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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 4 : Two Red beads have been placed in ‘second row, third column’ and ‘third row, second column’. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration?


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Explanatory Answer

The initial configuration is:

Maximum red beads for a given configuration.

To maximize the Rs, we need to move along the diagonal and also add R wherever we can see a space of 2 cells

Maximum red beads for a given configuration.

We can simply stop here and directly answer 6. But just to confirm:

Maximum red beads for a given configuration.


The answer is, " 6"

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