# Number sequences........... **URL:** \ **Category:** Factual Questions\ **Created:** [July 15, 2003, 4:02pm UTC](https://boards.straightdope.com/t/number-sequences/188684 "2003-07-15T16:02:28Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![swannguy](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@swannguy](https://boards.straightdope.com/u/swannguy)\ **Post date:** [July 15, 2003, 4:02pm UTC](https://boards.straightdope.com/t/number-sequences/188684/1 "2003-07-15T16:02:28Z")
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… ---
**Author:** ![Exapno\_Mapcase](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/exapno_mapcase/32/1051_2.png) [@Exapno\_Mapcase](https://boards.straightdope.com/u/Exapno_Mapcase)\ **Post date:** [July 15, 2003, 4:12pm UTC](https://boards.straightdope.com/t/number-sequences/188684/2 "2003-07-15T16:12:06Z")
Looks to me like what you’re doing is a variant on [Casting Out Nines](http://www.jimloy.com/number/nines.htm). It’s as old as the hills: [http://mathworld.wolfram.com/CastingOutNines.html](http://mathworld.wolfram.com/CastingOutNines.html) > [@](#): > > Casting out nines was transmitted to Europe by the Arabs, but was probably an Indian invention and is therefore sometimes also called “the Hindu check.” The procedure was described by Fibonacci in his Liber Abaci (Wells 1986, p. 74). ---
**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\ **Post date:** [July 15, 2003, 4:20pm UTC](https://boards.straightdope.com/t/number-sequences/188684/3 "2003-07-15T16:20:17Z")
It’s called the “digital root” and a search on that term will uncover oodles of info about it. ---
**Author:** ![swannguy](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@swannguy](https://boards.straightdope.com/u/swannguy)\ **Post date:** [July 15, 2003, 4:47pm UTC](https://boards.straightdope.com/t/number-sequences/188684/4 "2003-07-15T16:47:35Z")
Thanks… ---
**Author:** ![John\_Kentzel-Griffin](https://avatars.discourse-cdn.com/v4/letter/j/ccd318/32.png) [@John\_Kentzel-Griffin](https://boards.straightdope.com/u/John_Kentzel-Griffin)\ **Post date:** [July 15, 2003, 6:24pm UTC](https://boards.straightdope.com/t/number-sequences/188684/5 "2003-07-15T18:24:40Z")
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 = 100_a + 10_b + 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.