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-1B+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

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