ALL ROADS LEAD TO 9
The Rules of 9
Let's start here:
If any number is reversed and the smaller of the two numbers is subtracted from the larger, the resulting number will always be a multiple of 9.
657 reversed is 756
756 – 657 = 99
(a multiple of 9)
Let's expand:
98,723,456 – 65,432,789 = 33,290,667
(a multiple of 9)
Add each digit in the answer, above:
3+3+2+9+6+6+7 = 36
Now add: 3+6 = 9
(a multiple of 9, just sayin')
OK, now go to second base:
If a three digit number is reversed and the smaller number is subtracted from the larger and if the result is reversed and added to itself, the resulting number will always be 1,089
783 – 387 = 396 then,
396 + 693 = 1089
or
423 – 324 = 99
then
099 + 990 = 1089
Then there's this:
Total the digits of any multi-digit number and subtract that sum from the original number. The digits of the resulting number will always total 9.
Consider the number 35:
Add 3 + 5 = 8
35 – 8 = 27
2 + 7 = 9
How about: 429,517
Add each number: it equals 28
429,517 – 28 = 429,489
Add each number 4 + 2 + 9 + 4 + 8 + 9
it equals 36. Add 3 + 6 = 9
(just sayin')
He's got a big lead,
he's going for third
If any two digits of a multi-digit number are interchanged and the smaller of the two numbers is subtracted from the larger, the result will always be a multiple of nine.
Consider 142,897
Swap the 9 and 4 so that you have 192,847
192,847 – 142,897 = 49,950
which is a multiple of 9 x 5,550
(just sayin')
Something to ponder:
When any number is multiplied by nine, then the individual digits in the resulting number are added, they will always total nine.
2 x 9 = 18
1 + 8 = 9
6 x 9 = 54
5 + 4 = 9
54,321 x 9 = 488,889...
Add 4+8+8+8+8+9. It equals 45...
4 + 5 = 9; try it
(just sayin’)
He’s stealing home, folks!
If the digits of a number total 9 or a multiple of 9, then the number itself must be a multiple of 9...
Consider the number 1,233
(whose digits add up to 9) equal to 137 x 9.
What about 17,982, whose individual numbers
add up to 27. Now add 2 + 7 = 9...
Understand now?
And finally…
If a multi-digit number is a multiple of 9, all other numbers formed by rearrangement of its digits also will be a muliple of 9
