This is a homework question, so I am only looking for hints.

I got a question in an assignments which states :

Design a DFA that accepts strings having 1 as the 4th character from the end, on the alphabet {0,1}

I have been at this for a few hours now, and I think that designing such a DFA is not possible. However, I am not sure how to move forward in this direction to write up a somewhat formal proof.

So, what should I try to do to prove or disprove my hypothesis?