What is the 9 trick in math?

A Mathemagical Trick 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.

scientificamerican.com - The Magic of Number 9 (Part 1) - Scientific American

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Scientific American presents Math Dude by Quick & Dirty Tips. Scientific American and Quick & Dirty Tips are both Macmillan companies. 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. 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?

> Continue reading on QuickAndDirtyTips.com

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Why 6174 Is Mysterious number?

Kaprekar constant, or 6174, is a constant that arises when we take a 4-digit integer, form the largest and smallest numbers from its digits, and then subtract these two numbers. Continuing with this process of forming and subtracting, we will always arrive at the number 6174.

brilliant.org - Kaprekar's Constant | Brilliant Math & Science Wiki

An illustration:

Take a 4-digit number like 3215. Rearranging to form the largest and smallest with these digits, we get 5321 and1235. Now, subtract them: 5321-1235 = 4086. Continue with the process of rearranging and subtracting: 8640 − 0468 = 8172 8721 − 1278 = 7443 7443 − 3447 = 3996 9963 − 3699 = 6264 6642 − 2466 = 4176 7641 − 1467 = 6174. egin{aligned} 8640-0468&=8172\ 8721-1278&=7443\ 7443-3447&=3996\ 9963-3699&=6264\ 6642-2466&=4176\ 7641-1467&=6174. end{aligned} 8640−04688721−12787443−34479963−36996642−24667641−1467=8172=7443=3996=6264=4176=6174. We stop here since we will only get into a loop and keep getting 6174.

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