When I wrote a simple program to simply go through all values of n starting from 1 and counting the occurence of each digit, whenever I got to a n of 99...99 the total number of each digit from 1 to 9 was the same with 0 consistently trailing ... but gaining.
n=9: 0=0; 19=1
n=99: 0=9; 19=20
n=999: 0=189; 19=300
n=9999: 0=2889; 19=4000
n=99999: 0=38889; 19=50000
....
and the pattern continues.
I think I just described in layman terms what the true mathemiticians described earlier in formulae.
