[r-t] Crambo

[edward martin]

On 8/4/06, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
> On Fri, 4 Aug 2006, edward martin wrote:
>
> > I tried in vain to put myself in FS's shoes and figure out what
> > percievable logic was behind the principle Crambo
>
> I recently realised that there is a beautiful and mysterious logic behind
> Crambo.

et cetra

I am now thoroughly convinced that F.S. devised his crambo from his
principle and thanks to all for your patience & the (to me) very
interesting developments
He has a method called Orpheus which is alternating doubles & singles
- he follows the PN of the principle and sticks 123 in after every row
to give the extent in the plain course.

It is rather perverse of me but I was interested in the way pure
doubles can be cramboed. I went in the other direction & figured out
what place notation would rule out the possibility of cramboing ie
successive handstrokes would have to be jump changes as would
successive backstrokes. Is it poss tro get a true 120?

Here's a very tedious one:

       12345
----------------
12  5 12435
1  45 14235
12  5 14325"
1  45 13425
12  5 13245
123   13254
12  5 13524
1  45 15324
12  5 15234
123   15243
12  5 15423
123   15432
-----------------
Call this 10 times but with
345 instead of 125* in all parts
except 1 and 5

PEs : 15432; 32154; 54321; 21543; 43215;    45123; 23451; 51234; 34512; 12345
I could have been mowing the back yard & have been better employed
but, I thought it was interesting problem :-)
mew