Intersect Three

Consider a table of 7 rows and 7 columns. We want to fill some of the cells with a \( * \), such that the intersection of any 3 (not necessarily consecutive) rows and any 3 (not necessarily consecutive) columns will contain a cell with a \( * \). What is the minimum number of \(*\) required?

Details and assumptions

Clarification: The 4 by 4 table with only 1 \( * \) in the cell \( (3,3) \) doesn't satisfy the conditions, because the intersection of rows 1, 2, 4, and columns 1, 3, 4, do not contain any cell with a \( *\).

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