Solving the Circular Seating Arrangement Puzzle

This question involves a circular seating arrangement puzzle with six friends: A, B, C, D, E, and F. They are sitting around a circular table, all facing the center. We need to use the given clues to determine their positions and then find who is sitting between B and F.

Step-by-Step Seating Arrangement Solution

Let's break down the clues and place the friends one by one around the circular table of 6 seats:

1. Total Members and Setup: There are 6 friends sitting in a circle facing the center. Let's imagine 6 positions around the table.
2. Clue 1: D is third to the right of B.
   • Let's place B at any starting position.
   • Moving to the right (clockwise, as they face the center), count three positions from B.
   • Position 1 to the right of B.
   • Position 2 to the right of B.
   • Position 3 to the right of B is where D sits.
   • So, if we list positions clockwise starting from B: B, _ , _ , D , _ , _.
3. Clue 2: F is to the immediate right of D.
   • Looking at the arrangement from Step 2, the position immediately to the right (clockwise) of D is the next empty spot.
   • Place F in that spot.
   • Arrangement so far (clockwise from B): B, _ , _ , D, F, _.
4. Clue 3: C is between D and E.
   • "Between" in a circular arrangement means C is adjacent to both D and E.
   • Looking at our current arrangement (B, _ , _ , D, F, _), D's neighbors are the person in the spot two positions before D (let's call it P) and F.
   • So, C must be one of D's neighbors, and E must be the other neighbor of C.
   • D's neighbours are the person at the third position from B (P) and F. Since C is between D and E, C must be one of D's neighbours, and that neighbour must also be next to E.
   • F is already a person's name. The sequence around D must be E-C-D or D-C-E.
   • Since F is immediately right of D, the sequence around D must be D, F... or ...P, D.
   • If C is between D and E, the sequence is either E <- C <- D or D -> C -> E.
   • Given our partial arrangement (B, _, _, D, F, _), the positions around D are _, D, F. The spot to the left of D (going anti-clockwise) is two spots after B. The spot to the right of D is F.
   • C must be adjacent to D. So C is either in the spot two positions after B, or C is F. But F is already F. So C must be in the spot two positions after B.
   • Let's place C there: B, _, C, D, F, _.
   • Now, C is between D and E. C is in the third position clockwise from B. D is in the fourth. F is in the fifth.
   • The sequence must be E-C-D or D-C-E. We have ...C, D... in the sequence. So E must be adjacent to C on the other side. The other side of C (going anti-clockwise) is the spot immediately to the right of B.
   • Let's place E there: B, E, C, D, F, _.
5. Final Placement:
   • Our arrangement is now (clockwise from B): B, E, C, D, F, _.
   • We have used B, C, D, E, F. The remaining friend is A.
   • There is only one empty spot left, which is six positions from B.
   • So, A must be in the remaining spot.
   • The final arrangement (clockwise from B) is: B, E, C, D, F, A.

Verifying the Seating Arrangement

Let's check if the final arrangement meets all conditions:

• B is followed by E, C, D, F, A, then back to B.
• D is third to the right of B? Starting from B: 1st is E, 2nd is C, 3rd is D. Yes.
• F is immediate right of D? Right of D is F. Yes.
• C is between D and E? The sequence is E → C → D. Yes, C is adjacent to both E and D.

The arrangement B, E, C, D, F, A in clockwise order is correct.

Identifying Who Sits Between B and F

Now we need to find who is sitting between B and F based on the arrangement B, E, C, D, F, A.

Look at the positions around the circle:

Let's see the arrangement visually:

B — E — C — D — F — A — B (circularly)

The question asks who is between B and F. There are two paths around the circle:

• Path 1 (Clockwise): B → E → C → D → F. The people between B and F are E, C, and D.
• Path 2 (Anti-clockwise): B → A → F. The person between B and F is A.

When the question asks "who is sitting between X and Y" and the options are single individuals, it typically refers to the person who is adjacent to both X and Y, meaning they are directly in the middle on one side of the circle. In our arrangement, A is next to B and also next to F. Thus, A is sitting between B and F.

Final Answer Derivation

Based on our verified circular arrangement (B, E, C, D, F, A), A is positioned directly between B and F in the circle.

Revision Table: Key Clues and Deductions

Additional Information on Seating Arrangements

Seating arrangement puzzles are common in logical reasoning sections of competitive exams. They test your ability to follow instructions and visualize spatial relationships.

• Circular vs. Linear: Circular arrangements wrap around, so the first and last positions are adjacent. Linear arrangements are in a straight line.
• Facing Direction: Knowing whether people face the center or away from the center (or different directions) is crucial for determining "right" and "left". When facing the center, "right" is clockwise and "left" is anti-clockwise.
• "Between": In circular arrangements, "between X and Y" usually means the person(s) on the shortest path between them, or specifically the person adjacent to both on one side. The context and options usually clarify this.
• Solving Strategy:
  • Start with a definite clue that links two or more people or fixes someone's position relative to a known point (like an end in linear, or just place someone to start in circular).
  • Draw the diagram as you go.
  • Use placeholders for unknown positions.
  • Link clues together.
  • Systematically eliminate possibilities if needed.
  • Verify your final arrangement against all the given conditions.

Understanding these concepts helps solve complex seating arrangement problems efficiently.