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
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 | |
Subtract: | C | B | A |
A−C | 0 | C−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 | |
Subtract: | C | B | A |
A−1−C | 9 | 10+C−A |
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