### CAT 2020 Slot 2 - LRDI Question 13

Instructions

Twenty five coloured beads are to be arranged in a grid comprising of five rows and fiveĀ columns. Each cell in the grid must contain exactly one bead. Each bead is coloured eitherĀ Red, Blue or Green.Ā While arranging the beads along any of the five rows or along any of the five columns, theĀ 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 orĀ column.
3. There is at least one Blue and at least one Green bead between any two Red beadsĀ along the same row or column.

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

Question 13

# What is the minimum number of Blue beads in anyĀ configuration?

Solution

To solve this question we can use the answer of the previous question, since maximum 9 red beads are possible, filling the remaining space with green and blue beads, in such a way that number of blue beads is minimised

Hence number of blue beads is 6