[r-t] Easter challenge

[Matthew Frye]

Interesting concept, but impossible with that treble path.

Look at the rows with the treble in 3rds place in one half lead, for example:
23145
21345
23154
23514
32154
(the 2nd/4th rows aren't relevant and could be different, but the 3rd/5th rows are inevitable given the first)

Notice that the 3 rows have the same pairs of bells in 1-2 and in 4-5, there is obviously a forth similar row (32145) which is not included in the same half lead, and if you try to include that row in another lead, then you must also have 2 more rows with the same pair of bells in 1-2 and 4-5, ie 2 of the rows you already have. Hence it's not possible to get a true single extent with a fixed treble ringing that path.



> Date: Sat, 11 Apr 2009 19:21:22 +0100
> From: pje24 at cantab.net
> To: ringing-theory at bellringers.net
> Subject: [r-t] Easter challenge
> 
> I like the concept of the plain course of a method generating the extent.
> 
> On 5 bells, with a fixed treble and four working bells,  this gives 30
> changes per lead to play with.
> 
> There are some rung examples, shown on
> <http://www.methods.org.uk/online/tpl5.htm>, eg Daedalus Doubles.
> 
> One treble-work I like the look of is where the treble dodges in 1-2, 2-3,
> 3-4, 4-5 and does four blows at front and back.  Eg treble path:
> 
> 1121232343454555 (treble rings six blows in each position in the lead)
> 
> Is a plain course extent on such a plan possible?  I don't mind about more
> than four consecutive blows.
> 
> The possible changes are:
> 
> 1|125|145
> 3|345|5
> 3|345|5
> 3|345|5
> 1|145
> 1|145
> 1|145
> 125|5
> 125|5
> 125|5
> 1|3|123
> 1|3|123
> 1|3|123
> 345|5
> 345|5
> 
> It's easy to put together a simple false examples on this plan, but a good
> true one would be nice.
> 
> 
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