[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
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
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