[r-t] random pn

[Philip Saddleton]

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