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!

A pen

Paper

A friend to play with

• 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?

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!

Here's a variation:

1. Grab a book and open it at page 10
2. Find the 9th word of the 8th row
3. Write that word on a strip of paper:this will be your prediction
4. Repeat the original version
5. Ask the volunteer to find the 9th word of the 8th row of the 10th page
6. Reveal your prediction
7. 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!