There is a single player puzzle game where it start with one hexagon piece and you put one hexagon piece next to an existing piece A matching edge can either be different however extra score is given

One possible search method would be Monte Carlo Tree Search (MCTS). MCTS is a heuristic search algorithm that uses random simulations and statistical analysis to determine the best next move. It has been successfully applied to various games, including Go and Chess.

In the case of the hexagon puzzle game, MCTS could work by simulating a number of random moves from the current state of the board, and then selecting the move that leads to the highest score based on the simulation results. The simulation could be guided by heuristics such as prioritizing pieces that match the existing ones, or completing quests.

As the game progresses and the search space expands, MCTS could adapt by increasing the number of simulations or adjusting the selection policy to focus on promising branches. It could also consider the limited amount of future pieces by estimating the potential score of each move based on the remaining pieces and the current board state.

Overall, MCTS offers a flexible and robust search method that can handle the complexity and uncertainty of the hexagon puzzle game