Always End With 1089

Add two number together and always end with 1089.

Here is How:

Pick a three digit number.The three numbers used must be different*. i.e. 123		Reverse that number. 123 becomes 321
Take the smallest three digit number from the largest. 321 - 123 = 198		Take the answer and reverse that number. 198 becomes 891
Add that number to the answer of the subtraction. 891 + 198 = 1089		The answer will be 1089!
So Why does it do this? Find out here

Why is it always 1089

(This is the reasoning behind Always End With 1089)

You will need a little bit of algebra. But stick with it, it is not difficult.

Represent the number with ABC

Reverse this to get CBA

Remember that A is Hundreds B is tens and C is units Take CBA from ABC like this

Hundreds Tens Units A B C C B A

Now here is the trick: subtract 1 Hundred, and add 9 Tens and 10 Ones (-100, +90, +10 = 0, so won't change answer): Hundreds Tens Units A-1 B+9 C+10 C B A A-1-C 9 10+C-A

Last Step: Reverse the answer and add the two numbers together. A-1-C 9 10+C-A + 10+C-A 9 A-1-C 9 18 9 (simplify:) 10 8 9

As predicted the answer was 1089