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Difficulty: HardSeating Arrangement

Eight executives—Alice, Bob, Carol, David, Emma, Frank, Grace, and Henry—are sitting around a square table. Four of them sit at the four corners of the table facing outward (away from the center), while the other four sit exactly in the middle of the four sides facing inward (towards the center).

The following information is known about their seating arrangement:
• Bob sits at one of the corners.
• Emma sits in the middle of one of the sides and is third to the right of Bob.
• Only one person sits between Bob and Henry.
• Carol sits second to the left of Henry.
• Frank is not an immediate neighbor of Bob or Henry.
• Alice sits second to the left of David.
• David does not sit at any of the corners.
• Grace sits opposite to Alice.

Who among the following sits third to the right of Grace?

  1. A
    Bob
  2. B
    Henry
  3. FrankAnswer
  4. D
    Carol

Answer

Frank
Based on the clues, Grace sits in the bottom-middle position facing the center. Since she faces inward, her right side follows a counter-clockwise direction. Counting three positions counter-clockwise from Grace leads to the top-right corner, which is occupied by Frank.

Step-by-Step Solution

1
Determine directional rules for the square table.
Corners face outward (Left = Counter-Clockwise, Right = Clockwise). Middles face inward (Left = Clockwise, Right = Counter-Clockwise).
Establishing the correct left/right orientation based on facing direction is required before placing any individuals.
2
Place Bob and Emma.
Assume Bob is at the top-left corner (position 1). He faces outward, so his right is clockwise. Emma is third to his right, placing her at the right-middle (position 4).
Bob is a definitive starting point, and Emma's position is strictly relative to him.
3
Place Henry and Carol.
Henry is one seat away from Bob, so he must be at top-right (3) or bottom-left (7). If Henry is at 3 (outward), his second left (CCW) is position 1, which is occupied by Bob. Thus, Henry must be at 7. Carol is second to the left of Henry(7), placing her at the bottom-right corner (5).
Testing the constraint for Henry uniquely determines both his and Carol's positions.
4
Place Frank.
Frank cannot be adjacent to Bob(1) or Henry(7). The only remaining corner not adjacent to them is the top-right corner (position 3).
Eliminating neighboring seats leaves only one valid corner for Frank.
5
Place David, Alice, and Grace in the remaining middle seats (2, 6, 8).
David faces inward, so his left is clockwise. If David is at bottom-middle (6), Alice is at 8, leaving Grace at top-middle (2). But Grace must be opposite Alice(8), which is position 4 (Emma), creating a conflict. If David is at left-middle (8), Alice is at top-middle (2), leaving Grace at bottom-middle (6). Grace(6) is correctly opposite Alice(2).
Testing David's possible placements ensures all constraints, especially the opposite pairing of Grace and Alice, are satisfied without overlap.
6
Find the person third to the right of Grace.
Grace is at position 6 (bottom-middle) facing inward. Her right is counter-clockwise. Three positions counter-clockwise from 6 is position 3, where Frank is seated.
This directly answers the question prompt using the fully resolved seating arrangement.

Key Concept

Positional reasoning with inward and outward facing orientations on a polygonal table.
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Topics

Seating Arrangement

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