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<p class="MsoNormal"
style="margin-bottom:10.0pt;line-height:115%;mso-layout-grid-align:
none;text-autospace:none"><span
style="font-size:11.0pt;mso-ansi-language:
EN" lang="EN"> Hi All,<br>
</span></p>
<p class="MsoBodyText"><span
style="font-size:12.0pt;mso-bidi-font-size:
11.0pt" lang="EN">I named the result after Tony Smith who, as
far as I know, was the
first to mention its use in a ringing context at RW71/974. This
naming is not
unknown in the mathematical litereature - not after the
originator which Tony
did not claime - but after its populariser. (I know of another
much more famous
example - but can't find the reference).</span></p>
<p class="MsoNormal"
style="margin-bottom:10.0pt;line-height:115%;mso-layout-grid-align:
none;text-autospace:none"><span style="mso-bidi-font-size:11.0pt;
mso-ansi-language:EN" lang="EN">As it happens, we were
discussing in the car on Saturday night that it
is necessary, but not sufficient. All the theorem does is to
give a quick test
for one class of methods not having extents. As Richard says it
does not mean
an extent is possible. This asym. Doubles method - </span><span
style="mso-bidi-font-size:11.0pt">3.14.5.3.5.123.125.1.345 -
'passes the test'
but seems to have only one possible 'touch' - a 4-lead course
using 125 as the
lead end. Others have a set of 'required leads' but these cannot
be joined up
into an extent, such as 3.1.5.3.345.3.5.14.3 which has a maximum
length of 100
with any combination of lead-end change. </span></p>
<span
style="font-size:12.0pt;mso-bidi-font-size:11.0pt;font-family:"Times
New Roman";
mso-fareast-font-family:"Times New
Roman";mso-ansi-language:EN-GB;mso-fareast-language:
EN-US;mso-bidi-language:AR-SA">The only 4-lead doubles methods
which seem to
have extents are those for which the plain lead is plain hunt.
Another way
(most likely better) of looking at this is that an ‘omit’ is a
‘required call’
for the method. This requires thinking that a method is defined up
to the first
lead-end and the ‘plain course’ is just identically generated
leads joined up
by an agreed ‘silent’ call.<br>
<br>
Best wishes<br>
R<br>
</span>
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