original number! However, I do know that it equals x. So I subtract x and get x + 3 – x = 3.

Wait! I never needed to know your original number. In fact, you didn’t even need to select a number between 1 and 20. You can try an integer bigger than 20 and see that it still works. I’m going to stay within our original interval but be less rational and choose π.

Let’s see if that works. We double it and get 2π. Add 6 which results in 2π+6. Now, divide by 2 and get π + 3. Subtract the original number, which equals π, to get 3.

Such tricks can be fun and engaging ways to teach mathematical concepts. Martin Gardner was a master at it!

Thanks to Emily Sansale, a fellow in the 2011 Charlotte Teachers Institute Math through Popular Culture seminar, for inspiring this blog entry with her email.


  • This truly is one of the best type of math tricks to get students interested in algebra.

    Quick correction: The paragraph right after “Adding 6 yields 2x + 6.” reads:

    “Next, dividing by 3 gives us (2x + 6)/3=x + 3.”

    It should read:

    “Next, dividing by 2 gives us (2x + 6)/2=x + 3.”

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