[r-t] All runs in a quarter, proper version!

[Alexander Holroyd]

There was a mistake in the p.n. for the Block A line.  Here it is.

http://www.boojum.org.uk/cgi-bin/line.pl?bells=8&pn=56-4.56.1.56.1.34.5-36.5.34-4.3.6-56-5.34.1.34.5-5-3.4.3.56-5-1-4-34.6.5.6-4-4.56.1.56.4-34-3.6.5-56.4.36-4.56.1.34.1.34.5-34&qs=Line&action.x=1

On Fri, 30 Jan 2015, Alexander Holroyd wrote:

> On Fri, 16 Jan 2015, Philip Earis wrote:
>
>> As the overall aim here is to get all 480 run rows, I’m tempted to 
>> generalise and rephrase accordingly...what’s the shortest length 8-part 
>> anyone can produce which contains all 480 runs? Elegance and maximal 
>> symmetry are desirable.
>> 
>> Posing the question like this lends itself to interesting architectured 
>> approaches...previous 480-run solutions (whilst superb) have applied 
>> traditional constraints such as consisting of a number of different, 
>> treble-dominated methods.
>
> Thanks for this challenge, Philip.  After considerable effort I believe I 
> have a good solution.  All 480 runs (including 1234s this time) in a longish 
> quarter length (3.2 runs per row on average!).  16-part structure plus exact 
> rotation symmetry.  At most a 2-row gap between "potential runs" (including 
> things like 7812).  No long places.  No single or double changes.  Lots of 
> variety in run types, and lots of movement across 45.
>
> Also the simplicity and obvious structure make it the perfect thing for any 
> fledgling band to toss off on the way to the pub.
>
> 1536 Major
> Alexander E Holroyd
>
>    12345678
> ------------
> x   34562871 )
> 18  35426781 )A
> z   45678123 )
> ------------
> 2A  23456781
> ------------
> x   45673182 )
> 38  54637812 )
> y   65437281 )B
> 16  64573218 )
> z   54321876 )
> ------------
> x   32184675 )
> 38  23148765 )
> y   12348576 )
> 36  21384567 )C
> y   32184756 )
> 16  31248765 )
> z   21876543 )
> ------------
> 6C  87654321
> ------------
> B   56781234
> ------------
> 4A  12345678
> ------------
>
> x = 56-4.56.1.56.1.34.5-36.5.34-4.3.6-56-5.34.1.34.5-5-3.4.3.56-5-
> y = 4-4-6.3.56.34.1.34-5.4-56.1.56.34.6.3-5-5
> z = -4-34.6.5.6-4-4.56.1.56.4-34-3.6.5-56.4.36-4.56.1.34.1.34.5-34
>
> Blocks A, B and C each have rotational symmetry
>
> 24 each 1234s, 2345s, 3456s, 4567s, 5678s, forwards and backwards, front and 
> back (3.2 rows per run!)
>
>
> Block B grid:
>
> http://www.boojum.org.uk/cgi-bin/line.pl?bells=8&pn=56-4.56.1.56.1.34.5-36.5.34-4.3.6-56-5.34.1.34.5-5-3.4.3.56-5-3.4-4-6.3.56.34.1.34-5.%204-56.1.56.34.6.3-5-5.6-4-34.6.5.6-4-4.56.1.56.4-34-3.6.5-56.4.36-4.56.1.34.1.34.5-34&title=Block%20B&qs=Grid&lines=1&line=2&line1=a&line2=n&style=1&place-bellsx=on&miss-numbers=never&rule=36%3B61&action.x=1
>
> Block A line:
>
> http://www.boojum.org.uk/cgi-bin/line.pl?bells=8&pn=56-4.56.1.56.1.34.5-36.5.34-4.3.6-56-5.34.1.34.5-5-3.4.3.56-5.1.-4-34.6.5.6-4-4.56.1.56.4-34-3.6.5-56.4.36-4.56.1.34.1.34.5-34&title=Block%20A&qs=Line&action.x=1
>
>
>
>
>
>