[r-t] Method Generator
holroyd at math.ubc.ca
Fri Apr 17 11:22:52 UTC 2015
Yes, you are probably right here.
On Thu, 16 Apr 2015, Don Morrison wrote:
> 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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