Re: ISBN & undecimal counting

On Wed, 02 Nov 2005 10:01:03 -0000, Mark Brader <msb@xxxxxxx> wrote:
>
>
> "Ramkumar" writes:
>> A modern though little realised example of undecimal counting (i.e
>> based on 11) is seen in the ISBN of published books. Any ISBN comprises
>> ten digits. If you multiply the first by ten, the second by nine, the
>> third by eight, and so on, summing the results as you go along, the
>> result will always be divisible by eleven.
>>
>> Any special reasons why ISBN follows this?
>
> It allows the detection of any single-digit error and any transposition
> of two adjacent digits. This is better than the Luhn checksum, which
> does not detect the transposition of an adjacent 0 and 9.

I'm pretty sure that the ISBN method also detects any transposition of any
two nonadjacent digits.

--
------------------------
Mark Jeffrey Tilford
tilford@xxxxxxxxxxxxxxxx
.

Relevant Pages

  • ISBN & undecimal counting
    ... A modern though little realised example of undecimal counting (i.e ... based on 11) is seen in the ISBN of published books. ... Any ISBN comprises ... ten digits. ...
    (rec.puzzles)
  • Re: ISBN & undecimal counting
    ... >>> based on 11) is seen in the ISBN of published books. ... >> of two adjacent digits. ... This is better than the Luhn checksum, ... >> does not detect the transposition of an adjacent 0 and 9. ...
    (rec.puzzles)
  • Re: ISBN & undecimal counting
    ... > based on 11) is seen in the ISBN of published books. ... Any ISBN comprises ... It allows the detection of any single-digit error and any transposition ... of two adjacent digits. ...
    (rec.puzzles)
  • Re: Cantor Confusion
    ... for the second sequence use quarter an hour and so on. ... If, for example, the nth transposition exchanges the current occupants ... The replacement of members of a sequence by a rule depending only on the ... sequences can be applied independently to different digits ...
    (sci.math)
  • Re: "Elementary" number theory problem
    ... > It is a rule of thumb in accounting, I have this thanks to Gloria Newbery, ... > branch manager, that if a digit transposition error exists in an account, ... integer N iff it divides the sum of N's digits. ...
    (sci.math)
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