CAT 2020 Slot 2 — DILR Question 7
Answer the next 4 questions based on the information given below.
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:
- Two adjacent beads along the same row or column are always of different colors.
- There is at least one Green bead between any two Blue beads along the same row or column.
- 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.
What is the minimum number of Blue beads in any configuration?
Answer & solution
Answer: 6
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 or this new configuration below.
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Hence, 6.