# Fun With Nines (math tricks)

## Nine times any number equals nine

You may already know that nine times any number equals nine. There are some amazing puzzles or tricks that have been developed using this mathematical phenomenon.

First, let me explain what I mean by nine times *any number* equals nine. Look at the multiplication table under the 9. You will see that 9x1=9; 9x2=18...the 1 and 8, when added together, equals 9. Every multiple of nine, when added together equals nine: 27, 2+7; 36, 3+6, etc.

With that in mind, try the following trick on a friend (you will be able to tell them which number they have circled without ever having seen the numbers):

- Have them write
*any three to five digit number*without letting you see the number. Make sure they do not use zero or duplicate numbers. - Then, have them randomly rearrange the same numbers to form a new number.
- Now they have two different numbers with the same amount of digits.
- Have them subtract the smaller number from the larger number.
- Ask if their answer has any zeros.
- Tell them to circle one digit of the answer without letting you know any of the numbers. (Make sure they do not circle a zero)
- Ask what numbers are left over. The circled number being a secret.
- Add the total of the digits. The number they circled will be the difference between the total of the digits and the next higher multiple of nine.

**Example:**

259 (secret three digit number)

952 (randomly rearranged three digit number using the same three numbers)

952-259=693

They circle the 9. They tell you that they have a 6 and a 3 left. 6+3=9, the next multiple of nine is 18. So 18-9=9...this is how you know they circled a 9. :)

Easy enough? Let's do one more:

45689 (secret number)

98654 (the same digits randomly rearranged)

98654-45689=52965

They circle a 5. They tell you that they have 5,2,9,6 left. 5+2+9+6=22. The next higher multiple of nine is 27. So, 27-22=5...you know they circled a 5.

**TIPS:**

- If they make an error in their math, your answer will be wrong--so make sure they double check their math before telling you the numbers that are left over.
- You can do this with any number that is two digit or higher.
- Two digit numbers very quickly reveal how you know what number is circled, while larger numbers make it more likely that there will be an error in the math making your answer wrong.
- It is perfectly fine if they use a calculator.

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## Here's another good one:

- Have someone pick a number between 1 and 9 without telling you what number they chose.
- Tell them to multiply their chosen number by 9.
- Confirm that the answer is a two-digit number (but don't let them reveal the actual number to you).
- Tell them to add the two digits together.
- Now have them subtract 5 from that number.
- Explain that the number needs to be assigned a letter to represent it, and that 1=A, 2=B, 3=C, 4=D, 5=E, etc.
- Now have them think of a
**COUNTRY**that begins with the letter represented by their number. - Next, have them think of an
**ANIMAL**that begins with the*last letter*of the**COUNTRY.** - Then, have them choose a
**COLOR**that begins with the*last letter*of the**ANIMAL.** - Give them a moment to look at what they have written, then tell them "there are no orange kangaroos in Denmark!"
- 99% of the people will have written those three things down! It will blow away your friends when you try this. :)

Here's how it works: When they choose a number between one and nine, then multiply it by 9, the answer of the two digits added together will be 9 (every number multiplied by nine is nine, right?). Then you have them subtract 5 from that answer, leaving a 4. So, the representative letter will always be D. 99% of people will list Denmark as the country beginning with D, Kangaroo as the animal beginning with K, and Orange as the color beginning with O. Try this and let me know how it works for you. This is a great one to do over the phone--where the other party knows it is impossible for you to have seen what they wrote down. :)

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## Comments 13 comments

Interesting. Again a very good hub. See you soon. I will read more of your hub.

Thanks for sharing this great aticle. Put my brain in a spin until I figured it out. Well done!!

This is really fun! Thank you for sharing, I love the numbers' game, I will learn to play that :)

Great hub, great fun with numbers. Thank you for sharing this.

I am going to have to forward that last one to my nephew who LOVES magic and feeling superior when he holds us in the palm of his hand, lolol. This is awesome Lowell. You have made me laugh and will MAKE HIS DAY!!!

I love math and numbers! Great hub!

I am one of the 99%. Guess that makes me in good company?!

Great hub! I liked it.

13