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After our 3 frequently asked questions about math puzzles episode last week, math fan Cynthia wrote to tell me about one of her favorite puzzles. As luck would have it, Cynthia's puzzle is based upon one of the same ideas that—as we'll soon find out—makes our as-yet-unexplained third-and-final puzzle from last time tick.

What's the tie-in between the two? As we'll see, they're both based upon some pretty amazing properties of the mysterious and sometimes seemingly magical number 9. How does it all work? And what makes the number 9 so "magical?" Those are exactly the questions we'll be answering over the next few weeks!

A Mathemagical Trick
Before we get to those amazing properties of the number 9, I want to start by telling you about the mathemagical trick that math fan Cynthia sent me. This is definitely one that you'll want to play along with. Here's how it goes:

  • Start by thinking of a number, any number.
  • Now, multiply that number by 9.
  • If the result is a multi-digit number, add its digits together to come up with a new number.
  • If that new number is still a multi-digit number, add its digits together to come up with yet another new number. Continue doing this until you end up with a 1-digit number.
  • Once you have a 1-digit number, subtract 5 from it.
  • Now, using the standard numbering of the English alphabet (where 1 is A, 2 is B, and so on), find the letter corresponding to your number.
  • Next, think of a European country that begins with that letter.
  • Then take the last letter of that country and think of an animal that begins with that letter.
  • Finally, take the last letter of that animal and think of a color that begins with that letter.

Okay, now—oh, wait a minute—you do know that there aren't any orange kangaroos in Denmark, right?

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