[seqfan] Re: No progress on the classic "Football pools" problem in 52 years

[Neil Sloane]

Hi Benoit, The book by Gerard Cohen et al on Covering Codes is really
excellent.  I have it downstairs, if you seriously want me to go look.
Hamming codes are certainly relevant.

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com



On Wed, Jun 23, 2021 at 1:14 PM Benoît Jubin <benoit.jubin at gmail.com> wrote:

> It looks like A004044(0) = 1 !
> In that case, the trivial lower bound is attained.  Actually, in the known
> cases where 3^n/(2n+1) is an integer, then that lower bound is attained.
> This means that there is a solution with no overlaps.  If this is true in
> general, this is probably well-known by people knowing Hamming codes (of
> which I am not).  Or did I misinterpret the problem ?
> Best regards,
> Benoît
>
> On Mon, Jun 21, 2021 at 6:52 AM Neil Sloane <njasloane at gmail.com> wrote:
>
> > I grew up in a country where many people played the football pools every
> > week (trying to guess the winners of next week's games: you know
> Manchester
> > United is going to beat Arsenal, but there are 13 games to predict).
> >
> > The classical problem translates into finding the smallest covering code
> in
> > {0,1,2}^n with covering radius 1.  The sequence (A004044) begins
> > 1,3,5,9,27, but even after 52 years, a(6) is still not known.  Tonight I
> > came across a lot of references, which I have added to A004044.  a(6) is
> > known to be 71, 72, or 73.
> > If you can solve it, you might not make any money, but you will probably
> > get your name in the science section of the newspaper.
> >
> > Good publicity for the OEIS too!
> >
> >
> > Best regards
> > Neil
> >
> > Neil J. A. Sloane, President, OEIS Foundation.
> > 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> > Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> > Phone: 732 828 6098; home page: http://NeilSloane.com
> > Email: njasloane at gmail.com
> >
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