Monte-Carlo-Solution for masak's mini-challenge at http://irclog.perlgeek.de/perl6/2013-01-03#i_6294536

carlo.pl

for 1..* -> $N {
    my $sum   = 0;
    my $count =  $N**2;
    for ^$count {
        my @f = (^$N).pick(*);
        my %seen;
        %seen{0} = True;
        my $current = 0;
        repeat {
            $current = @f[$current];
            $sum++;
        } while !%seen{$current};
    }
    say join "\t", $N, $sum / $count;
}