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Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.

While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:

1. Two adjacent beads along the same row or column are always of different colours.

2. There is at least one Green bead between any two Blue beads along the same row or column.

3. There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.

Every unique, complete arrangement of twenty five beads is called a configuration.

Question 1 : The total number of possible congurations using beads of only two colours is:

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Since only 2 beads can be used, Red is automatically out as it requires at least 1 G and 1 B to be between 2 Rs

Given the condition that there can be no beads of the same colour adjacent to each other, we can have 1 of 2 arrangements: Either B in the corner or G in the corner

So only 2 arrangements are possible here (This can be concluded without actually drawing the grid, so a must attempt question)

The question is **"The total number of possible congurations using beads of only two colours is:" **

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