[r-t] Challenge
Robin Woolley
robin at robinw.org.uk
Tue Apr 30 10:27:04 UTC 2013
Hi All,
Talk of sets of true leads reminded me that there was something of the
sort in Giles B Thompson's 'Compleat Cambridge' (1997). The method
mentioned by John Goldthorpe and Glenn Taylor is discussed but perhaps
the best description of its concept is the analogy GBT gives:
Consider Chess. A Knight threatens eight squares. How many Knights can
be placed on a board so none threatens any other? Well, 64/8 = 8 but
this is not right. A Knight threatens squares of the opposite colour so
the answer is 32. As ringers, we happily say that a 'cps' method is true
if singles are not used.
GBT then quotes an article at RW62/838 by Gordon Halls and Denis
Carlisle. Inter alia they show that falseness of Group D (32546, 46253)
leads to a group of permitted course heads generated by 64523 -- if one
occurs, all may occur. Obviously, courses rather than leads were used in
1962 since it was the best that could be done at the time with this
technique give the size of the problem, but it would be interesting to
see the groups of permitted leads for the methods currently in question.
If an extent is required, the word 'permitted' becomes 'required'.
Just a thought.
Robin
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