Seating Arrangement at the Training Centre
Eight probationary officers-A, B, C, D, E, F, G and H-are seated in one row at a training centre, all facing north. The seats are numbered 1 to 8 from left to right. The following clues are displayed on the board: A sits fourth to the left of E. F sits second to the right of A. H sits third to the left of E. B sits at one of the extreme ends. D and C sit next to each other, with C immediately to the right of D. G sits adjacent to neither B nor H. B sits somewhere to the right of G. The trainer asks the group to arrange themselves accordingly and then answers three questions based on the final arrangement.
1. Who sits second to the left of the person who sits immediately to the right of E?
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Build the arrangement. Let positions be 1–8 from left to right. From E = A + 4, F = A + 2 and H = E − 3 = A + 1. Testing the viable placement with B at an extreme end and D–C consecutive gives: A1, H2, F3, G4, E5, D6, C7, B8. Check: C is immediately right of D; G at 4 is adjacent to F and E, not B or H; B at 8 is right of G.
The person immediately right of E is D at position 6. Second to the left of D is position 4, which is G. Answer: G.
2. If the eight officers are rearranged in alphabetical order from left to right, how many of them remain in their original seats?
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Original positions: A1, H2, F3, G4, E5, D6, C7, B8.
Alphabetical order: A1, B2, C3, D4, E5, F6, G7, H8.
Compare each officer:
- A: 1 → 1, same
- B: 8 → 2, changed
- C: 7 → 3, changed
- D: 6 → 4, changed
- E: 5 → 5, same
- F: 3 → 6, changed
- G: 4 → 7, changed
- H: 2 → 8, changed
Only A and E remain in their original seats. Answer: 2.
3. Suppose the clue 'B sits somewhere to the right of G' is removed. Does the remaining information still produce a unique arrangement? Justify with an alternative arrangement.
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No. Without the clue, a second arrangement satisfies all remaining conditions: B1, A2, H3, F4, G5, E6, D7, C8.
Check it: A is fourth to the left of E (2 → 6); F is second to the right of A (2 → 4); H is third to the left of E (6 → 3); B is at an extreme end; D and C are consecutive with C immediately right of D (6–7); G at 5 is adjacent to F and E, not B or H. The only removed clue was that B must be right of G, and here B is at 1 while G is at 5. Hence the data are not sufficient for a unique arrangement once that clue is removed.