Challenges for physical solitaire puzzle games are typically designed in advance by humans and limited in number. Alternatively, some games incorporate rules for stochastic setup, where the human solver randomly sets up the game board before solving the challenge. These setup rules greatly increase the number of possible challenges, but can often generate unsolvable or uninteresting challenges. To better understand the compromises involved in minimizing undesirable challenges, we examine three games where component design choices can influence the stochastic nature of the resulting challenge generation algorithms. We evaluate the effect of these components and algorithms on challenge solvability and challenge engagement. We find that algorithms which control randomness through entangling components based on sub-elements of the puzzle mechanics can generate interesting challenges with a high probability of being solvable.