[r-t] Triples puzzles

[Alexander E Holroyd]

Excellent questions.

 >>     This might be a silly question but do at least parts 1 and 3
 >>     definitely have a solution? Or might the answer be no to 
either/both?

If either 1 or 3 does not have a solution then it would resolve a famous 
60-year old mathematical problem, the Lovasz conjecture for Cayley graphs
http://en.wikipedia.org/wiki/Lov%C3%A1sz_conjecture
A proof that either was impossible would make you famous (in 
mathematics).  I think it's more likely that there are solutions to both 
1 and 3, but I don't know.

> Perhaps we should define question 0:
>      0. define 'good' ??

That's bound to be subjective, but what I have in mind is something that 
it would be fun and practical to ring as a peal.

>>         1. Find an extent using only the three place notations 3,5,147.
>>         2. Find a good one.
>>         3. Find an extent using only the three place notations 1,7,345.
>>         4. Find a good one.