[r-t] Crambo

[Alexander Holroyd]

Dear mew (and everyone),

Probably we are just talking at cross-purposes here, and are basically 
asking the same question.

The "logic" I am talking about in Crambo goes something like:

1. Stedman 5 is a beautiful in-course extent.

2. There is a general way of potentially going from an in-course extent to 
a full extent (which in general might yield no solutions, one solution, or 
many solutions, so far as I know)

3. Applied to Stedman 5, this way yields exactly one solution (even if we 
_don't_ insist on it being a 5-part), and that's Crambo.

4. Ergo, Crambo is an elegant gem, well worth ringing, naming and 
generally getting excited about!

That's all I meant by "logic".  (Incidentally very little trial-and-error 
is needed in step 3.  Just the fact that one mustn't repeat the same place 
notation immediately means that one has very little choice...  For sure FS 
_might_ easily have done this).

There are lots of other in-course extents of doubles other than the four I 
mentioned (most of them are just less pretty) - Richard Smith can supply a 
list.  My question is: is it true that the technique of step 2 can be 
applied to each of them to yield a full extent?  The fact that it can in 4 
cases certainly doesn't prove this.  In principle one could answer by a 
computer search, but I would prefer a simple argument if one exists (and I 
think it might...)  Just because none of us can see such an argument 
immediately doesn't mean there isn't one!  ;-)

all the best, ander


> Unless I'm mistaken, you yourself have demonstrated that it works on a
> plain course of Stedman, or of Carter's or of Grandsire called pbpbpb.
> Having demonstrated that it is indeed possible, why would you need
> proof that it is possible or do you know of other true extents of
> in-course Doubles other than the reverse of the above & rotations of
> the above etc?
>
> In short, I think that there is no percievable logic behind the
> production of Crambo and I am at a loss as to how Stedman discovered
> it or indeed - as I mentioned - How he discovered London Pleasure