[r-t] Place methods
richard at ex-parrot.com
Mon Oct 12 12:17:28 UTC 2009
I believe that, except Plain Hunt, there are no plain
methods which do not contain any points or dodges (i.e. are
Place methods) and which do not contain any adjacent
For example, Reverse Canterbury Doubles does not contain
either points or dodges, but the 345 place notation at the
start contains adjacent places.
I have done an exhaustive search on up to 7 bells and also
checked the case of symmetric methods on 8, 9 and 10 bells,
and I have found nothing, so I am moderately convinced that
Plain Hunt is the only example.
But I cannot see any obvious reason why this should be so.
Can anyone else?
I stumbled across this oddity while trying to prove that all
Place methods are trivial variants of non-Place methods made
by changes dodges into pairs of places and similar. It
turns out that this isn't true, though such 'intrisically'
Place methods are rare.
On four bells, Single, Reverse and Double Court all
intrinsic Place methods, as is Grandsire. A bobbed lead of
Plain Bob Doubles is an example on five bells, but that's
not a legal method as it has more hunt bells than working
bells. On five, if you limit it to legal methods (i.e. a
true plain course, no more than four blows in one place and
more working bells than hunt bells), there are only ten such
&22.214.171.124.5,1 Untitled Differential Place Doubles
&126.96.36.199.5,4 Oake Place Doubles
188.8.131.52.184.108.40.206.5.4 Untitled Place Doubles
220.127.116.11.18.104.22.168.5.1 Untitled Place Doubles
22.214.171.124.126.96.36.199.5.4 Untitled Place Doubles
188.8.131.52.184.108.40.206.5.1 Untitled Differential Place Doubles
220.127.116.11.18.104.22.168.5.1 Untitled Differential Place Doubles
22.214.171.124.126.96.36.199.5.1 Untitled Place Doubles
&188.8.131.52.2,1 Dunston Place Doubles
&184.108.40.206.5,1 Untitled Differential Place Doubles
On six there are 250 legal methods, but all are either
differential hunters or asymmetric. On seven symmetric
non-differential hunters methods exist (152 to be precise),
and, unsurprisingly, none have ever been rung. On eight, as
on six, there are no symmetric non-differential hunters.
I had thought that all of the methods contained four blows
at lead or lie with an adjacent place in the middle of it,
but this is not actually so -- on seven bells you can have
something like &220.127.116.11.34.1.34,1, which feels very
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