Thanks, Dave.  Very interesting.  How about:  A random string is the 
hardest password to guess.  In that sense a random string is optimal.  But 
use of * or ! in the shadow file does not provide a password so that is 
optimal when you don't need a password.

I had seen those asterisks and double-bangs !! in the shadow file for 
years and never knew what that was about.  Before that they used to be in 
/etc/password.  Remember that?  There wasn't always a shadow file and the 
encrypted passwords used to be readable by all!

Mike