Thus it was written in the epistle of Tony Summers,
> Can anyone explain why the works?  I know that any number multiplied by 9
> gives a number whose digits add up to 9, but why?
>
> And even better
>
> http://www.cut-the-knot.com/blue/divisibility.html

Thanks for posting this--I particularly like that he gave the generalization.
I'd worked out that it works for any number divisible by b-1 for base b, but I
didn't know the b+1 rule.  By the by, it not only works for b-1, but also for
any divisor of b-1.  That is, if we worked in base 13, we could discover if a
number was divisible by 2, 3, 4, 6 or 12 by adding the digits (and with the b+1
rule, also numbers divisible by 7 and 14).

Ted
--
Ted Ashton ([log in to unmask]), Info Serv, Southern Adventist University
          ==========================================================
Measure what is measurable, and make measurable what is not so.
                                           -- Galilei, Galileo (1564 - 1642)