Colouring a table with 4 colours

A \(15\times n\) table (where n is a positive integer) is divided into \(1\times 1\) squares. Each square is coloured red, orange, yellow, green, blue, indigo, or violet.

Find the minimum value for \(n\) so that for any coloring of the table, so that one can pick three rows and columns with all nine intersections being the same color.

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