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.
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