On Mon, 09 Dec 2013 20:27:38 +0000, Alan Gauld
<alan.ga...@btinternet.com> wrote:
Incidentally, I just remembered another completely different
way to do it, although I can't recall how it works! Maybe one
of the math gurus can explain it, and how to extend it. This
version only works for 2 digit numbers... and has a huge gotcha!
To get the sum for a two digit number X using 17 as example...
subtract X from 100 17->83
Sum the digits of that number 83->11
Subract that number from 19 11->8
That's the sum of the digits of X
popped into my brain. It seems to work reliably but I've no
Unfortunately it doesn't work for 10, 20, ...
This is related to a technique called casting out nines (and nine is
magic because it's one less than the base we work in).
When you cast out nines you get the remainder, modulo 9. But to cast
out nines you keep adding up the digits till you get a one digit
result. So:
149 == 14 == 5.
There's more but it's probably more fruitful to read the Wikipedia
post.
--
DaveA
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