Examkin

Question

Difficulty: MediumSeating Arrangement

Eight city planners—Aldo, Bianca, Cyrus, Diana, Ethan, Fiona, Gavin, and Hazel—are seated around a square discussion table. Four of them sit at the corners of the table facing the center, while the remaining four sit at the middle of each of the four sides facing outward.

- Cyrus sits third to the left of Aldo.
- Aldo sits at one of the corners.
- Only two planners sit between Cyrus and Ethan.
- Bianca sits to the immediate right of Ethan.
- Fiona sits second to the left of Bianca.
- Diana is not an immediate neighbor of Aldo.
- Gavin sits second to the right of Diana.

Based on this arrangement, who sits third to the right of Fiona?

  1. DianaAnswer
  2. B
    Gavin
  3. C
    Ethan
  4. D
    Cyrus

Answer

The correct answer is Diana.
Based on the step-by-step layout deduction, Fiona is seated at the middle of a side facing outward. When facing away from the center of the table, moving to the right corresponds to moving in a counter-clockwise direction around the perimeter. Counting three positions counter-clockwise from Fiona passes Ethan and Bianca, landing on Diana.

Step-by-Step Solution

1
Fix Aldo's position and find Cyrus.
Place Aldo at a corner (e.g., top-left) facing the center. Counting three seats to Aldo's left (clockwise) places Cyrus at the right-side middle seat, facing outward.
Establishing a reference point makes subsequent positional tracking deterministic.
2
Locate Ethan relative to Cyrus.
There are two seats between Cyrus and Ethan. Moving three seats from Cyrus in either direction leads to the top-left corner (already occupied by Aldo) or the bottom-left corner. Thus, Ethan sits at the bottom-left corner, facing the center.
Eliminating occupied seats logically forces Ethan into the only available valid position.
3
Place Bianca and Fiona.
Ethan faces the center, so his immediate right is counter-clockwise, placing Bianca at the bottom-side middle seat (facing outward). Fiona sits second to the left of Bianca. Since Bianca faces outward, left is clockwise, placing Fiona at the left-side middle seat (facing outward).
Relative directions invert depending on whether a person faces the center or faces outward.
4
Position Diana, Gavin, and Hazel.
The remaining seats are top-side, top-right corner, and bottom-right corner. Diana cannot be an immediate neighbor of Aldo (top-left), so she must sit at the top-right or bottom-right corner. Gavin sits second to the right of Diana. If Diana is at the top-right (facing center), second to her right is Aldo's seat (occupied). Thus, Diana must be at the bottom-right corner (facing center). Second to her right (counter-clockwise) is the top-right corner, where Gavin sits. The final empty seat (top-side middle) is taken by Hazel.
Checking logical constraints ensures the placement is valid without contradictions.
5
Determine the person third to the right of Fiona.
Fiona is at the left-side middle seat, facing outward. Her right is counter-clockwise. One seat right is Ethan, two seats right is Bianca, and three seats right is Diana.
Careful tracking of outward-facing directional rules avoids final step errors.

Key Concept

Positional and directional tracking in closed polygon seating arrangements with mixed facing orientations.
Rate this question

Topics

Seating Arrangement

More questions from this topic