Read the information given below carefully and answer the question that follows :
25 coloured beads are to be arranged in a grid comprising of 5 rows and 5 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 5 rows or along any of the 5 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.
4. Every unique, complete arrangement of twenty five beads is called a configuration.
Question :
What is the total number of possible configurations using beads of only two colours ?
- 25
- 24
- 6
- 2
- 0
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Answer: D official key
Approach: Test each pair of colours against the rules along a single row, then extend to the grid.
Solution:
Rule 1 forces adjacent beads to differ, so a two-colour row must alternate.
Red + Blue: R B R — two Reds with no Green between ✗.
Red + Green: R G R — two Reds with no Blue between ✗.
Blue + Green: B G B G B — every pair of Blues has a Green between ✓ (no rule for two Greens).
So only Blue/Green works, and every row and every column must alternate → a chessboard pattern.
A chessboard is fixed by the colour of the top-left bead: Blue or Green → 2 configurations.
Why the other options are wrong:
E (0) ignores the Blue–Green chessboard; A, B, C count arrangements the alternation rule does not allow.
Answer: D















