Taking those out of Alekhine/Vilner anecdote.
The game starts from following position.
White can do 8 moves in a row, but only on the first 4 ranks. Then, after this preparation, they have to mate Black in four moves or earlier, regardless of Black's replies.
The game begins from a standard position. White play the following moves: 1. f3 2. Kf2 3. Kg3 4. Kh4. Black can make any moves in reply (except those that hinder the King's journey to h4, so, for instance, they can't play 1. f3 e6 2. Kf2 Bd6), and after 4. Kh4, they have to checkmate the White King on that move.
I personally don't know the solutions.