[r-t] Calling Round Stedman - Minimum Sixes from Rounds

[Robert Bennett]

On Fri, Nov 19, 2021 at 12:00 AM <ringing-theory-request at bellringers.org>
wrote:

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>    1. Calling Round Stedman - Minimum Sixes from Rounds
>       (Andrew Rawlinson)
>
>
> ----------------------------------------------------------------------
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> Message: 1
> Date: Wed, 17 Nov 2021 14:56:16 +0000 (UTC)
> From: Andrew Rawlinson <andrewrawlinson at yahoo.co.uk>
> To: "ringing-theory at bellringers.org" <ringing-theory at bellringers.org>
> Subject: [r-t] Calling Round Stedman - Minimum Sixes from Rounds
> Message-ID: <1006026075.3050773.1637160976218 at mail.yahoo.com>
> Content-Type: text/plain; charset="utf-8"
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> Does anyone happen to know of a proof of the minimum number of sixes to
> rounds from any given position in Stedman on each stage? I've heard a few
> figures being rumoured and am curious if anyone knows of a conclusive proof.
> Best,
> Andrew
>
> Sent from Yahoo Mail on Android
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> Stedman Triples:

Second worst position: If the 7th is in 4-5 going down slow.  It will then
take 7 sixes before it gets to the back again.
By this time, the 6th has time to get to the back from any position.
For example, the quick six ending 3467251.

Worst position: If  6-7 are dodging in 6-7, it can take 9 bobbed sixes to
get round; or it can take 9 sixes before the bell that goes in slow (either
6 or 7) gets back to the back again. If it is arranged that they both go in
quick, by keeping one of them behind at a bob, it still takes them 9 sixes
to get to the back again.

As an example of this the slow six ending 3425167.

This agrees with the fact that there are many touches about 60 changes, but
very few shorter than 60.

Stedman Caters and Cinques:
The same reasoning applied suggests that the maximum number of sixes
required is 11 for Caters and 13 for Cinques.


This is a long way from conclusive proof.

Robert Bennett
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