Date: Thu, 01 Nov 2007 16:09:43 GMT
Bob Badour wrote:
> David Cressey wrote:
>> "Bob Badour" <bbadour_at_pei.sympatico.ca> wrote in message >> news:4728f759$0$14832$9a566e8b_at_news.aliant.net... >> >>> It's ironic you should mention base 9. It's a little-known fact that, if >>> a number is evenly divisible by 8, the sum of the digits of the number >>> in base 9 is also evenly divisible by 8. And if one repeats the process >>> with that sum until the resulting sum has only one digit and if the >>> original number was divisible by 8, the one remaining digit will be 8. >>> >>> It's like magic. So it's really ironic you should mention base 9 in >>> particular. >> >> This is a joke, right? For radix n, n-1 has this interesting property.
> Shhhhh! You've ruined it! Now nobody will bother converting numbers to
> base 9 to see if it actually works. Spoilsport!
>> Likewise, 9 has this fun property in decimals. Bookkeepers in the Bob >> Chratchit era used a property much like this one for error detection in >> manually managed numbers. >> >> If this were another person posting, I'd think it was simple oversight. >> But you, BB, are likely to know exactly what I've just said.
> If the number is divisible by any factor of n-1, the sum of the digits
> will be a multiple of that factor too. Thus, if one repeatedly sums the
> digits of a hexadecimal number, one can tell very quickly whether the
> number is divisible by 3, 5 or F.
> Base 9 is actually a little less useful because it can only tell you if
> the number is divisible by 2, 4 or 8, and these are often relatively
> obvious in other bases in any case.
Heh, personally, I prefer to think of all the numbers in my db as base 10**64 or so with a floating decimal, even if there isn't a dbms that supports that. Helps keep me from getting confused by more intricate representations. Received on Thu Nov 01 2007 - 17:09:43 CET