Re: atomic

From: Bob Badour <>
Date: Thu, 01 Nov 2007 12:36:37 -0300
Message-ID: <4729f288$0$14877$>

David Cressey wrote:
> "Bob Badour" <> wrote in message
> news:4728f759$0$14832$

>>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

> 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. Received on Thu Nov 01 2007 - 16:36:37 CET

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