# [r-t] Grandsire Triples

Fielding Ian I.Fielding at rbh.nthames.nhs.uk
Fri Oct 22 17:49:42 UTC 2004

```Therefore with one bob you have only 5 possible callings. Anyway, if you
have the callings from every lead end, then you have the proof. Does the
Thomson manuscript contain any clues?
Glint

-----Original Message-----
From: Fielding Ian
Sent: 22 October 2004 18:45
To: 'ringing-theory at bellringers.net'
Subject: RE: [r-t] Grandsire Triples

I thought there were only 5 leads in a course of Grandsire triples.
Glint

-----Original Message-----
From: Mark Davies [mailto:mark at snowtiger.net]
Sent: 22 October 2004 18:34
To: ringing-theory at bellringers.net
Subject: [r-t] Grandsire Triples

Percy:

> I was told once that Grandsire Triples can be called round from any
> change using three calls or less.
> I've failed to find a proof for this, in terms of logical reasoning.

I'm not sure you can prove this without checking all cases, because it
probably depends on that mysterious feature "linkage", however you can
certainly demonstrate a weaker premise, namely that it isn't impossible.

Consider all the possible arrangements of working bells. There are 6 working
bells and the plain course is of length 5, so there are 6x24 = 144 courses.
Half the courses are the reverses of the other half, so we only need to
consider 72 of them (remember there are two ways of coming round,
handstroke or backstroke).

Now with just one bob you have 6 possible callings (depending on how many
plain leads before the bob), with two bobs 6x6=36 callings, and with three,
6x6x6 = 216. If you take singles into account too you have 12, 144 and 1728.
Add these up and there are 1884 possible different ways of using three
calls. Some of these might give the same results, and we haven't shown that
there isn't some "rogue" course which isn't brought round by any of the
1884, but since 1884 is quite a lot larger than 72 it certainly shows it
might be possible.

MBD

_______________________________________________
ringing-theory mailing list
ringing-theory at bellringers.net
http://bellringers.net/mailman/listinfo/ringing-theory_bellringers.net

DISCLAIMER:

The information contained in this email may be subject to public disclosure
under the NHS Code of Openness or the Freedom of Information Act 2000.
Unless the information is legally exempt from disclosure, the

The information and material in this email is intended for the use of the
intended addressee or the person responsible for delivering it to the
intended addressee.  It may contain privileged or confidential information

using the reply facility in your email software or notify Royal Brompton &
Harefield NHS Trust Help Desk on +44(0) 20 7351 8696

Communication is not sent through a secure server; Royal Brompton &
Harefield NHS Trust cannot accept responsibility for the accuracy of
outgoing electronic mail.  Any views or opinions expressed are solely those
of the author and do not represent the view of Royal Brompton & Harefield
NHS Trust unless specifically stated.

_______________________________________________
ringing-theory mailing list
ringing-theory at bellringers.net
http://bellringers.net/mailman/listinfo/ringing-theory_bellringers.net

DISCLAIMER:

The information contained in this email may be subject to public disclosure
under the NHS Code of Openness or the Freedom of Information Act 2000.
Unless the information is legally exempt from disclosure, the

The information and material in this email is intended for the use of the
intended addressee or the person responsible for delivering it to the
intended addressee.  It may contain privileged or confidential information

using the reply facility in your email software or notify Royal Brompton &
Harefield NHS Trust Help Desk on +44(0) 20 7351 8696

Communication is not sent through a secure server; Royal Brompton &
Harefield NHS Trust cannot accept responsibility for the accuracy of
outgoing electronic mail.  Any views or opinions expressed are solely those
of the author and do not represent the view of Royal Brompton & Harefield
NHS Trust unless specifically stated.

```