Alright, we have a large set of possible moves (what the player is allowed to do). We also have a well defined state of success that defines the desired goal. We want to generate a configuration where for the purpose of this question, only 1 set of moves leads to a victory within k steps. We also have a solver that can find all possible solutions for a given configuration problem.
For example let's take Chess, how would you place a set of chess pieces on a board such that only a specific set of moves by White will result in Check Mate?