[Maths-Education] Re: Maths-Education Digest, Vol 49, Issue 10

[Ng Foo Keong]

i had the privilege of hearing Charles Patton (from SRI International)
talking about Sudoku
and the link with mathematics, but i forgot the details.

perhaps you can contact him at charles.patton at sri.com





2008/11/29  <maths-education-request at lists.nottingham.ac.uk>:
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> Today's Topics:
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>   1. RE: Group Theory and Soduko (Ernest, Paul)
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> ----------------------------------------------------------------------
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> Message: 1
> Date: Sat, 29 Nov 2008 11:30:13 +0000
> From: "Ernest, Paul" <P.Ernest at exeter.ac.uk>
> Subject: [Maths-Education] RE: Group Theory and Soduko
> To: Mathematics Education discussion forum
>        <maths-education at lists.nottingham.ac.uk>
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>        <574338AFA9B4EA4282A9EC0B3268A6131CF3643C at EXCHMBS04.isad.isadroot.ex.ac.uk>
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> Dear Colleagues
>
> My Group theory is a bit rusty, but I was looking at a completed Soduko  which is a 9X9 grid and it is obviously a permutation - each line is a rearrangemnt of previous with no elements staying in same place - so my thought is - it should (or could?) be a permutation group of order 9. Now I only recall 2 finite groups of order 9 - C9 (cyclic group of order nine) and C3XC3 (cartesian product of 2 cyclic groups of order 3)
>
> But playing with transformations/rearrangements of the Soduko square did not get me anywhere.
>
> The number of nine element permutations is 9! so the 9 shown in an S grid is a tiny part of all possible perms - do these form a group? If so, what operation transforms them into each other?
>
> The answer may differ for different completed Sodukos as they constitute different selections of 9 permutations
>
> To be a group, one of them has to be a unit transformation, and each needs an inverse
>
> Actually I'm starting to have doubts as to where an aribtrary Soduko grid does form a group
>
> I'm sure someone else has thought about this and can answer it better than me!
>
> More generally, how do you determine a group from a finite group table (without the labels)
>
> Any interest or answers?
>
> Best wishes
>
> Paul
> __________________
> Paul Ernest
> Emeritus Professor
> University of Exeter
> SELL, St Lukes, Heavitree Road
> Exeter  EX1 2LU, UK
>
> Visiting Professor, HiST-ALT, Norway
> Visiting Professor, UiO, Norway
>
> http://www.people.ex.ac.uk/PErnest/
> for Philosophy of Mathematics Education Journal - No. 23 is out now!
> No. 24 in 2009 will have theme 'Mathematics and Art' -- please consider contributing!
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> Forthcoming book in 2009 Critical Issues in Mathematics Education by Ernest, Greer and Sriraman (Eds) at http://www.infoagepub.com/products/content/p490a29296b4d1.php
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> End of Maths-Education Digest, Vol 49, Issue 10
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