[r-t] doubles principle

Philip Saddleton pabs at cantab.net
Mon Jul 31 21:02:07 UTC 2006

edward martin said  on 25/07/2006 12:15:
> On 7/24/06, Alexander Holroyd <holroyd at math.ubc.ca> wrote:
>> The best I can manage is the following frankly pathetic extent.  Surely
>> someone can do better...
> Well I haven't made an exaustive study, but I did try to keep the
> structure in tact (iie Pn 5-1-5-1 or at worst at PN 5 allow 125 or
> 345; at 1 allow 123, 145; and at 3 allow 123, 345) Even so I didn't
> seem to be able to avoid having to reverse the normal flow of 5-1-5-1
> to 1-5-1-5 and often had to use jump changes to get any linkage.
> I would like to know the mathematics of why this principle doesn't
> work but since I have no mathematical training  I have to revert to
> flow charts noting that if this then that; and try to see the overal
> picture of the consequences of splitting plain hunt blocks in two
> halves.
> The result is I don't really see why it doesnt work except that I
> don't see hpw !it might work!!
> mew

This is similar to Handstroke Triples (see RW 99/728). My idea there was 
to find a block giving half the extent using half of each plain hunt 
block. Rotating this through 180 degrees gives the other half. The 
obvious calls would be 123 or 345 instead of 3. If an extent cannot be 
found with this approach it is probably because there is not enough room 
for manoeuvre. I would guess that with 125 or 145 as well that there 
might well be.


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