[r-t] Spliced Doubles puzzle
Philip Saddleton
pabs at cantab.net
Wed Mar 5 18:30:28 UTC 2008
Very good. Concentrating on the more difficult frontworks in two extents
seems a good idea. The arrangement does have the slightly inelegant
feature that each each extent contains repeated leads. Can you find an
arrangement where each contains 12 methods? No.3 is easily fixed with
lead splices, but for the first two you will need to interchange leads
of C and D between them.
Philip
Matthew Frye wrote:
> Interesting problem, it took a bit of thinking about but I think that
> i may've solved this one. Just a slight warning, i've been working
> with pencil + paper and haven't run this through any proving software,
> so there's a chance that everything im about to say is nonsense, but i
> think that im right.
>
> Firstly, i picked a backwork for each bell and assigned each frontwork
> a letter:
> 2 = 3.1
> 3 = 3.145
> 4 = 345.1
> 5 = 345.145
>
> A = 5.1.145
> B = 5.123.145
> C = 125.1.345
> D = 125.3.145
>
> The methods are referenced using this number and letter (followed by
> the pn of the lead end), so "3C 123" would be 3.145.125.1.345 with 123
> at the lead end which you called 129V. Sorry if this system isn't very
> clear (especially with the different lead ends) but it's what i've used.
>
> The three extents each focus on a different frontwork, with the
> methods with the remaining frontwork scattered throughout the 3 extents.
>
> The first extent has frontwork C throughout, except when the 2 is 3
> pb, when it has frontwork B. With careful selection of lead ends, this
> wraps up all the "C" methods.
>
> 12345 3C
> _15342_ 123
> 15324 3B
> _14325_ 123
> 14352 3C
> _12354_ 1
> 13245 2C
> _14235_ 1
> 12453 4C
> _13452_ 123
> 13425 4B
> _15423_ 1
> 14532 5B
> _13542_ 123
> 13524 5C
> _12534_ 123
> 12543 5C
> _14523_ 1
> 15432 4C
> _12435_ 1
> 14253 2C
> _15243_ 123
> 15234 2C
> _13254_ 1
> 12345
>
> There will almost certainly be other arrangements, but i couldn't find
> anything resembling a regular 2- or 3-part extent that provides the
> required methods.
>
> The second extent is basically the same as the first one, with a few
> swaps: frontwork D is used instead of C, backworks 2 and 5 swap,
> backworks 3 and 4 swap. This gives 2 extents including all the C and D
> frontworks and 6/8 of the B frontwork.
>
> The last extent needs a bit more tweaking than just swaping in
> frontwork A, as this leaves us 1 method short, this can be solved by
> ringing backwork 4 when the 5 is pivot and backwork 5 when 4 is pivot,
> this mixes up the extent from what's shown above, but provides the
> required lead ends to fit all the methods using lead splices between A
> and B.
>
> 12345 3A
> _15342_ 123
> 15324 3A
> _14325_ 123
> 14352 3A
> _12354_ 1
> 13245 2B
> _14235_ 1
> 12453 5B
> _15423_ 1
> 14532 4A
> _12534_ 123
> 12543 4A
> _13542_ 123
> 13524 4A
> _14523_ 1
> 15432 5A
> _13452_ 123
> 13425 5A
> _12435_ 1
> 14253 2A
> _15243_ 123
> 15234 2A
> _13254_ 1
> 12345
>
>
>
>
> > Date: Tue, 4 Mar 2008 17:55:16 +0000
> > From: pabs at cantab.net
> > To: ringing-theory at bellringers.net
> > Subject: [r-t] Spliced Doubles puzzle
> >
> > Consider the symmetrical single-hunt doubles methods with
> >
> > - 3pb making 3rd's to start with and pivoting at the half-lead
> > - 4th's at the half-lead
> > - PN 1 or 123 at the lead-head
> >
> > (e.g. the reverses of St Simons/St Martins etc.)
> >
> > There are
> > 4 backworks (3.1, 3.145, 345.1, 345.145)
> > 4 frontworks (5.1.145, 5.123.145, 125.1.345, 125.3.145)
> > 2 lead-heads (1, 123)
> >
> > Any combination gives a valid method with a 3 or 4 lead course, so
> 4x4x2
> > = 32 methods.
> >
> > It is easy enough to splice 12 methods into an extent: pick a different
> > backwork for each 3pb, and a different frontwork for each bell making
> > 4th's (either 4pb or 5pb, depending on the backwork), and choose the
> > lead-heads to join the bits together. 24 methods in two extents is also
> > straightforward. But can you fit all 32 into three extents? It seems
> > that there ought to be enough freedom to manage it, particularly as the
> > first two frontworks are lead splices.
> >
> > If anyone wants to take up the challenge, I attach the methods and some
> > sample extents in siril.
> >
> > regards,
> > Philip
> >
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