# 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.

×