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Difficulty: HardSeating Arrangement

Seven scientists—Dr. Aris, Dr. Bell, Dr. Chen, Dr. Diaz, Dr. Evans, Dr. Ford, and Dr. Grant—are seated at equal distances around a circular table. Some are facing the center, while others are facing outward.

1. Dr. Ford faces the center. Dr. Chen sits second to the left of Dr. Ford.
2. Dr. Grant sits third to the right of Dr. Chen. Dr. Grant faces outward.
3. Dr. Aris sits to the immediate left of Dr. Grant.
4. Dr. Evans sits second to the right of Dr. Aris, and faces the same direction as Dr. Ford.
5. Dr. Bell is not an immediate neighbor of Dr. Chen.
6. Dr. Diaz and Dr. Bell face opposite directions.
7. Both immediate neighbors of Dr. Chen face the center.

Based on the seating arrangement, which of the following statements is definitely true?

  1. Exactly two scientists sit between Dr. Ford and Dr. Evans when counted clockwise from Dr. Ford.Answer
  2. B
    Dr. Ford sits second to the left of Dr. Chen.
  3. C
    Dr. Diaz sits third to the right of Dr. Grant.
  4. D
    Dr. Bell faces the center and sits to the immediate left of Dr. Evans.

Answer

Exactly two scientists sit between Dr. Ford and Dr. Evans when counted clockwise from Dr. Ford.
When the complete seating arrangement is deduced, Dr. Ford is at position 1 and Dr. Evans is at position 4. Counting clockwise from Dr. Ford (positions 1 to 4), there are exactly two seats (positions 2 and 3), which are occupied by Dr. Diaz and Dr. Chen.

Step-by-Step Solution

1
Fix Dr. Ford's position and place Dr. Chen.
Dr. Ford is at position 1 (facing center). Since left is clockwise for center-facing, Dr. Chen is at position 3.
Establishing a relative starting point is necessary for circular arrangements.
2
Determine Dr. Chen's facing direction to place Dr. Grant.
If Dr. Chen faced outward, Dr. Grant would be at position 6, forcing Dr. Aris to position 5, and Dr. Evans to position 7. This leaves positions 2 and 4 for Dr. Bell and Dr. Diaz. However, Dr. Bell cannot be adjacent to Dr. Chen, so Dr. Bell would have no valid seat. Thus, Dr. Chen MUST face the center. Therefore, Dr. Grant sits at position 7 (facing outward).
Testing hypotheses for facing directions ensures we avoid logical dead-ends later in the puzzle.
3
Place Dr. Aris and Dr. Evans.
Dr. Grant faces outward, so left is anti-clockwise. Dr. Aris sits at position 6. To place Dr. Evans second to the right of Dr. Aris into an empty seat, Dr. Aris must face the center (placing Dr. Evans at position 4). Dr. Evans also faces the center (same as Dr. Ford).
Directionality of Dr. Grant directly determines Dr. Aris's location, which chains into Dr. Evans's location.
4
Place the remaining scientists and determine final facing directions.
Positions 2 and 5 are empty. Dr. Bell cannot be adjacent to Dr. Chen (position 3), so Dr. Bell takes position 5, leaving position 2 for Dr. Diaz. Dr. Chen's neighbors (Dr. Diaz and Dr. Evans) both face the center. Since Dr. Diaz faces the center, Dr. Bell must face outward (opposite to Dr. Diaz).
Fulfilling the negative constraint (not an immediate neighbor) resolves the final positions, and the neighboring condition resolves the remaining directions.

Key Concept

Circular seating arrangements with mixed facing directions
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Topics

Seating Arrangement

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