[r-t] Minimum calls in mx maximus

[Philip Saddleton]

Richard Pullin said  on 29/09/2009 07:53:
> What is the minimum number of calls possible in an Mx maximus method for 
> a peal of at least 5040 changes?
> 1.) Result without singles?
> 2.) Result with singles?

With tenors together and starting and finishing at the lead end we can 
have a 5040 with 17 calls, e.g.

   23456   M  W  H
   52436      -
   64235   -     -
   36245      -
   42563   -  -
   24365   2     2
   62345      -
   25346   -     2
   23456      -  2

Any fewer calls would have to have at least an extra course, so consists 
of 99+n leads.  As we cannot go a whole course without a call, the least 
dense we can have is calls at every other calling position, i.e. three 
calls in every two courses. The best we can hope to manage is then 14 
calls in nine courses, giving a 5424.

-- 
Regards
Philip
http://myweb.tiscali.co.uk/saddleton/