Seating Arrangement Puzzle Solution

This problem requires us to determine the seating arrangement of eight people (Rohan, Raunak, Sushma, Sandip, Reshma, Sahil, Ruhi, and Sristi) sitting around a circular table, facing the centre. We will deduce their positions step-by-step based on the given clues and then identify which pair are not neighbours.

Detailed Seating Arrangement Derivation

Let's represent the 8 positions in a circle as P1, P2, P3, P4, P5, P6, P7, P8 in a clockwise direction.

1. Rohan is second to the right of Reshma.
   Let's assume Reshma is at position P1.
   The person to Reshma's first right is P2.
   The person to Reshma's second right is P3.
   So, Reshma = P1, Rohan = P3.
2. Reshma is the neighbour of Sushma and Sahil.
   Reshma is at P1. Her neighbours are P8 and P2. So, Sushma and Sahil must occupy P8 and P2.
3. Sahil is the neighbour of Ruhi.
   We have two possibilities from clue 2:
   • Case A: Sahil is at P2 and Sushma is at P8.
     If Sahil is at P2, his neighbours are P1 (Reshma) and P3.
     However, Rohan is already at P3. This means Ruhi would have to be either Reshma or Rohan, which is not possible as they are distinct individuals.
     Therefore, Case A is incorrect.
   • Case B: Sahil is at P8 and Sushma is at P2.
     If Sahil is at P8, his neighbours are P1 (Reshma) and P7.
     From Clue 3, Sahil is the neighbour of Ruhi. Since Reshma is already at P1, Ruhi must be at P7.
     This arrangement is consistent.

   Current fixed positions:

   • Reshma = P1
   • Sushma = P2
   • Rohan = P3
   • Ruhi = P7
   • Sahil = P8

   Remaining people: Sandip, Raunak, Sristi.

   Remaining positions: P4, P5, P6.

4. Sandip is not the neighbour of Rohan.
   Rohan is at P3. His neighbours are P2 (Sushma) and P4.
   This means Sandip cannot be at P4.
   So, Sandip must be placed at either P5 or P6.
5. Sristi is not between Ruhi and Sandip.
   This means we cannot have Ruhi - Sristi - Sandip or Sandip - Sristi - Ruhi as consecutive positions.
6. Raunak is not between Sandip and Sristi.
   This means we cannot have Sandip - Raunak - Sristi or Sristi - Raunak - Sandip as consecutive positions.

Placing Sandip, Raunak, and Sristi in P4, P5, P6

Since Sandip cannot be at P4, he must be at P5 or P6.

• Possibility 1: Sandip at P5.
  This means P4 and P6 are occupied by Raunak and Sristi.
  • Subcase 1.1: P4 = Sristi, P6 = Raunak.
    Arrangement: ... Rohan (P3) - Sristi (P4) - Sandip (P5) - Raunak (P6) - Ruhi (P7) ...
    Check Clue 6 ("Sristi is not between Ruhi and Sandip"): The sequence is Sristi(P4) - Sandip(P5) - Raunak(P6). Sristi is not between Ruhi (P7) and Sandip (P5). This holds true.
    Check Clue 5 ("Raunak is not between Sandip and Sristi"): The sequence is Sristi(P4) - Sandip(P5) - Raunak(P6). Sandip is between Sristi and Raunak. Thus, Raunak is not between Sandip and Sristi. This also holds true.
    This subcase satisfies all conditions.
  • Subcase 1.2: P4 = Raunak, P6 = Sristi.
    Arrangement: ... Rohan (P3) - Raunak (P4) - Sandip (P5) - Sristi (P6) - Ruhi (P7) ...
    Check Clue 5 ("Raunak is not between Sandip and Sristi"): The sequence is Raunak(P4) - Sandip(P5) - Sristi(P6). Sandip is between Raunak and Sristi. So Raunak is not between Sandip and Sristi. This holds true.
    Check Clue 6 ("Sristi is not between Ruhi and Sandip"): The sequence is Sandip(P5) - Sristi(P6) - Ruhi(P7). Sristi(P6) IS between Sandip(P5) and Ruhi(P7). This violates Clue 6.
    Therefore, this subcase is incorrect.
• Possibility 2: Sandip at P6.
  This means P4 and P5 are occupied by Raunak and Sristi.
  • Subcase 2.1: P4 = Sristi, P5 = Raunak.
    Arrangement: ... Rohan (P3) - Sristi (P4) - Raunak (P5) - Sandip (P6) - Ruhi (P7) ...
    Check Clue 5 ("Raunak is not between Sandip and Sristi"): The sequence is Sristi(P4) - Raunak(P5) - Sandip(P6). Raunak(P5) IS between Sristi(P4) and Sandip(P6). This violates Clue 5.
    Therefore, this subcase is incorrect.
  • Subcase 2.2: P4 = Raunak, P5 = Sristi.
    Arrangement: ... Rohan (P3) - Raunak (P4) - Sristi (P5) - Sandip (P6) - Ruhi (P7) ...
    Check Clue 5 ("Raunak is not between Sandip and Sristi"): The sequence is Raunak(P4) - Sristi(P5) - Sandip(P6). Sristi is between Raunak and Sandip. So Raunak is not between Sandip and Sristi. This holds true.
    Check Clue 6 ("Sristi is not between Ruhi and Sandip"): The sequence is Sristi(P5) - Sandip(P6) - Ruhi(P7). Sandip is between Sristi and Ruhi. So Sristi is not between Ruhi and Sandip. This also holds true.
    This subcase satisfies all conditions.

We found two possible arrangements that satisfy all the clues (Subcase 1.1 and Subcase 2.2).

Let's list them and check the options. Often, in such questions, only one arrangement will lead to a unique correct answer from the given options.

Arrangement 1 (from Subcase 1.1):

Arrangement 2 (from Subcase 2.2):

Analyzing the Options for "Not Neighbours"

We need to find the pair that are NOT neighbours based on the established arrangement.

Checking Arrangement 1:

• Sahil and Ruhi: Sahil (P8) and Ruhi (P7) are neighbours. (Incorrect answer)
• Raunak and Rohan: Raunak (P6) and Rohan (P3). Not neighbours. (Correct answer candidate)
• Sristi and Raunak: Sristi (P4) and Raunak (P6). Not neighbours. (Correct answer candidate)
• Sandip and Sahil: Sandip (P5) and Sahil (P8). Not neighbours. (Correct answer candidate)

If Arrangement 1 is correct, there would be multiple correct options, which is usually not the case for MCQs. Let's check Arrangement 2.

Checking Arrangement 2:

The circular order is: Reshma → Sushma → Rohan → Raunak → Sristi → Sandip → Ruhi → Sahil → Reshma.

• Sahil and Ruhi: Sahil is at P8 and Ruhi is at P7. They are immediate neighbours. Therefore, they are neighbours.
• Raunak and Rohan: Raunak is at P4 and Rohan is at P3. They are immediate neighbours. Therefore, they are neighbours.
• Sristi and Raunak: Sristi is at P5 and Raunak is at P4. They are immediate neighbours. Therefore, they are neighbours.
• Sandip and Sahil: Sandip is at P6 and Sahil is at P8.
  Neighbours of Sandip (P6) are Sristi (P5) and Ruhi (P7).
  Neighbours of Sahil (P8) are Ruhi (P7) and Reshma (P1).
  Sandip and Sahil are not adjacent in the arrangement. Therefore, they are not neighbours.

Based on Arrangement 2, only "Sandip and Sahil" are not neighbours among the given options. This confirms Arrangement 2 as the intended solution.

The final answer is
Sandip and Sahil