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Difficulty: MediumSeating Arrangement

Five delegates—Alice, Ben, Clara, David, and Emma—are sitting in a single straight row facing North during a conference.

Read the following conditions carefully:
1. David is sitting at the extreme left end of the row.
2. Ben is sitting second to the right of Alice.
3. Clara is an immediate neighbor of Ben, but does not sit next to Alice.

Arrange the delegates in their correct seating order from the extreme left end to the extreme right end of the row.

  1. 1David
  2. 2Alice
  3. 3Emma
  4. 4Ben
  5. 5Clara

Answer

The correct sequence from left to right is: David, Alice, Emma, Ben, Clara.
The arrangement must logically begin with David at position 1. Alice must sit at position 2 and Ben at position 4; otherwise, Clara would be forced to sit next to Alice (if Alice were at 3 and Ben at 5). Consequently, Clara takes position 5, leaving position 3 for Emma.

Step-by-Step Solution

1
Place David according to the first condition.
David is at position 1. The row configuration from left to right is: David, _, _, _, _.
The condition explicitly states David is at the extreme left end.
2
Determine the possible positions for Alice and Ben.
Since Ben is second to the right of Alice, the possible position pairs for (Alice, Ben) are (2, 4) or (3, 5).
This maintains exactly one empty seat between Alice and Ben to her right.
3
Evaluate the (3, 5) position pair using Clara's constraint.
If Alice is at 3 and Ben is at 5, Clara must be at 4 to be an immediate neighbor of Ben. However, this places Clara next to Alice, which violates the third condition.
Testing hypotheses against negative constraints is necessary to eliminate invalid scenarios.
4
Place Alice, Ben, and Clara in the only valid remaining configuration.
Alice is securely at position 2, and Ben is at position 4. Clara must sit at position 5 to be next to Ben but not next to Alice.
This is the only configuration that satisfies both the 'second to the right' rule and the negative neighbor constraint.
5
Place Emma in the final remaining seat.
Emma sits at position 3. The final order is David, Alice, Emma, Ben, Clara.
There is only one person left (Emma) and one seat available (position 3).

Key Concept

Linear Seating Arrangement with negative constraints
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Topics

Seating Arrangement

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