[r-t] RE: good puzzles

Andrew Tibbetts ajwxyzt at hotmail.com
Wed Jun 29 11:31:09 UTC 2005

That was fascinating. Maybe we should have afternoon puzzles on every day of 
the week!


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>To: ringing-theory at bellringers.net
>Subject: ringing-theory Digest, Vol 11, Issue 14
>Date: 29 Jun 2005 04:00:35 -0700
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>Today's Topics:
>    1. Re: Monday afternoon puzzle (Richard Smith)
>Message: 1
>Date: Tue, 28 Jun 2005 15:20:47 +0100 (BST)
>From: Richard Smith <richard at ex-parrot.com>
>Subject: Re: [r-t] Monday afternoon puzzle
>To: Ringing Theory <ringing-theory at bellringers.net>
>	<Pine.LNX.4.58.0506281311510.6538 at sphinx.mythic-beasts.com>
>Content-Type: TEXT/PLAIN; charset=US-ASCII
>Philip Earis wrote:
> > OK folks, time for a quick starter for ten:
> >
> > - In what way is the seemingly unremarkable method Biddlesden Surprise
> > Major (&-5-4.5-5.36-4-,2) similar to Cambridge Surprise
> > Minor?
>Phil does seem to want to explain his somewhat cryptic
>question, and, unsurprisingly, no one has managed to
>guess the similarity.
>Cambridge Minor is a regular method and has a regular
>half-lead variant, Ipswich.  There's nothing particularly
>unusual in that, except that Cambridge does not have regular
>half-leads -- that is, back rounds does not appear at a
>half-lead in the plain course of Cambridge.
>Most half-lead variants (e.g., on six bells, Durham and
>Beverley) have regular half-leads.  Changing an (N-1)ths
>place half-lead to a 1sts place half-lead cycles the bells
>one step through the coursing order, meaning that if one
>method has a regular lead end, the other will too.  (Or it
>will come round after one lead, or be a regular short course
>So how does Cambridge work?  Instead of having all the
>coursing pairs coursing at the half-lead, it has none of
>them coursing:
>   Cambridge  Ipswich
>   624513     624513
>   265431     265431
>   256413     256413
>   524631     524631
>   256431     542361
>   524613     453216
>   542631     435261
>   456213     342516
>At the half-lead, the bells are coursing in the order 25436.
>(This is easier to see in Ipswich than in Cambridge.)  The
>important thing to notice is that the pairs coursing at the
>half-lead are pairs separated by one in the lead-end
>coursing order.  By changing the half-lead, the bells move
>one position through the half-lead coursing order which is
>equivalent to moving two positions through the lead-end
>coursing order.
>All pairs of six-bell half-lead variants must have either
>the regular coursing order or this involution[*] of it at
>the half-lead.
>(I'm not convinced this is the correct use of the term
>involution, but Brian Price uses it extensively in "The
>Composition of Peals in Parts" to mean a pair of coursing
>orders (or N-cycle permutations) where adjacent pairs in one
>coursing order are M bells apart in the other, and
>where M+1 and N are coprime.)
>Phil's example, Biddlesden S Major, also has this property,
>and is one of very few major methods to have it.
>   Biddlesden      [Unnamed]
>   45237618        45237618
>   54273681        54273681
>   54726318        54726318
>   45762381        45762381
>   54673281        47526831
>   45637218        74562813
>   45362781        74658231
>   54326718        47685213
>The half-lead coursing order is 3654728 and the bells in
>every adjacent pair in this coursing order are two apart in
>the lead-end coursing order.  (On eight bells, suitable
>coursing orders can be found by taking bells one or two
>apart in the regular coursing order.)
>Unsurprisingly there are relatively few rung methods with
>this property -- no doubt partly because separating coursing
>pairs in this manner is very bad from a musical perspective.
>However it is probably also partly because it is quite
>difficult to move the bells through each to separate all of
>the coursing pairs in the available space.
>The difficulty in separating the coursing pairs is even more
>apparent on higher numbers.  There are no rung surprise
>royal methods that have this property, and it is quite
>difficult to produce one.  Starting with Cambridge and
>inserting pairs of adjacent places is often a good start,
>but ends up producing truly hideous methods, for instance,
>   &9.3-4-25-36-47-58-6-,2
>   &9.3-4-25-36-47-58-6-,2
>After a bit more thought, I came up with the following
>creation, which at least has an interesting line and grid.
>   &,2
>   &,2
>It's just a shame it has almost no musical merit.  Counting
>its 4-runs gives 22 -- quite an achievement given that the
>regular lead heads and ends alone give 13!
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>End of ringing-theory Digest, Vol 11, Issue 14

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