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Nowadays, the field of Artificial Intelligence in Computer Games (AI in Games) is going to be more alluring since computer games challenge many aspects of AI with a wide range of problems, particularly general problems. One of these kinds of problems is Exploration, which states that an unknown environment must be explored by one or several agents. In this work, we have first introduced the Maze Dash puzzle as an exploration problem where the agent must find a Hamiltonian Path visiting all the cells. Then, we have investigated to find suitable methods by a focus on Monte-Carlo Tree Search (MCTS) and SAT to solve this puzzle quickly and accurately. An optimization has been applied to the proposed MCTS algorithm to obtain a promising result. Also, since the prefabricated test cases of this puzzle are not large enough to assay the proposed method, we have proposed and employed a technique to generate solvable test cases to evaluate the approaches. Eventually, the MCTS-based method has been assessed by the auto-generated test cases and compared with our implemented SAT approach that is considered a good rival. Our comparison indicates that the MCTS-based approach is an up-and-coming method that could cope with the test cases with small and medium sizes with faster run-time compared to SAT. However, for certain discussed reasons, including the features of the problem, tree search organization, and also the approach of MCTS in the Simulation step, MCTS takes more time to execute in Large size scenarios. Consequently, we have found the bottleneck for the MCTS-based method in significant test cases that could be improved in two real-world problems.