[r-t] Practical Extension

Robin Woolley robin at robinw.org.uk
Fri Aug 3 18:03:51 UTC 2018

Well, let's find out what Don actually thinks with a direct question.

Marple D6 is &x34x4x2x1.34x34.1,1.

It has four decision compliant extensions (RAS):

2DE/2FG -34-4-2-1.34-34.1.56-56.1,2 (8 [2] 60)
2DE/5FG -34-4-2-1.34-34.1.34-34.1,2 (8 [2] 60)
2BC/2FG -34-4-256-6.34-34.1.56-56.1,2 (8 [2] 60)
2BC/5FG -34-4-256-6.34-34.1.34-34.1,2 (8 [2] 60)

Don said he preferred the 56x56 extension of Kent to, inter alia, the 
34x34.1.56x56 or the 56x56.1.56x56. These, on symmetry grounds, are 
exactly the extensions below the treble in these four versions.

[The extensions above are the Kent/York and Cambridge versions)

In order to fully understand your position, can you 'criticise' - in the 
sense of 'To evaluate (something), and judge its merits and faults' 
rather than 'find fault with' these extensions?

The first question which arises to me is, given these are the only 
compliant extensions, would you say that Marple is inextensible? (Yes or 
no would do very well here!) Why?

b.t.w., when you mention the 4-colour problem, what was the context of 
this? As I recall, a computer was used to check a large number of 
situations but this had already been reduced to c2000 from infinity by 
using mathematics.

There are some hard problems. Some are theoretically hard like Quantum 
Theory. Others, like extension, are easy conceptually but it is the size 
of the problem which makes them hard.

On another point, aren't we being sidetracked by difficult cases such as 
Bristol. If we haven't sorted the easy ones, then it makes no sense to 
tackle the odd-ball ones. We must walk before we can run.

I seem to remember something from 40-odd years ago, and it has been 
repeated since, that Bristol 4n is a different sequence to Bristol 
(4n+2) Perhaps it's true!


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