[r-t] Practical Extension

Robin Woolley robin at robinw.org.uk
Sat Jul 28 10:18:01 UTC 2018

What does the Exercise know - based on previously published collections 
of extensions?

RAS provided extensions for six-bells methods 'from the book' and 
included both plain and treble dodging methods - about 15 years ago.

GACJ, MBD et al. provided extensions of all the treble-dodging Minor 
methods about 18 months ago.

The fallacy, as far as I can see, is the assumption that there is always 
an algorithm to find a 'contraction' - for want of a better word. This 
is based upon the idea that every method and stage n is related to a 
method at stage n-2. Not everything has to be an extension somehow of a 
Minimus or Doubles method. Some methods have two parents.

I also have no problem with some methods being in-extensible such as 
Norfolk S6.

Let us take Yorkshire S8 for example. This is regarded as the progenitor 
of a set of extensions. However, this is a case where, if adjacency is 
removed, Yorkshire is an extension of Cambridge S6. (Someone told me on 
this line once that this was nonsense, so what do I know?)

Andrew Johnson hits the obvious nail over the head. We know that there 
are only eleven plain Minimus methods. The starting point is to find all 
extensions of these eleven, followed by the extensions of all the 
single-hunt doubles methods. This, in every day terms, is a very small 
problem - there are at most 36 lead-structures with 4 lead-ends.

Finally, method extension is a practical subject and is best understood 
by doing it yourself by hand. When you were at school, what did you do 
in maths. lessons? You did lots and lots and lots of problems and, if 
you were lucky, when you got to the exam, you didn't even have to think 
much about the answer as it was almost instinctive.

You understand it by doing. You also learn from those who know how to do 
it - not by assuming they don't know what they are doing!

Some years ago on this list, one or two of us were having difficulty 
with the interpretation of some element by the MC of the Extension 
Decision. Then one of us remarked, let us assume that the MC's 
interpretation (by example) is correct, then that would enable us to 
understand the Decision. As I have remarked before, having an idea is 
easy, writing it down so everyone understands it immediately, or easily, 
is not. It was a case of trying to find out, not how they said it, but 
what they meant.

Don. Have you ever tried extending a method by hand? No? Oh, "you really 
should (Lestrade)".

Alternatively, look at some extensions such as:

&-1-23-3,2 [Buxton]
1DE/5FG &-1-23-3-3,2 (8 [2] 60)
1DE/1EF &-1-23-45-5,2 (8 [2] 60)
1DE/5EF &-1-23-23-3,2 (8 [2] 60)
4AB/2EF &-4-23-25-5,2 (8 [2] 60)

&-1-3-3,2 [St Clement's College]
1DE/5FG &-1-3-3-3,2 (8 [2] 60)
1DE/2CD &-1-1-5-5,2 (8 [2] 60)
4AB/2EF &-4-3-5-5,2 (8 [2] 60)

&-1-1-5,1 [Reverse]
1DE/5FG &-1-1-5-5,1 (8 [2] 60)
1DE/4EF &-1-1-1-7,1 (8 [2] 60)

Best wishes

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