Solving the Circular Seating Arrangement Puzzle

This question involves arranging six friends around a circular table based on given clues. We need to determine the position of each person to answer who sits between Aman and Elizabeth.

Understanding the Clues

We have six friends: Aman (A), Biplab (B), Chirantan (C), Divya (D), Elizabeth (E), and Firoz (F). They are sitting around a circular table, all facing the center.

• Clue 1: Aman sits third to the left of Biplab.
• Clue 2: Chirantan is an immediate neighbour of Aman.
• Clue 3: Elizabeth sits second to the right of Divya.
• Clue 4: Chirantan is not an immediate neighbour of Divya.

Step-by-Step Solution Process

Let's represent the circular table with 6 positions. We can fix one person's position to start relative placements.

Step 1: Place Biplab and Aman using Clue 1.

Let's place Biplab (B) at a starting position. Since it's a circular table, the exact starting spot doesn't matter for relative positions. Aman is third to the left of Biplab. In a circular arrangement facing the center, 'left' is typically clockwise.

If we number positions 1 to 6 clockwise starting from Biplab at position 1:

• Position 1: Biplab (B)
• Position 2: 1st left of B
• Position 3: 2nd left of B
• Position 4: 3rd left of B

So, Aman (A) is at Position 4.

Current arrangement snippet: B (P1), _ (P2), _ (P3), A (P4), _ (P5), _ (P6).

Step 2: Place Chirantan using Clue 2.

Chirantan (C) is an immediate neighbour of Aman (A). In our arrangement, A is at P4. Its immediate neighbours are P3 and P5. So, Chirantan is either at P3 or P5.

Let's consider these two cases:

• Case 1: Chirantan is at Position 3. Arrangement: B (P1), _ (P2), C (P3), A (P4), _ (P5), _ (P6).
• Case 2: Chirantan is at Position 5. Arrangement: B (P1), _ (P2), _ (P3), A (P4), C (P5), _ (P6).

Step 3: Place Divya and Elizabeth using Clue 3 and Clue 4.

Elizabeth (E) sits second to the right of Divya (D). In a circular arrangement facing the center, 'right' is typically anti-clockwise. The pattern is D, _, E.

Also, Chirantan (C) is not an immediate neighbour of Divya (D).

Let's examine Case 1: B (P1), _ (P2), C (P3), A (P4), _ (P5), _ (P6).

The remaining positions are P2, P5, P6. The remaining people are D, E, F. We need to place D and E such that E is 2nd right of D (D _ E), using only P2, P5, P6, and the existing people at P1, P3, P4 as potential intermediate spots.

• If D is at P2, 2nd right (anti-clockwise) is P4 (A). E would have to be A, which is not possible as A is already placed.
• If D is at P5, 2nd right (anti-clockwise) is P1 (B). E would have to be B, which is not possible as B is already placed.
• If D is at P6, 2nd right (anti-clockwise) is P2. This means D is at P6 and E is at P2. This placement uses two of the available spots (P2, P6) and fits the D _ E pattern.

So, in Case 1, placing D at P6 and E at P2 gives the arrangement: B (P1), E (P2), C (P3), A (P4), _ (P5), D (P6).

The remaining person is Firoz (F), and the remaining position is P5. So, F is at P5.

The full arrangement for Case 1 (Clockwise): B, E, C, A, F, D.

Let's check Clue 4: Chirantan (C) is not an immediate neighbour of Divya (D). In this arrangement, the neighbours of D are F (at P5) and B (at P1). Chirantan (C) is at P3, which is not adjacent to D. This arrangement satisfies all clues.

Let's examine Case 2: B (P1), _ (P2), _ (P3), A (P4), C (P5), _ (P6).

The remaining positions are P2, P3, P6. The remaining people are D, E, F. We need to place D and E such that E is 2nd right of D (D _ E), using P2, P3, P6 and existing people at P1, P4, P5.

• If D is at P2, 2nd right is P4 (A). E would have to be A, not possible.
• If D is at P3, 2nd right is P5 (C). E would have to be C, not possible.
• If D is at P6, 2nd right is P2. This means D is at P6 and E is at P2. This placement uses two of the available spots (P2, P6) and fits the D _ E pattern.

So, in Case 2, placing D at P6 and E at P2 gives the arrangement: B (P1), E (P2), _ (P3), A (P4), C (P5), D (P6).

The remaining person is Firoz (F), and the remaining position is P3. So, F is at P3.

The full arrangement for Case 2 (Clockwise): B, E, F, A, C, D.

Let's check Clue 4: Chirantan (C) is not an immediate neighbour of Divya (D). In this arrangement, the neighbours of D are C (at P5) and B (at P1). Chirantan (C) IS an immediate neighbour of D. This arrangement contradicts Clue 4.

Therefore, Case 2 is invalid. The only valid arrangement is the one derived from Case 1:

Valid Circular Arrangement (Clockwise from Biplab): B, E, C, A, F, D

Answering the Question

The question asks: Who sits between Aman and Elizabeth?

Looking at the valid arrangement B, E, C, A, F, D:

• Aman (A) is at Position 4.
• Elizabeth (E) is at Position 2.

Moving from A to E anti-clockwise, we pass Chirantan (C) directly (A to C to E). Moving from A to E clockwise, we pass Firoz (F), Divya (D), and Biplab (B).

When options provide a single person, "between" usually refers to the person(s) immediately adjacent along the shorter path, or the person(s) connecting them directly. In this case, Chirantan (C) is immediately between Aman (A) and Elizabeth (E) along one side of the circle (A-C-E segment).

Thus, Chirantan sits between Aman and Elizabeth.

Revision Table: Key Facts

Additional Information on Seating Arrangement Puzzles

Seating arrangement questions test your logical deduction skills. Key concepts include:

• Circular vs. Linear Arrangements: Circular arrangements involve relative positions around a circle, where the start and end points are connected. Linear arrangements are in a line.
• Facing Direction: In circular arrangements, knowing if people face the center or away from the center is crucial for determining left and right. Facing the center means 'left' is typically clockwise and 'right' is anti-clockwise.
• Relative Positions: Clues like 'third to the left', 'immediate neighbour', 'second to the right' describe positions relative to a specific person.
• Negative Information: Clues like 'not an immediate neighbour' are important for eliminating incorrect possibilities, as seen with Chirantan and Divya in this problem.
• Case Analysis: When a clue presents multiple possibilities (like Chirantan being on either side of Aman), it's often necessary to explore each case until one satisfies all conditions and others are eliminated.