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Difficulty: HardSeating Arrangement

Eight friends—A, B, C, D, E, F, G, and H—are seated around a square table. Four of them sit at the four corners of the table and face the center, while the other four sit in the middle of each of the four sides and face outward (away from the center).

The following information is known about their seating arrangement:
• A sits third to the left of C, who does not sit at any of the corners.
• E sits second to the right of A.
• Only two people sit between E and B.
• D sits to the immediate left of H, who faces the center.
• H is not an immediate neighbour of A.
• F is not an immediate neighbour of C.

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

  1. A
    G sits to the immediate left of B.
  2. B
    H sits third to the right of F.
  3. C
    A sits second to the right of E.
  4. E sits exactly opposite to G.Answer

Answer

The true statement is that E sits exactly opposite to G.
Based on the fully deduced arrangement (clockwise starting from top-middle): C (Out), H (In), D (Out), E (In), F (Out), A (In), B (Out), G (In). Checking the correct statement: E is at the bottom-right corner and G is at the top-left corner, making them diagonally opposite to each other.

Step-by-Step Solution

1
Determine the basic orientation and place C and A.
C is at a middle position (facing outward). A is placed 3 positions counter-clockwise from C (since left of outward is counter-clockwise). This places A at a corner facing the center.
The first clue provides a fixed starting relationship. 'C does not sit at a corner' confirms C is in the middle of a side.
2
Determine the positions of E and B based on A's position.
Since A faces the center, right is counter-clockwise. E is placed 2 positions counter-clockwise from A (at the next corner). B is placed 3 positions away from E, which lands exactly opposite C on the middle of a side.
The clues 'E sits second to the right of A' and 'Only two people sit between E and B' dictate these exact relative placements.
3
Identify the positions of H and D.
H must face the center, meaning H is at a corner. The only corners left are adjacent to C. Since H cannot be next to A, H takes the corner on C's right. Because H faces inward, its immediate left is the adjacent middle seat, which is given to D.
Combining 'H faces the center', 'D is immediate left of H', and 'H is not adjacent to A' leaves only one valid corner-middle pair for H and D.
4
Place the remaining friends F and G.
Only one middle seat and one corner seat remain. Since F cannot be next to C, F takes the remaining middle seat. G takes the remaining corner seat.
Process of elimination based on the constraint 'F is not an immediate neighbour of C' perfectly resolves the final two seats.

Key Concept

Mixed-orientation spatial reasoning and relative directional assignment in closed shapes.
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Topics

Seating Arrangement

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