[r-t] 40320 Spliced Major (3m)
mark at snowtiger.net
Tue Jul 3 07:01:25 UTC 2012
> 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
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
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.
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