[r-t] 40320 Spliced Major (3m)

[Mark Davies]

MF writes,

> Interesting. How exhaustive was your search for other methods that might work?
 > Obviously a theoretical explanation would be nice, but how sure of
> this"fact" are we already, empirically/computationally. Did you check
 > if there were blocks that got the right rows but couldn't be joined
 > up?

I believe so. The second stage of my pipeline applied this algorithm to 
every expanded Helixoid:

1. Partitioned the first three leads into eight sets of changes with the 
treble in the same position in each, the same length as our desired 
block of the Plain method. Each set has 42 members, representing the 42 
half-leads of a 3-course block of a Plain method.

2. In each set, the sign of the row was preserved, and the exact 
positions of (1,2,3), but the positions of the back five were discarded 
(masked out).

3. Starting with the 42 members with the treble at lead, I searched for 
place notations which would link to the set with the treble in 2nd's 
place, and so on.

The results of doing this were fairly startling, leading me to suggest 
either some deep fundamental truth is at work, or I am missing something 
very obvious! *Every* Helixoid produces a half-lead which links by the 
algorithm above into 42 sets of half-plain-hunt. In many these 
half-leads cannot be joined, but in a substantial minority they do join 
up using 12 or 78 leadheads/halfleads, forming courses of Plain, Reverse 
or Double Bob.

To be fair, after a few million methods I realised that, since this was 
always happening, I could speed things up by considering *only* the 
leadhead rows, and linking them by Plain Hunt, so dropping the check 
that Plain Hunt was the only working plain method, or indeed would work 
at all. The latter assumption has not failed me, though.

Thoughts?

MBD