[r-t] Spliced Courses

[Graham John]

Robin wrote:

> It is possible to obtain a spliced course of seconds place
> methods which include every plain course lead head and end.

Yes. I assume that you mean with mixed lead orders, otherwise it would be
very trivial. You can also produce a course containing all the major lead
orders in a six lead course e.g. abfdec or ghmklj. 

> Is it possible to generate any 'mixed' *plain* courses, i.e.,
> including 2nd and 8ths place methods without using any calls?
> (I don't think so, but would be glad of a proof if any -
> especially a counter example.)

Yes, it is possible if you don't constrain it to be a round block e.g.
mbbfbgm = BCCLCGB S. Major. In fact I used this course in my 6-Spliced S.
Major (BCFGLS) between Wrong and Middle.

http://www.changeringing.co.uk/ssmajor.htm#5024-6m1

Reducing the requirement for a seven lead course opens up enormous numbers
of mixed course possibilities. Using a good example of a Surprise Major
method from each of the 12 PB lead orders, I have found 11,295 true
arrangements of a plain course. In theory this should make splicing these
methods easy, but in practice the enormous number of ways of arranging each
course of a peal makes the possible peal arrangements astronomic and finding
one that is atw and tenors together is difficult. 

Graham