Number sequences...........

Factual Questions
1

Hello all,

I’m sure someone is able to help me out…It’s been quite some years since I last dealt with calculus/math.

Something has been bothering me lately and there probably is a perfectly normal explanation for, I just don’t know it but would like to know.

Take the following number sequence 72298822
If I add all digits and calculate to ‘one’ digit like this
7+2+2+9+8+8+2+2=40=4+0=4
why does it give me the same outcome if I do;
7+2=9+2=11=1+1=2+9=11=1+1=2+8=10=1+0=1+8=9+2=11=1+1=2+2=4 (I hope the way I calculate makes sense)

This has worked for any sequence I have been using so far…Is there a common law/rule/principle named for this?

In case you’re wondering where the numbers come from - they are sequence numbers on dollarbills (but I doubt that has anything to do with it)

Thank you so much for shedding any light on this…

2

Looks to me like what you’re doing is a variant on Casting Out Nines.

It’s as old as the hills:
http://mathworld.wolfram.com/CastingOutNines.html

3

It’s called the “digital root” and a search on that term will uncover oodles of info about it.

4

Thanks…

5

The result will be 9 if and only if the number is divisible by 9. Otherwise, the result will be the remainder you get after dividing by 9. Take a 3 digit number abc. abc = 100a + 10b + c = (99+1)a + (9+1)b + c = 99a + a + 9b + b + c. Since subtracting multiples of 9 does not affect the remainder we can drop the terms 99a and 9b. So abc has the same remainder as a + b + c. The result generalizes to any number of digits.