Write down a 3 digit number whose numbers are decreasing
Then reverse the digit to create a new number, and subtract this number from the original number.
With the resulting number, add it to the reverse to itself.
The number you will get 1089
This works by:
Represent the number with ABC
Represent this to get CBA
A is hundreds B is Tens C is Units
Hundreds Tens Units
A B C
- C B A
A B C
- C B A
Subtract 1 hundred, and add 9 tens and 10 Ones (-100, +90, +10 = 0, so the answer won't change). To the number ABC we wont make any difference (as we are adding 100 and taking 100 away, This just lets us specify that C had to be bigger than A).
Hundreds Tens Units
A B C
- C B A
A B C
- C B A
- 1
+ 9 10
(A-1-C) 9 (10+C-A)
Reverse the answer and add the two numbers together.
A-1-C 9 10+C-A
A-1-C 9 10+C-A
+ 10+C-A 9 A-1-C
---------------------------
9 18 9
+ 10+C-A 9 A-1-C
---------------------------
9 18 9
(Simplify:)
10 8 9