[r-t] challenge: Brunel, Cabot, Birmingham Carter (off list)

[edward martin]

On 25 January 2012 17:58, Hayden Charles <hcharles at grandsire.co.uk> wrote:
>
> I know little of serious theory, so hesitate sending to the list, but there
> has not been much response to Ander's challenge. I had a look at lower
> stages.
>
> A fairly brute-force search came up with this 3-part touch for triples:
>
>  1234567
>  6421375 Cabot
>  1764253 Brunel
>  5471632 Cabot
>  3145726 Cabot
>  1526374 BirCar
>  -------
>  7651243 Cabot
>  1476532 Brunel
>  3641725 Cabot
>  2163457 Cabot
>  1357246 BirCar
>  -------
>  4731562 Cabot
>  1647325 Brunel
>  2761453 Cabot
>  5172634 Cabot
>  1234567 BirCar
> 180 rows ending in 1234567
>
> all methods as in Ander's message.
>
> Start is a full Q six.
>
> There were more triples 3-parts with these part ends but this was the
> shortest, I think.
>
> Looking a caters, with just changes of method and no calls, I think that it
> is not possible to get out of course course ends. Or maybe I am just being
> dim.
>
> Hayden Charles
>

Hello
I thought that Ander's challenge was very interesting. but I've been
rather poorly over the last couple of weeks & have not been able to
work on any ideas
However, here are some thoughts/beliefs on the methods at lower stages:
The only pure doubles principles are
3.1.5.3.1.3.1.3.5.1.3.1 = Stedman Doubles
3.1.5.3.1.3.1.3.5.1.3.5 = Carter Doubles
and their reverses
Each = a full slow six and a full quick six, set up as they are so
that the first and last rows are from plain hunt ie from rounds to
54321 Stedman gives 53412 & Carter gives 45231. In both cases the full
true 60 rows can be had by repeating the block 4 times .
5040s of Stedman Triples can be had where the PN =
3.1.7.3.1.3.1.3.7.1.3.1 and the building material has PN =
3.1.5.3.1.3.1.3.5.1.3.1. Presumably the extent on higher numbers could
be had where PN 3.1.n.3.1.3.1.3.n.1.3.1 from blocks with PN
3.1.5.3.1.3.1.3.5.1.3.1 and peal lengths from blocks where PN =
3.1.n-1.3.1.3.1.3.n-1.1.3.1

Cabot Cinques =   3.1.E.1.3.E.3.1.E.1.3.1  = Stedman Cinques but with
a full quick six instead of a full slow
Brunel Cinques =  3.1.E.3.1.E1.3.E.1.3.1  =  Stedman Cinques but a
split slow six
Brum Carter 11 =  3.1.E.3.1.3.1.3.E.1.3.E =  Stedman Cinques but with
a split quick six (ie the same idea as in Carter Doubles)

At the Triples stage, if the building material is to be sixties of
either Carter or Stedman Doubles then the only hopeful one is
Birmingham Carters but with bobs in lieu of each 7ths place (to give
60s of Carter Doubles)

At the Caters stage there should be no problem getting 5000 other than
the fact that without singles, pure Caters rows are all pos.

At the moment the boiler has a gas leak & my attention is needed elsewhere!!

Eddie