[r-t] Crambo theorem revisited

edward martin edward.w.martin at gmail.com
Tue Sep 28 17:47:41 BST 2010

On 28 September 2010 15:53, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
> This looks interesting, Eddie.  What properties does it have?

each of the 120 rows occurs once at hand and once at back

> I suspect what Philip wanted was different however: something with all
> changes being single, and alternate rows forming Andrew's thing.  (Like
> Crambo).
> However, this will no longer have the each-row-once-at-hand-and-once-at-back
> property, because all th in-course rows will occur at the same stroke.

that's what I thought, hence the format as per orpheus ie  alternating
a double  and a single .
 Philip actually did say "by the addition of a single change between
alternate rows" which I take to mean alternate one double & one single
change,or as F.S says (p.119 Campanalogia) :" One change is double,
the next single, and so by turns.".
following his actual crambo (p.117 of Campanalogia, he says: "the
changes are all single" but as you say, this being the case then all
neg rows will be at back and all pos rows at hand.
so to get all changes of a 120 at both hand & back,Orpheus works but
crambo doesn't

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