[r-t] random pn
Philip Saddleton
pabs at cantab.net
Mon Dec 6 19:41:25 UTC 2004
Richard Smith wrote:
>Chris Poole wrote:
>
>
>
>>Here's a Friday teaser - suppose we're looking at methods on N bells. If
>>I just write down random pieces of valid place notation, and look at the
>>method that is the outcome of these ordered bits of pn, when do I expect
>>it to come round?
>>
>>
>
>Empirically, the answer seems to be about N!. Here are the
>results of 1000 random walks on 3 <= N <= 8 bells:
>
> Bells Mean S.D.
> 3 6.024 +/- 6.11812
> 4 23.451 +/- 32.8958
> 5 117.524 +/- 160.984
> 6 729.176 +/- 927.313
> 7 5367.71 +/- 6063.72
> 8 40103.5 +/- 4.2949e+06
>
>
>
The mean is precisely n!
Take any sequence containing m different elements, and join up the ends.
The mean distance between occurrences of the same element is m (this is
independent of the length of the sequence or the distribution of the
individual elements).
I initially thought Chris was asking a completely different question:
pick a random lead head, and what is the mean number of leads in a course?
--
pabs
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