## Introduction: Magic 1089

Hi,i'm Dulna777 and this is my first instructable.

Today i'm going to show you a cool math trick.

Grab your pens and get ready!

## Supplies

A pen

Paper

A friend to play with

## Step 1: How to Do the Trick

- Write the number 1089 on a piece of paper:this will be your prediction
- Ask your friend to pick a 3-digit number
- Ask him (or her) to flip the number and subtract the greater number
- Repeat the above step but instead of subtracting ask them to add the two numbers
- Ask them the result
- Reveal your prediction
- The prediction is right!But why?

## Step 2: Why It Worked

Let's represent hundreds, tens, and ones with variables,and set some existence conditions

x=hundreds

y=tens

z=ones

0≤x≤9

0≤y≤9

0≤z≤9

x≠z

Now let's repeat the steps using the variables

first number

100x+10y+1z

first flipped number

100z+10y+1x

difference between the two numbers

100x+10y+1z-(100z+10y+1x)=99a-99c

let's remove one of the 99s

the equation becomes 99(x-z)

we know that 0≤a-c≤9

so the possible results are (0)99,198,297,396,495,594,693,792,891

the following table represents the possible additions and answers

ADDITION RESULT

(0)99+990 1089

198+891 1089

297+792 1089

396+693 1089

495+594 1089

594+495 1089

693+396 1089

792+297 1089

891+198 1089

as you can see,the result is always 1089!

## Step 3: Variation

Here's a variation:

- Grab a book and open it at page 10
- Find the 9th word of the 8th row
- Write that word on a strip of paper:this will be your prediction
- Repeat the original version
- Ask the volunteer to find the 9th word of the 8th row of the 10th page
- Reveal your prediction
- Voilà! Now,we don't need to re-explain the whole thing because you know it already.

Bye-bye,see you in the next instructable!