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Explanation:

To minimize blue beads, we have to use maximum number of red and green beads.

There must be a blue and a green bead between two red beads, we cannot choose one the two colors as red, and 

There is at least one green bead between any two blue beads along the same row or column.

Consider the configuration in the previous questions. We can replace blue beads, which are not in between two red beads, with green beads.

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Hence, 6.