Why is it always 1089


This is the reasoning behind Always End With 1089.

We will need a little bit of algebra, but stick with it, it is not difficult.


Show the number as ABC

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Reverse this to get CBA

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

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Hundreds Tens Units

A B C
Subtract: C B A

A−C 0 C−A

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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
Subtract: C B A

A−1−C 9 10+C−A

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Last Step: Reverse the answer and
add the two numbers together.


Hundreds Tens Units

A−1−C 9 10+C−A
Add: 10+C−A 9 A−1−C

9 18 9
Simplify: 10 8 9

As predicted the answer was 1089