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

Logical Reasoning

Grids

Hard

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 colours.

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.

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

Entered answer:

✅ Correct Answer: 2

Slide 1/2

Understanding the set :-

It says, there are 25 beads to be arranged in a grid comprising of five rows and five columns.

Each bead is coloured either Red, Blue or Green.

we need to arrange the beads according to the rules given :

a) Two adjacent beads are always of different colour

b) There is at least one Green bead between any two Blue beads

c) There is at least one Blue and at least one Green bead between any two Red beads

This set gives information about 25 beads, which we need to arrange in a grid of 5 rows and 5 columns,

so there will be n different configurations we can make of these 25 beads arrangement.

Therefore, this is a question based set,

which we need to solve according to the question's demand.

Question says,

possible configurations using beads of only two colours

Since we are required to use only two colours, these can be either

Green + Blue
⁠Blue + Red
⁠Green + Red

But clue 3 says,

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

=> Hence without both Green and Blue, Red beads cannot be used to fill the grid.

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

Solution figure for CAT 2020 DILR question 1 (Logical Reasoning)

Question 2

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

Question 3

What is the minimum number of Blue beads in any 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?

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

Solution

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