I know that answer already before I did it
The Hardest Puzzle Ever Composed
To me this is the hardest puzzle ever composed. Composed by J.N. Babson for Bretano's Chess Monthly in 1882. Mate on the 1220th move, after compelling Black to make three successive and complete Knight's tours! This is from The Fireside Book of Chess. Page88.
Mate in 1, not mate in 1220.

Regarding Babson's mate in 1220 after compelling three complete knight tours, um, what month of Brentano's Chess Monthly was that published in? I'm guessing April. As no solution to this puzzle was ever given, this smells like an April Fools joke.
If you go to youtube, search "hardest checkmate in one puzzle in the world", and skip to the answer, it will be an enpasant or whatever that is called.