I'd confer with that - for the outline of a proof (hey I haven't done
formal maths for 20 years, so don't belittle my outline).
Start with a n digit number.
xxxxxxYxxx
Scramble that number
xxYxxxxxxx
As far as "Y" is concerned the difference between the two numbers is
00Y0000000 minus
000000Y000
Which will reduce to something like
Y * (100000 - 1000 )
And even further to
1000 * Y ( 100 - 1 ) = 1000 * y * "a guaranteed mutiple of 9".
Repeat the above for all other digits in the original number - and sum
the results.
And you can rely upon the fact that the sum of the digits of any
multiple of 9 is also a multiple of 9. (I'm sure the proof for this
final statement can be found somewhere on the internet)
-----Original Message-----
From: HP-3000 Systems Discussion [mailto:[log in to unmask]] On
Behalf Of Bob Comeau
Sent: 21 January 2005 13:03
To: [log in to unmask]
Subject: Re: [HP3000-L] Fun with numbers
It has to do with the fact that the difference between numbers which
have been transposed is always divisible by nine. Jumbling up the
digits and finding the difference will give you such a number.
A number which is divisible by nine has digits which add up to a number
divisible by nine.
By removing one of those digits you can easily determine what it was by
determining what you need to make the total of the digits add up to
nine.
Not sure why he says to not circle a zero, you would think that would be
just as easy to determine, may be it's just a red herring.
Bob Comeau
Sr. Systems Programmer Analyst
Crossley Carpet Mills Ltd.
(902)895-5491 ex 139
-----Original Message-----
From: HP-3000 Systems Discussion [mailto:[log in to unmask]]On
Behalf Of John Dunlop
Sent: January 21, 2005 5:08 AM
To: [log in to unmask]
Subject: OT: Fun with numbers
To all you smart mathematicians out there, can anyone explain to me (in
simple terms) how this works?
See : http://digicc.com/fido/
I can't figure it out, especially as you can jumble up the numbers and
it still works.
Doh!
Cheers,
John Dunlop
E-mail : [log in to unmask]
Web : http://www.jdunlop.net
* To join/leave the list, search archives, change list settings, *
* etc., please visit http://raven.utc.edu/archives/hp3000-l.html *
* To join/leave the list, search archives, change list settings, *
* etc., please visit http://raven.utc.edu/archives/hp3000-l.html *
______________________________________________________________________
This email has been scanned by the MessageLabs Email Security System.
For more information please visit http://www.messagelabs.com/email
______________________________________________________________________
The contents of this email are confidential to the intended recipient
and may not be disclosed. Although it is believed that this email and
any attachments are virus free, it is the responsibility of the recipient to confirm this.
Smith & Williamson Corporate Finance Limited - A member of M&A
International Inc. http://www.mergers.net Registered in England No.
4533970. Authorised and regulated by the Financial Services Authority
Smith & Williamson Investment Management Limited, Registered No. 976145. Authorised and regulated by the Financial Services Authority.
Smith & Williamson Pension Consultancy Limited - Independent
Intermediary. Registered No. 3133226. Authorised and regulated by the
Financial Services Authority.
Smith & Williamson Fund Administration Limited, Registered No. 1934644. Authorised and regulated by the Financial Services Authority.
Smith & Williamson Limited - A member of Nexia International.
Registered in England No. 4534022. Regulated by the Institute of
Chartered Accountants in England & Wales for a range of investment
business activities.
Registered Office: No 1 Riding House Street, London W1A 3AS
Telephone: 020 7637 5377 http://www.smith.williamson.co.uk
Nexia Audit Limited - A member of Nexia International. Registered in
England No. 4469576. Registered to carry on audit work and regulated by the Institute of Chartered Accountants in England & Wales for a range of investment business activities.
Registered Office: No 1 Riding House Street, London W1A 3AS
Telephone: 020 7637 5377 http://www.nexiaaudit.co.uk
NCL Investments Limited, Registered No. 1913794.
Member of the London Stock Exchange authorised and regulated by the Financial Services Authority.
Registered Office: Bartlett House, 9-12 Basinghall Street, London EC2V 5NS
Telephone: 020 7600 2801
______________________________________________________________________
This email has been scanned by the MessageLabs Email Security System.
For more information please visit http://www.messagelabs.com/email
______________________________________________________________________
* To join/leave the list, search archives, change list settings, *
* etc., please visit http://raven.utc.edu/archives/hp3000-l.html *
|
