[r-t] Crambo

Philip Earis pje24 at cantab.net
Sat Aug 5 18:02:00 UTC 2006

Professor Holroyd, you're a genius.

A random question - do any 'perfect' 6-part principle extents of minor exist 
(ie a plain course with 120 rows per lead which generates the extent)?  I 
can't think of anything off the top of my head, but may be missing something 

----- Original Message ----- 
From: "Alexander Holroyd" <holroyd at math.ubc.ca>
To: <ringing-theory at bellringers.net>
Sent: Friday, August 04, 2006 9:30 PM
Subject: Re: [r-t] Crambo

> Are you saying that you can prove it's always possible to get an extent in
> this way from any in-course extent?  If so I don't get it.  Obviously
> there are lots of ways to resolve the double changes into pairs of single
> changes, but one has to do it in such a way that the 60 out-of-course rows
> so introduced are all different.  Most ways fail to achieve this, e.g.
> turning 3.1 into 345.123.123.145 !
> ander
>>> All of them are strange and unsymmetrical, so what is really going one
>>> here?  I don't know.  E.g. can you prove or disprove that any in-course
>>> extent of doubles can be treated in this way?
>> I wpuld have said yes in that if you have an extent of pure doubles
>> (say Grandsire or Rev Grandsire called P B P B P B or the plain course
>> of Stedman or Rev Stedman or Carter's or Rev Carters) then, since each
>> row is produced by a double then two singles are bound to accomplish
>> the same thing. Thus if we compare the backstroke rows of Crambo we
>> get:
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