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Difficulty: MediumSeating Arrangement

Seven diplomats—Alan, Boris, Chloe, David, Elena, Felix, and Grace—are sitting around a circular table facing the center.

Read the following conditions carefully:
1. Alan sits third to the right of Boris.
2. Chloe sits second to the left of Alan.
3. David sits immediately between Elena and Felix.
4. Elena is not an immediate neighbor of Boris.

Based on the above seating arrangement, who sits second to the right of Grace?

  1. A
    Boris
  2. B
    Felix
  3. ElenaAnswer
  4. D
    Alan

Answer

Elena sits second to the right of Grace.
Following the conditions step-by-step: If we place Boris at position 1, Alan goes to position 4 (third to the right, anti-clockwise). Chloe goes to position 2 (second to the left of Alan, clockwise). The three consecutive seats for Elena, David, and Felix must be 5, 6, and 7, meaning David is at 6. Grace takes the only empty seat at 3. Because Elena cannot be next to Boris (position 1), she must take position 5, leaving Felix at position 7. The complete anti-clockwise order is Boris, Chloe, Grace, Alan, Elena, David, Felix. Grace is at position 3; the second person to her right is at position 5, which is occupied by Elena.

Step-by-Step Solution

1
Place Boris and determine Alan's position using the first condition.
Assume Boris is at position 1. Since they face the center, 'right' is anti-clockwise. Alan is third to the right, placing him at position 4.
Fixing a reference point is the standard method for solving circular arrangements.
2
Place Chloe using the second condition.
Chloe sits second to the left (clockwise) of Alan (position 4). Thus, Chloe is placed at position 2.
Chloe's position is strictly relative to Alan's fixed position.
3
Identify the seating block for David, Elena, and Felix.
David sits immediately between Elena and Felix, requiring three consecutive empty seats. The currently occupied seats are 1, 2, and 4. The only consecutive empty seats are 5, 6, and 7. Therefore, David must sit exactly in the middle of them, at position 6.
This is the only way to satisfy the requirement of three people sitting together without splitting the group.
4
Place Grace in the arrangement.
With positions 1, 2, 4, 5, 6, and 7 accounted for, position 3 is the only remaining seat. Grace must sit at position 3.
By the process of elimination, the last remaining person takes the last available seat.
5
Determine the exact positions of Elena and Felix using the final condition.
Elena and Felix occupy positions 5 and 7 in some order. Boris is at position 1, making positions 2 and 7 his immediate neighbors. Since Elena cannot be an immediate neighbor of Boris, she cannot sit at position 7. Therefore, Elena is at position 5, and Felix is at position 7.
This fully resolves all ambiguities in the arrangement while satisfying the negative constraint.
6
Answer the specific question asked in the stem.
Grace is at position 3. Facing the center, the second seat to her right (anti-clockwise) is position 5. Elena occupies position 5.
Applying the final relative directional check on the completed diagram.

Key Concept

Solving complex circular seating arrangements by logically deducing relative positions and applying negative constraints.
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Topics

Seating Arrangement

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