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The PAH-water (PAH = polycyclic aromatic hydrocarbon) interactions occur in interstellar ice grains and in atmospheres of planets and can serve as models for the interaction between water and graphite-like structures. We investigated clusters of several PAHs (naphthalene, cyanonaphthalene, phenanthrene, and anthracene) with water in a molecular beam experiment supported by theoretical calculations. The mass spectra of the negatively charged [(PAH)<sub><i>m</i></sub>(H<sub>2</sub>O)<sub><i>n</i></sub>]<sup>-</sup> ions show strong "magic peaks" for <i>n</i> = 4. At the same time, it is well-known that the bare water tetramer anion (H<sub>2</sub>O)<sub>4</sub><sup>-</sup> is quite elusive. We argue that the observed magic peaks originate from the higher stability of the neutral water tetramer that is attached to the charged PAH cluster. Our calculations of the structure and energetics of the neutral clusters (Np)<sub><i>m</i></sub>(H<sub>2</sub>O)<sub><i>n</i></sub> with <i>m</i> = 1 and 2 and <i>n</i> = 1-9 (Np = naphthalene) confirm this conclusion. They reveal another "magic" number <i>n</i> = 8 that is also seen experimentally. These findings advance our understanding of PAH-water interaction at a molecular level and provide preferred structural patterns for medium-size PAH-water clusters, which have implications for astrochemistry.