[r-t] Minor Blocks
Matthew Frye
matthew at frye.org.uk
Tue Jul 1 05:10:53 UTC 2014
On 1 Jul 2014, at 02:58, Tim Barnes <tjbarnes23 at gmail.com> wrote:
> Graham - you were able to determine very quickly that Magenta was the only
> existing method with a divisible place notation. Are you able to similarly
> determine what percentage of group A methods with 6ths place lead ends
> would be divisible (and ideally also 2nds place group M methods, plus the
> higher number equivalents)? It would be good to know if this is, say, a
> 0.05% issue or a 5% issue, at least in relation to methods that have been
> named so far.
Presumably it's a fairly simple computer search if you have the method libraries in a sensible format.
For the treble bob minor (treble dodging only once and whole lead palindromic) divisible in two, we can work it out fairly simply. 6ths place bell will obviously have to treble bob down to the front in the first half lead and the half-lead will have to be palindromic, so we really have very little leeway. The 1-2 section each of the 3 pn can be x or 34, giving 8 possibilities in total, or 2 if we care about truth (x34x, 34x34 == Kent/Oxford up). The 2-3 section must be pn 16. In the 3-4 section each notation may be x,12,56 or 1256. It must be palindromic so we have 2 pn to fill and 16 possibilities of which 4 are false and 12 true. Half lead/lead end (must be the same) could be 16,1236,1256,1456,123456. That's 96 possibilities which aren't trivially false (though may still be less obviously false) and 640 including false ones (512 if you don't like the null change). I don't know what proportion of these come around at the first treble lead end, but I would guess about half. I don't know how many have been rung, but I would guess only about 4 (including Morning Star).
On higher numbers you'll have more possibilities, but I don't think any of them will have been rung.
MF
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