[r-t] Spliced Doubles puzzle

Thu Mar 6 00:22:47 UTC 2008

Ignor my previous message, i've found a solution.

The first extent is rearranged a bit (i think it's basically a reversal) and D is substituted for C when 5 is making 4ths.

12345  3C15342  113524  5C12534  12312543  5C14523  115432  4C12435  12312453  4D13452  12313425  4B15423  114532  5B13542  115324  3B14325  12314352  3D12354  113245  2D14235  12314253  2C15243  12315234  2C13254  112345As before, the second extent is as the first, but with works swaped as before (C and D swap, 2 and 5 swap and 3 and 4 swap). The 3rd extent needs to be slightly different from before, but the version i've arrived at is fairly simmilar to the first two in several ways.

12345  3A15342  12313524  3A12534  112543  4A14523  12315432  4A12435  112453  5A13452  12313425  5A15423  12314532  5A13542  115324  4A14325  114352  3A12354  113245  2A14235  12314253  2A15243  12315234  2A13254  112345

With leads of B in place of A as nescessary.

I think that that rounds up all the methods with 12 methods per extent.

> Date: Wed, 5 Mar 2008 18:30:28 +0000> From: pabs at cantab.net> To: ringing-theory at bellringers.net> Subject: Re: [r-t] Spliced Doubles puzzle> > 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> > > > > > > _______________________________________________> ringing-theory mailing list> ringing-theory at bellringers.net> http://bellringers.net/mailman/listinfo/ringing-theory_bellringers.net
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