[r-t] Place methods

[Richard Smith]

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 
places.

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 
methods:

   &5.1.2.1.5,1 Untitled Differential Place Doubles
   &5.1.2.1.5,4 Oake Place Doubles
   5.1.2.1.5.1.5.1.5.4 Untitled Place Doubles
   5.1.5.1.2.1.5.4.5.1 Untitled Place Doubles
   5.1.5.1.5.1.2.1.5.4 Untitled Place Doubles
   5.1.5.1.5.1.2.4.5.1 Untitled Differential Place Doubles
   5.4.2.1.5.1.5.1.5.1 Untitled Differential Place Doubles
   5.4.5.1.2.1.5.1.5.1 Untitled Place Doubles
   &5.4.5.1.2,1 Dunston Place Doubles
   &5.4.5.1.5,1 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 &34.1.7.1.34.1.34,1, which feels very 
Magenta.

RAS