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.
The total number of possible configuration using beads of only two colours is:
[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.
The total number of possible configuration using beads of only two colours is:
[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.
The total number of possible configuration using beads of only two colours is:
[This Question was asked as TITA]
Updated On: Jul 3, 2024
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The Correct Option is B
Approach Solution - 1
As we need to use only two colours, in any row or column these two coloured beads will be placed alternately like
So we cannot place Red coloured beads at position 1 or two as between any two Red beads there must at least two beads (at least one green and at least one Blue). Hence, we can use only Green and Blue coloured beads.
We can have two possible configurations:
Configuration 1: Green bead is placed at top left corner
Configuration 2: Blue bead is placed at top left corner
So, the correct option is (B): 2
So we cannot place Red coloured beads at position 1 or two as between any two Red beads there must at least two beads (at least one green and at least one Blue). Hence, we can use only Green and Blue coloured beads.
We can have two possible configurations:
Configuration 1: Green bead is placed at top left corner
Configuration 2: Blue bead is placed at top left corner
So, the correct option is (B): 2
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Approach Solution -2
According to the question, we can use only two colours in any row or column so these two coloured beads will be placed alternatively. Therefore, we cannot place red colour bead at position one or two as between any two red beads there must be at least two beads (at least one green and at least one blue).
Therefore we can use only green and blue colour beads.
Therefore we can use only green and blue colour beads.
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