Seating Plan for a Credit-Appraisal Panel
Seven probationary officers-A, B, C, D, E, F and G-are seated in a single row facing north for a credit-appraisal panel. The seating plan must satisfy the following conditions. A sits third to the left of D. D sits at the extreme right end of the row. C sits immediately to the right of A. G sits second to the right of B. F is not adjacent to B. The panel coordinator has to place name cards at positions 1 to 7 from left to right before the candidates arrive. The HR team has a tentative chart that places E at position 2, but the coordinator is not sure whether that chart satisfies every condition. No two officers share a position, and all seven positions are filled. The coordinator must confirm the final order and answer queries without redrawing the entire chart.
1. Determine the final seating order from positions 1 to 7. Show each deduction and state whether the tentative chart placing E at position 2 is correct.
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Deduction: D is at position 7. A is third to the left of D, so A = 4. C is immediately right of A, so C = 5. G is second to the right of B. B cannot be 2 because G would be 4, which is occupied by A; B cannot be 3 because G would be 5, occupied by C; B cannot be 5 because G would be 7, occupied by D; B cannot be 6 because G would be 8, outside the row. Therefore B = 1 and G = 3. The remaining positions are 2 and 6 for E and F. F is not adjacent to B, so F cannot be 2; hence F = 6 and E = 2. Final order: 1 B, 2 E, 3 G, 4 A, 5 C, 6 F, 7 D. The tentative chart showing E at position 2 is correct.
2. Answer the coordinator's queries: who sits immediately to the left of A, and how many persons sit between C and F? What would fail if F were placed at position 2 instead?
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A is at position 4; position 3 is G, so G sits immediately to the left of A. C is at position 5 and F is at position 6, so no person sits between C and F. If F were placed at position 2, F would be immediately adjacent to B at position 1. That would violate the condition that F is not adjacent to B. The rest of the arrangement would also need E at position 6, but the adjacency violation alone is sufficient to reject the alternative.