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Mystery Math

Announcer: Frostbite Theater presents... Cold Cuts! No baloney!

Joanna and Steve: Just science!

Joanna: Hi! I'm Joanna!

Steve: And I'm Steve!

Joanna: In honor of April Fools' Day, we're going to teach you a trick you can play on your friends. This is how it plays out.

First, find a friend who is reasonably good in math, and have them write down a five digit number.

Once they have it, have them create a second number by scrambling the first number.

This is very important. The two numbers must have the same digits. So, if their first number has two 8's, two 5's and a three, then their second number must also have two 8's, two 5's and a three.

When they're ready, have them subtract the smaller number from the larger number.

hen, have them cross out one of the digits from their answer, except for zero, since zero is just too easy.

Finally, have them read off all of the remaining digits.

Steve: 2, 9, 0, 0.

Joanna: And then you'll say...

"You crossed out seven!"

And they'll be amazed!

Steve: I am... amazed.

Joanna: So, how does this work? For you to do this trick, you need to know how to find a number's digital root.

Steve: While the name might sound a little scary, it's actually pretty easy. To find a number's digital root, just add all of its digits together. If the sum has more than one digit, then you add its digits together. Keep doing this until your answer contains just one digit.

Joanna: Now, go back to how we set things up. We had them make two numbers using the same digits. Since addition is commutative, both numbers have the same digital root. It turns out that when different numbers with the same digital root are subtracted, the digital root of the answer is always equal to nine.

Steve: And that's the key to this trick. You know the digital root of their answer is equal to nine. And what do you have them do?

Joanna: You have them tell you the digits they didn't cross out.

Steve: And what do you do with those digits?

Joanna: You find the digital root and whatever you need to add to get to nine is what they crossed out.

Steve: Back to our example.

I said "2, 9, 0, 0." Add those numbers up and you get 11. 11 isn't a single digit, so you add its digits together, and you get 2. If the digital root of what I said is equal to 2, and you know the digital root of the whole thing is equal to 9, then what's missing?

Joanna: The seven!

Steve: And that's how it works!

Joanna: Although, it's not quite that easy.

Steve: Yeah, it never is...

Joanna: Remember how we said to cross out a digit, except for zero? We said it was because zeros are too easy. But, that was a clever lie. Adding or removing zeros from a number doesn't change its digital root. Unfortunately, adding or removing 9s doesn't change the digital root, either. You can work through some examples for yourself to see that this is true.

Steve: What does this mean for us? It means that we can't tell if they crossed out a zero or a nine. We need to stop them from doing one or the other, so we plant a believable lie. "Zeros are too easy."

If the digital root of the numbers they give you equals nine, then they either crossed out a zero, or they crossed out a nine. You say, with great confidence, "You crossed out a nine," and you secretly hope they didn't disobey instructions and crossed out a zero anyway.

Joanna: The upside to this is, since 9s behave just like 0s, you can ignore any of the 9s they tell you.

Ready for some practice?

So, if we say "1, 0, 4," what did we cross out?

Hopefully, you said "4."

Steve: How about 5, 8, 2?

The answer to that would be 3.

Joanna: What about 9, 1, 3, 3?

That's a 2.

Steve: How about 7, 7, 6, 7?

That's one of those tricky ones where the digital root is equal to 9. If we followed instructions, then we crossed out the nine.

Joanna: And, finally, how about 9, 9, 9, 1?

Remember, you can throw away the 9s, so 9, 9, 9, 1 is the same thing as just saying 1.

The answer, of course, is 8!

Feel ready? Try it on a friend and let us know how it goes. You can also leave the numbers you didn't cross out in the comments, and we'll try to figure out the numbers you did cross out!

Steve: Just make sure the math is right. Otherwise, it's embarrassing.

Joanna: Yeah.

Thanks for watching! I hope you'll join us again soon for another experiment!

Steve: Want to try some?

Joanna: Yeah!

Steve: Okay. How about 8, 6, 1?

Joanna: 3.

Steve: Yeah. How about 6, 3, 0, 1, 1, 2?

Joanna: 5!

Steve: Yeah. How about 3, 8, 7, 0, 9, 1, 8, 8, 5, 4, 5, 4, 6!

Joanna: 4!

Steve: Wow...

Joanna: Yeah. I also know what 3 plus 2 is.

Steve: What??

Joanna: You'll find it. Eventually...

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