# [r-t] Method Generator

Richard Smith richard at ex-parrot.com
Thu Apr 30 16:38:45 UTC 2015

```Alexander Holroyd wrote:

> To get a very rough idea of the possible numbers, consider the (false) method
> &xxx4xxx36xxx5xxx7,2.  This has 42 locations in the half lead where you can
> insert two consecutive places in a dodge, giving 2^42 > 4 billion
> possibilities.  If you want no 3 consecutive blows, it will be closer to
> 1.618^42 ~ 500 million (1.618 is the golden ratio).  Some of these will be
> false - since falseness can occur in 2 possible places in each section, the
> probability of such a method being true might be something like (7/8)^8 =
> 0.34, leading to an estimate of maybe 200 million methods of this type.
>
> Of course, these methods are far from being the only ones.
>
> Based on the above and vague intuition, I would guess the total number is
> between a billion and a trillion.

You've misjudged quite how large a contribution comes from
the Derwent-like methods you considered first.  There are in
fact only 541,822,598 palindromic treble-dodging major
consecutive blows in one place.

The complete list is 18GB long and was generated in 13 days
with the following command:

methsearch -b8 -p2 -G1 -sr -Cu -R'\$q' -o td8.txt