Home | FAQ | Server | Presentations | Mailing Lists/Archives | Member Tools | Links | Sponsors | ContactHome | FAQ | Server | Presentations | Mailing Lists/Archives | Member Tools | Links | Sponsors | ContactI did a google search for 'casting out nines' and the first result had an EXCELLENT description. I emphasized excellent because the other pages had horrible explanations.
http://www.mcn.net/~jimloy/nines.html
(I think I understand this enough to attempt an explanation).
Basically it said that the digit sum of the numbers will add up (or multiply,divide or subtract depending on what you are doing) to the digit sum of the answer. Add all of the digits in the first number (you can forget about nines, or 'cast them out') and add up all of the digits in the second number until you get a single digit, called the digit sum (if you get a 9, it becomes 0). The digit sum of the answer will be the sum (or product, difference or quotient) of the digit sums of the other two numbers. This will catch 8/9 arithmetic errors.
238943
* 423423
-------
101173861889
becomes:
238943=> 2+3+8+(we can forget the nine) + 4 + 3 = 20 => 2 + 0 = 2
423423 => 4 + 2 +3 +4+2+3 = (4+2+3 = 9 so we can forget about the whole thing) 18 => 9 => 0
101173861889=> 6 + 8 (because all other numbers can be paired to add to 9) => 14 => 5.
2 * 0 != 5 so the answer is wrong.
the real answer: 101173961889 => 0 (all can be paired to add to 9)
and since 2 * 0 = 0, we have 8/9% chance the answer is correct.
-----Original Message-----
From: Mikhail Kovalenko [mailto:EMAIL:PROTECTED]
Sent: Tuesday, May 01, 2001 1:33 PM
To: EMAIL:PROTECTED
Subject: [MLUG - DISCUSSION] Lost knowledge (was: Broadband besides DSL
or cable)
Jonathan King wrote:
>
> On Tue, 1 May 2001, Finn, Michael wrote:
>
> > We have lost the ability to manufacture the guns (16" variety) used on the
> > now mothballed Iowa class battleships. We no longer have the knowledge,
> > equipment or skilled workers to do it. Now that given, we could easily
> > "relearn" it, so we haven't forgotten the base knowledge, just some
> > specifics...
> >
> > And though we can build a pyramid, we aren't sure exactly how it was done...
> > again, close, but not quite fitting your quandary.
>
> The only things I could come up with on short notice that fit were all
> very artsy-like and trade secrets. So, everybody agrees that part of the
> "sound" of the Stradivarius violin derives from the strange lacquer that
> was used to finish them, but nobody has the recipe or figured out what the
> secret is. That one is amenable to solution, maybe.
>
> Human languages and cultures die out, of course, but that's not quite
> right, either.
>
> Now, I was *shocked* to find out the other day that today's undergrads
> were never taught how to perform the procedure we were taught as "casting
> out nines". In other words, consider the following arithmetic problem:
>
> 238943
> * 423423
> -------
> 101173861889
>
> I can tell that this is the wrong answer in about 4 seconds without
> a calculator of any kind. So much for "progress".
>
Would you like to explain a bit more here? The correct answer is
101173961889, according to my calculator :) What is "casting out nines"?
More on topic -- someone recently has figured out the secret of Damascus
steel. Pretty impressive. But again, it's knowledge, not an object.
The utility of the pyramids' many internal chambers is still mostly a
mystery. I don't know if they were actually used for anything. I think
that many people soon will not know what a sickle is and how to use it
:)
--
Misha Kovalenko
Webmaster Columbia College
Tel.: 573-875-7314 1001 Rogers
Fax: 573=875=7320 Columbia, MO 65216 USA
Please be much notice! http://www.engrish.com
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