[r-t] extents in half leads, again

Mike Ovenden mike.ovenden at homecall.co.uk
Wed Jul 13 22:25:24 UTC 2005

We've had a couple of letters in the comic recently referring to "methods
with -1256- when the treble is in 3-4 which cannot generate an extent
without special half lead calls" (p619, p644).

That seems a bit optimistic.  I don't think you can get an extent of most of
them even *with* half lead calls (unless they're extraordinarily special
calls, like substituting leads of other methods perhaps :)

Do enlighten me if I'm missing something obvious here.

I had a look at the most recent batch only: Hafnium - Mica.  Assuming the
treble stays in the hunt, and no more than 2 types of call at either half or
full lead, the closest I got was with Mendelevium and Pearl, neither of
which quite works.  Using previous definitions of sets L and R, I get ...

Mendelevium Delight x,34,x,1456,x,1256,x,16,x,12,x,56, L12 (142635)
L {123456,123465,134256,134265,142356,142365}
R {124356,124365,132456,132465,143256,143265}
so if the half lead head 123456 is present, the HLH 124365 can't be, i.e. an
extent can't contain any plain leads.

Pearl Delight x,56,x,16,x,1256,x,36,x,34,x,56, L12 (142563)
L {123456,125463,126435,143256,145263,146235}
R {123465,125436,126453,143265,145236,146253}
In this case the lead end is 145236, which is in set R, i.e. an extent can't
contain any plain half leads.

However, in both cases you get something vaguely acceptable by changing the
lead end / half lead places.

(1) Ring Mendelevium variant with a 16 lead end; half lead single in 12;
lead end single in 23.
    720 (3 pt)
s s 163254
s   123465
s s 125643
s s 156324
  s 134256

(2) Ring Pearl variant with 16 half lead and 14 lead end; both singles are
    720 (3 pt)
  s 162543
s s 163245
s   152643
s s 125463
s s 134256

Yes, it's the same pattern of singles, rotated a bit.  (And it's the same as
the extent I gave recently for some other Delight Minor method.)

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