[r-t] Treble Dodging Royal (Universal Four Part)

[J. J. Bissell]

Dear All,

In case anyone is interested (and apparently very few of you are), I decided to write a script to search for other arrangements on the four-part plan described in my previous post to this list. 

It looks like I got lucky. Possibility of faulty code excepted, results indicate that the arrangement I proposed originally is unique in containing all LB5 courses in full (see appended text*). No arrangements exist with all LB5 course in full for the lead-head groups not covered by my original composition.

Is anyone willing to verify this result? I admit to finding it slightly surprising.

Best wishes,


John


*Appended text:

Four-part plan: Three courses called using a sequence S of bobs; one course called using a sequence x of bobs; call S four times to give 12 courses; insert x at two equidistant points to give 14 courses total. For example, S = {H,W,M,W,H}, with x = {M,W}; call S four times, insert x as courses 2 & 9 of composition.

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Summary results from search over arrangements of four-part plan:

[Using LHG a (likewise for all LHGs a, d1, & e, and on reversal, LHGs m, j1 & h)]

total possible arrangements (including degenerate arrangements): 28672

false arrangements : 26582
true  arrangements : 2090

true arrangements that don't come round : 1201
true arrangements that come round       : 889

true arrangements that come round without all LB5 courses in full : 889
true arrangements that come round with all LB5 courses in full    : 0
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Summary results from search over arrangements of four-part plan:

[Using LHG f (likewise for all LHGs b, c1, & f, and on reversal, LHGs l, k1 & g)]

total possible arrangements (including degenerate arrangements): 28672

false arrangements : 26909
true  arrangements : 1763

true arrangements that don't come round : 1077
true arrangements that come round       : 686

true arrangements that come round without all LB5 courses in full : 685
true arrangements that come round with all LB5 courses in full    : 1
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As expected, the arrangement with all LB5 courses in full is identical to the one I posted originally.