[r-t] Principles

[Matthew Frye]

On 6 Jul 2011, at 07:48, Alexander Holroyd wrote:
> -4589TA-4589TA-34EB-EB-4589TA-4589TA-3470EB-70EB-4589TA-4589TA-3670-3670-4589TA-4589TA-36-36

Very clever.
The use of the places in 34 to mix the paths adjacent pairs is inspired, of course this doubles the length of the method, but the winking up process has already halved the relative length, so you're still OK.


On 6 Jul 2011, at 07:50, Alexander Holroyd wrote:
> Nice caters example!  I'd like to see the others too ("the structure of the method" doesn't seem so clearly defined to me!)  At this point I would be keen to see all examples of methods of this type that people can construct - I find it far from obvious what the general patterns are...

As I understood it, the defining feature is the pair of bells hunting from the back down to the front, the remaining bells making places in their positions till disturbed. (Naturally, this alters the length of the lead between stages and so wouldn't be recognised as the same method my the cc, for those that care about such things.)
So, Major was x123458x1238x1678x145678, 87214365, 4 leads
Minor would be x1236x16x1456, 651234, this doesn't come round properly (214365 after 3 leads, rounds next change), more importantly, the blocks of places is a bit shorter, so bells come out opposite way round to how they went in, stopping the two lines being identical, a quick looks at this reveals the conditions are only right for 4n bells.
For completeness:
Minimus, x14x14, 4321, 2 leads.
Royal, x12345670x123450x123890x167890x14567890, 0912345678, reaches 2134658709 after 5 leads.
Max, x123456789Tx1234567Tx123450ETx123890ETx167890ETx14567890ET, TE2143658709, 6 leads.
I'm sure you can derive any further stages wanted...

MF