[r-t] Method Generator

[Richard Smith]

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 
methods with regular lead heads and no more than two 
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

If anyone wants access to the list, or want any statistical 
analysis carrying outing out on it, please let me know.

RAS