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Difficulty: HardSeating Arrangement

Six software engineers—Arthur, Bianca, Caleb, Daphne, Elias, and Fiona—are seated in a single straight row facing their monitors (North). Read the conditions below and determine their exact seating arrangement from left to right.

1. Elias sits exactly fourth to the right of Arthur.
2. Bianca sits immediately to the left of Daphne, but neither of them sits at an extreme end of the row.
3. Caleb sits somewhere to the right of Bianca but is not an immediate neighbor of Daphne.
4. Fiona does not sit next to Arthur.

Arrange the engineers in the correct seating order from extreme left (position 11) to extreme right (position 66).

  1. 1Arthur
  2. 2Bianca
  3. 3Daphne
  4. 4Fiona
  5. 5Elias
  6. 6Caleb

Answer

The correct sequence from left to right is Arthur, Bianca, Daphne, Fiona, Elias, and Caleb.
By analyzing the widest gap constraint, Elias must be at position 55 and Arthur at position 11, or Elias at position 66 and Arthur at position 22. Placing Arthur at 22 forces Bianca and Daphne into internal slots that inevitably eliminate any valid position for Caleb (who must be right of Bianca but not next to Daphne). Therefore, Arthur must be at position 11 and Elias at position 55. Bianca and Daphne must sit at positions 22 and 33. Caleb must be placed at position 66 to be right of Bianca and avoid neighboring Daphne at 33. Finally, Fiona takes the remaining position 44, successfully ensuring she is not adjacent to Arthur at 11.

Step-by-Step Solution

1
Analyze the widest positional gap between Elias and Arthur.
Elias is fourth to the right of Arthur. This requires a block of five seats (Arthur, _, _, _, Elias). They can only occupy positions (1 and 5) or (2 and 6).
Starting with the largest spatial footprint limits the overarching frameworks available for the remaining conditions.
2
Place the Bianca-Daphne pair into the possible frameworks.
Bianca is immediately left of Daphne. In framework (2 and 6), they must occupy (3,4) or (4,5). In framework (1 and 5), they must occupy (2,3) or (3,4). Since neither can be at the extreme ends, all these pairs initially seem viable.
Contiguous blocks must fit into unbroken sequences of empty seats without touching the ends.
3
Test Caleb's placement based on Bianca and Daphne's positions.
If Arthur is at 2 and Elias at 6, Bianca and Daphne at (3,4) forces Caleb to 5, which makes Caleb and Daphne immediate neighbors (violating condition 3). Thus, Arthur must be at position 1 and Elias at 5.
Eliminating invalid frameworks ensures a singular logical path forward.
4
Finalize positions within the confirmed (Arthur at 1, Elias at 5) framework.
Bianca and Daphne must be at (2,3). If they were at (3,4), Caleb (who must be right of Bianca) would have to be at 6, but Fiona would be forced to position 2 (next to Arthur, violating condition 4). With Bianca at 2 and Daphne at 3, Caleb must be at 6 to avoid neighboring Daphne. Fiona takes the remaining position 4.
Iteratively applying the negative constraints (not neighboring) eliminates the final false sub-cases.

Key Concept

Linear seating arrangement with overlapping positional and negative constraints
Estimated Time:2m 30s
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Topics

Seating Arrangement

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