[r-t] random pn

[Richard Smith]

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

Richard