Re: [MMM] Symmetrical Latin Squares for David Bowen

Jacky, I GIVE UP!

I tried it at 14 but all I got was a diagram of a ginger-bread man.

jacky_ligon@... wrote:

> David,
>
> Just so it's clear what I'm talking about, here is the symmetrical
> Latin Square for number 12:
>
> 1 2 3 4 5 6 7 8 9 10 11 12
> 2 4 6 8 10 12 1 3 5 7 9 11
> 3 6 9 12 2 5 8 11 1 4 7 10
> 4 8 12 3 7 11 2 6 10 1 5 9
> 5 10 2 7 12 4 9 1 6 11 3 8
> 6 12 5 11 4 10 3 9 2 8 1 7
> 7 1 8 2 9 3 10 4 11 5 12 6
> 8 3 11 6 1 9 4 12 7 2 10 5
> 9 5 1 10 6 2 11 7 3 12 8 4
> 10 7 4 1 11 8 5 2 12 9 6 3
> 11 9 7 5 3 1 12 10 8 6 4 2
> 12 11 10 9 8 7 6 5 4 3 2 1
>
> The one for 14 is what I'd like to see. And if I remember reading
> correctly - even Euler found it to be impossible to create. This
> variety can only be created with even numbers (except for 14 - *I
> think*). I've worked them out up to 18 - BTW. Note that this is the
> one which is similar to Schoenberg's.
>
> Hope you'll prove me wrong.
>
> Many Thanks in advance,
>
> Jacky Ligon
>
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

I don't know if it can't be done, I see a shot at a cheap joke and I take
it. I thought Latin Squares was a game show.
GZ

jacky_ligon@... wrote:

> --- In MakeMicroMusic@y..., George Zelenz <ploo@m...> wrote:
> > Jacky, I GIVE UP!
> >
> > I tried it at 14 but all I got was a diagram of a ginger-bread man.
>
> G,
>
> That's because it *can't* be done.
>
> David?
>
> This is fun!
>
> Jacky
>
> >
> >
> >
> >
> >
> >
> > jacky_ligon@y... wrote:
> >
> > > David,
> > >
> > > Just so it's clear what I'm talking about, here is the symmetrical
> > > Latin Square for number 12:
> > >
> > > 1 2 3 4 5 6 7 8 9 10 11 12
> > > 2 4 6 8 10 12 1 3 5 7 9 11
> > > 3 6 9 12 2 5 8 11 1 4 7 10
> > > 4 8 12 3 7 11 2 6 10 1 5 9
> > > 5 10 2 7 12 4 9 1 6 11 3 8
> > > 6 12 5 11 4 10 3 9 2 8 1 7
> > > 7 1 8 2 9 3 10 4 11 5 12 6
> > > 8 3 11 6 1 9 4 12 7 2 10 5
> > > 9 5 1 10 6 2 11 7 3 12 8 4
> > > 10 7 4 1 11 8 5 2 12 9 6 3
> > > 11 9 7 5 3 1 12 10 8 6 4 2
> > > 12 11 10 9 8 7 6 5 4 3 2 1
> > >
> > > The one for 14 is what I'd like to see. And if I remember reading
> > > correctly - even Euler found it to be impossible to create. This
> > > variety can only be created with even numbers (except for 14 - *I
> > > think*). I've worked them out up to 18 - BTW. Note that this is
> the
> > > one which is similar to Schoenberg's.
> > >
> > > Hope you'll prove me wrong.
> > >
> > > Many Thanks in advance,
> > >
> > > Jacky Ligon
> > >
> > >
> > >
> > >
> > > Your use of Yahoo! Groups is subject to
> http://docs.yahoo.com/info/terms/
>
>
>
>
> Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/