Coloured Beads

CAT 2020 Slot 2 · DILR · Hard · Grid Arrangement

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Passage / data set

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 of 4

The total number of possible configurations using beads of only two colours is:

Answer

2

Explanation

Configurations using only two colors can be constructed using Blue and Green beads alternating such that adjacent cells have different colors and green beads appear between blue beads. There are 2 such configurations.

Question 2 of 4

What is the maximum possible number of Red beads that can appear in any configuration?

Answer

9

Explanation

By placing Red beads at optimal locations such that between any two Red beads in a row/column there is at least one Blue and at least one Green bead, the maximum number of Red beads that can be placed in a 5x5 grid is 9.

Question 3 of 4

What is the minimum number of Blue beads in any configuration?

Answer

6

Explanation

To satisfy all placement conditions across 5 rows and 5 columns, the minimum number of Blue beads required in any valid configuration is 6.

Question 4 of 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 to maximise the number of Red beads used in the configuration?

Answer

6

Explanation

Given the initial placement of two Red beads, up to 6 additional Red beads can be placed following the rules, bringing the total to 8 (or maximum additional possible 6).

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