# [r-t] doubles principle

Alexander Holroyd holroyd at math.ubc.ca
Thu Jul 13 04:15:18 UTC 2006

```> As I understand the problem: There are 24 row types in the extent (if
> you like the row types can be defined by setting out the 24 rows with
> say 5 always in 5ths place)
> Your principle has 5 row types in its plain course
> Since there are only 24 row types, one cannot set out the extent on
> paper as being so many plain course structures because 24 is not
> divisible by 5

I'm not quite sure what you are saying here.  Using the group of order 20
generated by 23451 and 13524 there are indeed 24 row types, but there is
no requirement to do this.  Certainly there is no set of plain courses
which give the extent, but this is true of many methods (eg Grandsire 5,
Stedman 7), and should not in itself be considered a serious problem...

You could perhaps have 4 plain course structures
> containg 20 row types but the remaining 4 row types would be hard to
> get  in sets of 5 rows

The example I gave shows that you can do exactly this.  The problem is to
join the 4 leads to the 4 courses.

Alternatively, obviously one can split the extent into leads in many ways
(since if you start your lead at the 3, it is just half a course of plain
hunt).  So just find a reasonable way to join them together.

What do I mean by a passable extent?  Of course this is open to
interpretation, but how about: at most 3 types of call (potentially
occurring in different places in the lead), and at least a few (preferably
a lot) whole plain leads.

cheers, Ander

```