[r-t] A plea for help

[Mark Davies]

Philip writes,

> Please, please, please can somebody generate a list of “double
> helix”-style differential major methods for me?

Since no-one else replied I thought I'd have a look at this.

I think the full search is order-of-the-universe-big, so we definitely 
do need something to make it more manageable. I have chosen these 
general constraints:

- The 3-cycle is (1,2,3)
- Place notations are chosen from the set (x, 14, 16, 18, 36, 38, 58)
- Two blows is the longest a bell can stay in one place

Within these constraints, I have tried several searches, of which only 
the first two have so far completed (having spent a maximum of 24 hours 
run-time so far):

Search 1 - Double*, with non-halflead/leadhead PNs chosen from the 
subset (x, 14, 58, 18). This generates seven basic possibilities:

67845312 -18-14-14-18-18-14-14-18-18-18-14-18-58-36 (58,38,36,56)
85476312 -18-14-14-18-18-14-14-18-18-18-14-58-14-18 (56,36,16,58,38,18)
85476231 -18-14-14-58-58-14-58-18-18-14-18-58-18-18 (56,36,16,58,38,18)
78564231 -18-58-14-18-14-18-58-18-18-14-18-14-18-36 (56,36,16,58,38,18)
78564231 -18-58.14-58-18-18-14-18-58-18-14-18-14-14.36  (56,36,16,58,38,18)
78456312 -18-58.14-58-18-18-14-18-58-18-58.14-14-18-36 (18,38,16,36)
65874312 -14-18-14-18-58-18-58-58-58-18-18-14-14-18 (56,36,16,58,38,18)

The row at the start of each line is that of the handstroke halflead; 
the figures for the first quarter-lead only are given, plus (in 
brackets) potential half-lead changes (not all of which yield true 
Double methods, hence the * above, but all of which do have at least one 
leadhead change which generates a valid 3*5-lead course).

Search 2 - Double, with non-halflead/leadhead PNs chosen from the subset 
(x, 14, 58, 18, 36). This generates over 7,000 possibilities, which can 
be found in the attached file (if it manages to get through the list 
controls). (Note the PN for the full halflead is given in the file).

Search 3 - Double, with PNs chosen from the full non-contiguous set, as 
described above. This is still running. This search space should contain 
the original "Double Helix" method.

Search 4 - Ordinary symmetry, but strictly right-place, with the full 
non-contiguous PN set. This is still running, and has generated several 
megabytes of output so far. It shows signs of being a good proportion of 
the way through the search after 24 hours of (severely non-optimised 
Scala!) runtime.

I'll let you know if searches 3 & 4 complete, although it might be 
difficult to deliver the results. If anyone wants me to carry out 
different searches, e.g. for different PN sets, let me know.

Also if someone can check the results of searches 1 and 2 to make sure I 
haven't got any silly bugs in there, that would be good. :-)

MBD