[r-t] Method Generator

Don Morrison dfm at ringing.org
Thu Apr 16 21:03:35 UTC 2015

On Wed, Apr 15, 2015 at 7:07 PM, Alexander Holroyd <holroyd at math.ubc.ca> 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.

But he said "regular" by which I assumed he meant Plain Bob lead
heads. If I've figured the combinatorics correctly doesn't that reduce
it by a further factor of about 15? Not a big difference, of course, I
presume the end result when you consider other cross section changes
is still well into the billions.

Don Morrison <dfm at ringing.org>
"I rejoice that there are owls."
          -- Henry David Thoreau, _Walden_

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