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Explanation:

We can use beads of only two colors.

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

Hence, the two colors that can be used are green and blue.

Also, two adjacent beads along the same row or column are always of different colors. Hence, blue and green beads can only be placed alternately.

∴ The following 2 configurations are possible.

Configuration 1:

Configuration 2:

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Hence, 2.

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