This problem took me at least 90 seconds to solve. Initially, I was looking at all the wrong ideas. It took me so long it that chess.com only gave me one rating point for solving it.
I didn't like the White response after the first move, because I thought it was dumb. It is the choice that delays mate the longest. I had a different White defense in mind, so I went into the analysis option and it turns out my defense (2. f4) allows mate in 1, which I didn't see.
P.S. Check out this article. I am not convinced that there is a solution. http://www.telegraph.co.uk/
science/2017/03/14/can-solve- chess-problem-holds-key-human- consciousness/