Question:
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.
What is the minimum number of Blue beads in any configuration?
[This Question was asked as TITA]
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.
What is the minimum number of Blue beads in any configuration?
[This Question was asked as TITA]
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.
What is the minimum number of Blue beads in any configuration?
[This Question was asked as TITA]
Updated On: Jul 3, 2024
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The Correct Option is D
Approach Solution - 1
To minimise number of Blue beads we need to maximise number of Red and Green beads.
From the previous question solution, Maximum no. Red beads can be 9.
The row in which has two red beads, we will place two green and one Blue bead additionally.
The row with only one red bead we will place two green and two blue beads additionally.
So overall there will be minimum 6 Blue beads.
Answer: 6
From the previous question solution, Maximum no. Red beads can be 9.
The row in which has two red beads, we will place two green and one Blue bead additionally.
The row with only one red bead we will place two green and two blue beads additionally.
So overall there will be minimum 6 Blue beads.
Answer: 6
So, the correct option is (D): 6.
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Approach Solution -2
Given a maximum of 9 red beads, we aim to fill the remaining space with green and blue beads while minimizing the number of blue beads used.
Hence number of blue beads is 6.
Hence number of blue beads is 6.
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