Assignment 3 Blues

DFSA became extremely difficult extremely quickly this week. Even attempting to do question 1 on Assignment 3 was very challenging, and I am still had trouble coming up with a proper proof statement.
I created this diagram to help me understand how the automata in question one works but, I'm still having issues gaining some insight into how to actually tackles the proof that proves this machine needs a minimum of 16 states.... In this diagram the red arrows indicate accepting 0's, and the green accepting of blue. As recommended by Danny Heap the start state is indeed at the state where a string with no 0's resides as this is the only state that doesn't reach an accepting state in three hops. It would be easier to prove question one with this diagram then without, as it can be clearly seen that if two of the four bit string resided in the same state would be impossible as each state has a unique connection to other states...