[r-t] 147 TDMM

[Richard Smith]

Stephen Penney wrote:

> Does all this tell you if it's possible to get the 
> standard 41 surprise methods into 7 distinct extents? Or 
> if not then what the fewest extents is?

It's always been assumed that you need considerably more 
than 7 extents to ring the standard 41 in whole extents, but 
I don't believe this has ever been firmly proved.  However 
we can now definitively say that you need at least twelve 
extents to get all 41.  I'm not sure I've ever seen a recipe 
for doing it in twelve extents before -- I think the best 
I've seen is thirteen, but I may be out of date.

Kelso, Warkworth and Norwich don't have any splices with 
methods amongst the 41.  (As has already been mentioned, the 
grid splice betwen Norwich, Westminster and Netherseale 
cannot be realised in a round block.)  A few other methods 
are also problematic: Lincoln only splices with Coldstream, 
Westminster only with Allendale, and Bamborough only with 
Bacup.  That's six extents straight away.

There are no splices between right-place and wrong-place 
overworks in the 41, so we can consider the Cambridge / 
Norwich overworks separately to the Carlisle / London ones. 
Let's look at the right place ones first.  Wearmouth is a 
good starting point as it only splices with Lightfoot and 
optionally Netherseale, together with their sixth place 
variants.  So we need something like the Lightfoot six as an 
extent.

That leaves the twelve Cambridge methods.  The most we can 
get into a single extent is ten (it misses Ipswich and 
Norfolk), so we may as well use the two usual Cambridge 
extents: the six right place ones in one, and the six wrong 
place ones in another.

(There are alternative ways of dividing the eighteen 
remaining Norwich and Cambridge methods into three extents. 
One possibility is to have the ten method extent of 
Cambridge methods, the Cambridge - Ipswich - Netherseale 
grid splice, and the four Lightfoot methods.  I expect there 
are other possibilities too, but you definitely need three 
extents to mop them all up.)

After that, Wells can be spliced with London and optionally 
Cunecastre.  We cannot get anything further (e.g. Carlisle) 
into an extent with Wells.  That wraps up the London over 
methods.

The Carlisle-over methods don't splice with any of the 
right-place overworks, and it's not possible to get all 
eleven into a single extent.  Even getting them into two 
exents is surprisingly tricky.  But a good start might be 
the eight method extent (excluding Northumberland, Whitley 
and Carlisle) and then the missing three.

I don't believe I've ever seen this eight method extent 
published before, so I'll give it here.  However, I'm sure 
someone (probably JSW) has come up with something on this 
plan before.

   720 Spliced Surprise Minor (8m)

     123456 Nw       162345 Ch       164235 Mu
   - 156423 Nw     - 162453 Sa     - 164352 Mo
     134256 Nw     - 134625 Mu       152436 Mo
     162534 Nw       142356 Mu       136245 Nw
   - 134562 Ak       125463 Ct     - 145236 Ch
     125634 Mu       163542 Sa     - 145362 Nw
     153246 Mu       156234 Ch       123645 Nw
   - 153462 Wo     - 156342 Mo     - 145623 Mo
     124653 Ak       142635 Mo       123564 Nw
     136524 Ch       135264 Nw     - 164523 Mo
     162345        - 164235          123456

That gets you the 41 in 12 extents, e.g.:

   1.  Ke
   2.  Li Co
   3.  We Lo Cu

   4.  Sa Wo Mu Ak Ct Nw Mo Ch
   5.  Nb Wh Cl

   6.  Wk
   7.  No
   8.  Ws Ad
   9.  Bm Bc
   10. Ne Ab Lf Ro Wm St

   11. Ip Nf Cm Pr Bo Hu
   12. Su He Yo Du Bv Bk

This also means that the CC Spliced Minor Collection is out 
of date when it states on page 50 that "the maximum number 
of regular surprise methods from the 1961 collection which 
can be splcid into seven extents is 31".  We can get 34 by 
taking the extents above, dropping the three single methods 
extents and two of the double method extents.

RAS