Circular Seating Arrangement Puzzle Explained

This problem involves determining the seating positions of six people (M, N, O, P, Q, R) around a circular table based on given relational clues. All individuals are facing the centre of the table. We need to find out who is sitting immediately to the right of P.

Analyzing the Seating Clues

Let's break down the information provided:

• Setup: Six people (M, N, O, P, Q, R) are seated around a circular table, all facing the centre.
• Clue 1: "R sits second to the left of N." This means if we start at N and move two positions anticlockwise (to the left), we find R.
• Clue 2: "P is an immediate neighbour of O and R." This tells us P must be sitting exactly between O and R. The sequence must be O-P-R or R-P-O around the table.
• Clue 3: "M sits second to the left of Q." Similar to the first clue, this means if we start at Q and move two positions anticlockwise, we find M.

Determining the Arrangement Step-by-Step

We can determine the seating arrangement by combining the clues. Let's assume the seats are numbered 1 to 6 clockwise.

1. Position N: Let's place N at Seat 1 (an arbitrary starting point).
2. Position R relative to N: Since everyone faces the centre, 'left' refers to the anticlockwise direction. The seat immediately to N's left is Seat 6. The second seat to N's left is Seat 5. Therefore, R sits at Seat 5. Current arrangement schematic (clockwise): N(1), Seat 2, Seat 3, Seat 4, R(5), Seat 6.
3. Position P and O: Clue 2 states P is an immediate neighbour of O and R. This implies P sits directly between O and R. As R is at Seat 5, P must be adjacent to R. P can be at Seat 4 or Seat 6.
   • Case 1: If P is at Seat 4. P's neighbours are Seat 3 and R(5). Since P must also neighbour O, O must be in Seat 3. The arrangement looks like: N(1), Seat 2, O(3), P(4), R(5), Seat 6.
   • Case 2: If P is at Seat 6. P's neighbours are N(1) and R(5). P must also neighbour O. This would require O to be in Seat 1, but N is already there. This case is impossible.
   Therefore, the arrangement must be: N(1), Seat 2, O(3), P(4), R(5), Seat 6.
4. Position M and Q: The remaining people are M and Q, and the remaining seats are 2 and 6. We use Clue 3: "M sits second to the left of Q."
   • Test Case A: Assume Q is at Seat 2 and M is at Seat 6. The arrangement is: N(1), Q(2), O(3), P(4), R(5), M(6). Let's check Clue 3: Q is at Seat 2. The seat to Q's left is Seat 1 (where N is). The second seat to Q's left is Seat 6. M is indeed at Seat 6. This arrangement is valid.
   • Test Case B: Assume Q is at Seat 6 and M is at Seat 2. The arrangement is: N(1), M(2), O(3), P(4), R(5), Q(6). Let's check Clue 3: Q is at Seat 6. The seat to Q's left is Seat 5 (where R is). The second seat to Q's left is Seat 4 (where P is). Clue 3 requires M to be at Seat 4, but M is at Seat 2 in this case. This arrangement is invalid.
5. Final Arrangement: The only valid seating order (clockwise) derived from the clues is N, Q, O, P, R, M.

Identifying the Person to the Immediate Right of P

Based on the confirmed arrangement:

• P is located at Seat 4.
• The person sitting to the immediate right of P is the person in the next seat clockwise, which is Seat 5.
• According to our deduced arrangement, R is sitting at Seat 5.

Therefore, R sits to the immediate right of P.