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Monte Carlo tree search is the state of the art for multiple games and for solving puzzles such as Morpion Solitaire. Nested Monte Carlo (NMC) search is a Monte Carlo tree search algorithm that works well for solving puzzles. We propose to enhance NMC search with beam search. We test the algorithm on Morpion Solitaire. Thanks to beam search, our program has been able to match the record score of 82 moves. Monte Carlo beam search achieves better scores in less time than NMC search alone.