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The maximum number of clues in an \( n \times n \) American-style crossword puzzle grid is explored. Grid constructions provided for all \( n \) are proved to be maximal for all even \( n \). By using mixed integer linear programming, they are verified to be maximal for all odd \( n \leq 49 \). Further, for all \( n \leq 30 \), all maximal grids are provided.