[r-t] MUG minor

[Graham John]

On Sat, 5 Dec 2015, Philip Earis wrote:
> To recap, MUG is a neat method with 8 changes per division (
http://ringing.org/main/pages/method?title=MUG+Minor)
>
> The challenge is to produce an extent (720 changes, ie 90 divisions) with
just one type of call, only at the division end.
>
> (I'm assuming nobody still has proved this isn't possible)

Having devised this principle as a teenager in the early 1970s, I spent an
inordinate amount of time trying to produce an extent with pen and paper.
Intuitively, it seemed that it ought to be possible.

I later wrote a dedicated (16 bit) assembly program in the 1990s to search
for extents with 14 bobs and 1456 singles, but it never completed. One
significant pruning optimisation was to avoid ever generating "ss" or "-s"
in successive divisions as they contain the same rows and end point as "--"
and "s-".

In
http://www.bellringers.net/pipermail/ringing-theory_bellringers.net/2007-December/008114.html,
there is a reference to Mike Ovenden exhausting that same search after some
months of processing.

I also confirmed that a bobs only extent is not possible using SMC32 in
2002. It only took an hour and a half. I can provide those results if
anyone is interested. The longest round block is 624.

It would be useful to know whether any extents exist using division end
calls alone (from combining the only possibilities 14, 1456, 36, 1236).

Graham
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://bellringers.net/pipermail/ringing-theory/attachments/20151206/b6aec409/attachment-0003.html>