[r-t] Crambo

[edward martin]

Ander,
Thanks for your very friendly reply.
Having thought more about it and also having taken a look at Orpheus,
I am persuaded that you are right. First came Stedman's Principle from
which he derived both Crambo & Orpheus.

Using nothing but 1sts 3rds & 5ths places I only know of true 60s   as
those obtained from  Grandsire (P B P B P B)  its reverse and
rotations
and from the plain course of Stedman / Carter and their reverses &
rotations. As you say that there are in fact lots others, I wonder if
you have the time, would you send them to me?
Thanks
mew

On 8/6/06, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
> 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
>