[r-t] New mirror principles

Philip Saddleton pabs at cantab.net
Mon Feb 15 18:08:16 GMT 2021

On Sun, 2021-02-14 at 16:53 +0000, Philip Saddleton wrote:
> On Thu, 2021-02-04 at 21:56 +0000, Richard Pullin wrote:
> > On eight bells there are 384 mirror rows, the permitted place
> > notations being 18, 36, 1458, 1278, 3456, 123678, X. The nicest of
> > these are 18, 36, X, but it seems you can only attain 192 rows
> > using just these place notations, in much the same way that you can
> > only ring 60 rows in Doubles without using single changes. 
> The reason for this is that the changes that the even change (X)
> keeps bells in the same half of the row, while the odd ones swap a
> pair in 4-5. So the possible rows are the in  course ones with an
> even number of bells in the half they started in, and the out of
> course ones with an odd number.

This is true of the whole group - what I meant to say is that if bells
in the wrong half of the row are swapped with their partner, if an odd
number of swaps is required then each half of the resultant row will be
out of course.

> I came up with
> this: https://complib.org/method/41162?accessKey=a829c83566f003025dcb638e01a32df35e3064e1
>  - which I believe is the only possibility for a palindromic method
> with Original lead heads. It has similarities with Quick Six Triples:
> ring quick sixes at front and back with double dodging in the middle,
> then replace 18 with x when it would come round.

This can be extended by effectively singling in the opposite block with
a pair of places in 45, though  to keep it palindromic we lose the
Original lead heads or  have to finish with x:

I think this would best be rung with 14 bobs.


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