Is there a name for puzzles where the goal is to avoid being checkmated in x moves? An example is this puzzle:
[Title "White to play and avoid being mated on or before move 4 (there is a unique solution)"]
[FEN "8/3r3K/8/7k/8/8/8/8 w - - 0 1"]
1. Kg8 Kg5 2. Kf8 Kf6 3. Kg8 Ra7 4. Kh8