[r-t] internal runs

[Alan Reading]

Sounds like a massive challenge Ander!
It's something I've thought about before as well but only in passing as I'd
considered it outside the realms of the practical - but maybe it isn't...
I guess time will tell.

Cheers,
Alan

On 24 January 2013 21:50, Alexander Holroyd <holroyd at math.ubc.ca> wrote:

> Both of these look very impressive - thanks for sharing!
>
> Perhaps this is a suitable time for the following challenge (one that I
> first considered about 20 years ago)!  Find a normal length peal
> composition of major containing all the rows that contain a 4-bell run
> (back, front *or internal*).
>
> There are 1002 such rows (if my use of the inclusion-exculsion principle
> is correct).  Can it be done in a way that anyone would want to ring?
>
> Ander
>
> On Thu, 24 Jan 2013, Simon Gay wrote:
>
>
>> Here's the quarter peal composition (of Major) that David referred to. It
>> has 400 runs of 4 or more bells at the front or back, which I think is
>> pretty good in a quarter peal length.
>>
>> The quarter contains several Little methods, so alternate parts have the
>> treble hunting from the back and not reaching the front. Actually, as far
>> as I remember, when David first described his peal plan it also had this
>> feature, but now he is using Alliance methods rather than Little methods to
>> get the desired length.
>>
>> Simon
>>
>>
>>
>>
>> 1680 (1260) Spliced Major (7m)
>>
>> Simon J. Gay (based on an idea by David Hull)
>>
>>              12345678
>> ----------------------
>> Norwich LS -  14235678
>> Norwich LS -  13425678
>> Norwich LS    12364857
>> Oxford DLB    13286745
>> Norwich LS -  18326745
>> Norwich LS -  12836745
>> Norwich LS s  12378564
>> Bastow     s  12753486
>> Original      25147638
>> Original      54261873
>> Original      46582317
>> Original   s  68435271
>> Rev Bastow    83624751
>> Rev Bastow    32876541
>> ----------------------
>> 14 part
>>
>> - = 14
>> s = 1238 in Norwich LS, 1678 in Original
>>
>> In even-numbered parts, replace every method by its reverse and
>> swap bobs and singles between the front and the back. Original remains
>> the same method but its single becomes 1238.
>>
>> Contains 400 runs of 4 consecutive bells at the front or back.
>>
>>
>> For 1260 replace 35 leads of Norwich by Bastow.
>> To avoid losing runs, replace Norwich by Bastow
>> in the following places.
>>
>> 2a and 2b mean the first and second blocks of
>> 3 leads of Norwich in part 2, and so on.
>>
>> Keep 1 of the 36 leads as Norwich.
>>
>> Blocks: 2a,2b,3b,5a,6a,6b,9a,9b,10b,**12a,13a,13b
>>
>>
>> Unnamed methods:
>>
>> Norwich Little Surprise:
>> -34-14-12-14 le 18   14263857
>>
>> Reverse Norwich Little Surprise:
>> -56-58-78-58 le 18   24163758
>>
>> Oxford Differential Little Bob:
>> -1234 le 18   13264857
>>
>> Reverse Oxford Differential Little Bob:
>> -5678 le 18   24153768
>>
>> Reverse Bastow Little Bob:
>> -78 le 18   24163758
>>
>>
>>
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