[r-t] Odd Start Grandsire Doubles

[Mark Davies]

Robin writes,

> It seems to be true that - all 'plain' starts have an 'single' start
> 'dual' ending with the 'opposite' call
> (here's one: 91 bpbpsbpps)
> BUT
> there are some touches starting with a 'single' which have a 'plain' ending.
> (here's one: 61 ppsbpp)

Ah no sorry I'm with you. There is an asymmetry, because if we start 
with a single, we're only ringing half of it - the 3rd's place as the 
treble comes to lead is missed. However if we end with a single, the 
full thing is rung.

So, if we start with a plain and end with a single, there is dual 
calling, starting with a single and ending with a bob:

	p(bpbpsbpp)s
	s(bpbpsbpp)b

However if we start with a single and end with a plain, there is no 
reversal - we would need a new call with place notation 5.123.

Therefore there are three sets of solutions, depending on the starting 
and finishing call:

	1. P->S
	2. S->B
	3. S->P

There are equal numbers of touches in the first two sets.

Note that you might equally well say that touches start with a bob or plain.

MBD

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