[r-t] Long lengths of Bristol Surprise Major

[Richard Grimmett]

On 18/03/2016 12:08, Richard Smith wrote:
> Sadly it's one of those questions where gut instinct is all we've 
> got.  I'm not even aware of a valid theoretical basis to use to get an 
> upper bound on the longest possible touch of a method.
>
> I recall Rod Pipe telling me that he and Peter Border believed the 
> longest length should be a nice, round fraction of the extent.  I 
> forget the forget the value Rod suggested; possibly it was 2/3 (i.e. 
> 26800).  But whatever it was, it was ruled out before Andrew's most 
> recent contribution, which now rules out 3/4 (i.e. 30240).
>
> Whilst I'd like to believe the longest possible length is a round 
> number, I don't actually think it's likely to be the case.
>
> RAS 

FFrom Rod's write up:


        31,136 Bristol Surprise

This is not an actual composition, but an identification of the 973 
leads that are mutually true, It is based on a 7-part plan, the 
part-ends being the lead-ends of the plain course, e.g. 3527486, It was 
produced in the late 1960’s, Peter and I were convinced that one more 
set of seven leads must be possible on this plan (since 973 = 7 x 139, 
an implausible maximum number), but we never improved on it, We also 
explored the more general problem of identifying a maximum set, given 
the false lead heads, Can an analytical solution be found? Do the 
relationships between the FCHs point to a structure of mutually true 
leads? Are there clues to indicate whether a 3, 5 or 7-part plan is most 
efficient? It would indeed be interesting to see whether anyone can shed 
some light on this. Here are the 139 header leads (i.e. with the 8th at 
home):

        -----------------------------------------------------------------------
        000007       000070       000700       007000       070000       700000
        All          265374       000764       607050       070604       700402
        except                    000762       407060       570060       740060
        256347                    000763       007024       076050       700054
                                  000753       207004       070504       700024
                                  000754       327564       374562       732564
                                  000752       357462       274365       725364
                                  000732       567432       675432       764253
                                  000734       647532       476532       764532
                                  000724       527634       675324       726534
                                                                         752634
        -----------------------------------------------------------------------
          59            1           27           17           17           18
        -----------------------------------------------------------------------


Richard




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