[r-t] Method symmetry

[Alexander Holroyd]

On Thu, 23 Aug 2012, Graham John wrote:

> Am I missing something?

I don't think so (unless it is exactly which questions people have been 
answering).

> Ander's example has rotational symmetry and has 8 hunt bells (note: not 
> a method according to CC decisions as it is not divisible into leads). 
> 3478.1478.1258.1256.1456.3458

Quite correct.  This was to simply to show that it's possible to have 
all bells "symmetric about a point" while maintaining truth.

> Mark's first example has palindromic symmetry:
> -1-5.4.5 = 12647583
>
> Mark's second example however, is asymmetric, so does meet the criteria:
> -1.2.25.4.5 = 12647583

Yes, he said so in the two messages.

> I wonder though whether Ander's stated problem sufficiently constrained.

It has many possible variations.  There are quite a few types of symmetry 
(see Martin Bright's article).  Any examples in which all the lines have 
more symmetries than the method seem potentially of interest.

> For example if you put Cambridge Minor on top of Cambridge Minor (but 
> offset by say two changes), you create a Differential Maximus method 
> that fulfills the criteria, but I doubt that this is in the spirit of 
> the challenge.

My original message contained exactly this example (but using plain bob 
minimus), and I asked for more interesting examples (deliberately left 
undefined, but I think it's clear that the Cambridge version does not 
qualify).

I think Mark's second example certainly qualifies as an answer to the 
original challenge.

Perhaps the next question should be: is there one that people might 
reasonably want to ring?

  Perhaps the problem should be constrained to a single 
> hunt method, or principle?

Also an interesting question.