A, B, E, F, L, M and P are sitting around a circular table, facing the centre. Only three people sit between P and E when counted from the left of P. Only three people sit between M and A when counted from the right of A. L sits to the immediate right of M. F is an immediate neighbour of A as well as E. Who sits second to the left of B?
F
Solving the Circular Table Seating Arrangement Puzzle
This problem requires us to figure out the seating positions of seven people around a circular table based on a set of clues. The people are A, B, E, F, L, M, and P, and they are all facing the centre. Our goal is to find out who is seated second to the left of person B.
Analyzing the Seating Clues
Let's break down each clue to understand the relationships between the people:
- People: A, B, E, F, L, M, P (7 total).
- Arrangement: Circular table, facing the centre.
- Clue 1: "Only three people sit between P and E when counted from the left of P." In a circle of 7 people, if there are 3 people between two individuals, they must be sitting directly opposite each other.
- Clue 4: "F is an immediate neighbour of A as well as E." This means F sits between A and E (A-F-E or E-F-A).
- Clue 3: "L sits to the immediate right of M." This gives us a fixed pair: M followed immediately by L in the clockwise direction (M-L).
- Clue 2: "Only three people sit between M and A when counted from the right of A." This clue helps place M and A relative to each other.
Step-by-Step Arrangement Construction
Step 1: Placing P and E
From Clue 1, P and E are opposite each other. Imagine the 7 seats numbered 1 to 7 clockwise. Let's place P at seat 1. Counting three seats to P's left (seats 7, 6, 5), we find E must be at seat 4.
Current Placement: P is at 1, E is at 4. Seats 2, 3, 5, 6, 7 are empty.
Step 2: Placing F and A
Clue 4 states F is a neighbour to both E and A. Since E is at seat 4, F must be in either seat 3 or seat 5. A must be next to F on the other side.
Let's consider the two possibilities for F:
- Possibility 1: F is at seat 3. Then A must be at seat 2 (neighbour of F, cannot be seat 4 where E is). Arrangement: P(1), A(2), F(3), E(4), _, _, _.
- Possibility 2: F is at seat 5. Then A must be at seat 6 (neighbour of F, cannot be seat 4 where E is). Arrangement: P(1), _, _, E(4), F(5), A(6), _.
Step 3: Using Clue 2 to Test Possibilities
Clue 2: "Only three people sit between M and A when counted from the right of A."
- Testing Possibility 1: P(1), A(2), F(3), E(4), _, _, _. A is at seat 2. Counting from A's right: seat 3 (F), seat 4 (E), seat 5. This means M must be at seat 5. Arrangement: P(1), A(2), F(3), E(4), M(5), _, _.
- Testing Possibility 2: P(1), _, _, E(4), F(5), A(6), _. A is at seat 6. Counting from A's right: seat 7, seat 1 (P), seat 2. This means M must be at seat 2. Arrangement: P(1), M(2), _, E(4), F(5), A(6), _.
Step 4: Using Clue 3 to Finalize the Arrangement
Clue 3: "L sits to the immediate right of M."
- Continuing Possibility 1: We have P(1), A(2), F(3), E(4), M(5), _, _. M is at seat 5. M's immediate right is seat 6. So, L must be at seat 6. Arrangement: P(1), A(2), F(3), E(4), M(5), L(6), _. The only remaining person is B, who goes to seat 7. Final Arrangement 1: P, A, F, E, M, L, B (clockwise).
- Continuing Possibility 2: We have P(1), M(2), _, E(4), F(5), A(6), _. M is at seat 2. M's immediate right is seat 3. So, L must be at seat 3. Arrangement: P(1), M(2), L(3), E(4), F(5), A(6), _. The only remaining person is B, who goes to seat 7. Final Arrangement 2: P, M, L, E, F, A, B (clockwise).
Step 5: Verifying the Correct Arrangement
Let's check if Final Arrangement 2 (P, M, L, E, F, A, B) satisfies all conditions:
| Seat 1: | P |
| Seat 2: | M |
| Seat 3: | L |
| Seat 4: | E |
| Seat 5: | F |
| Seat 6: | A |
| Seat 7: | B |
- Clue 1 Check: P(1) and E(4). Counting left from P: 7(B), 6(A), 5(F) are between them. (3 people). Correct.
- Clue 2 Check: M(2) and A(6). Counting right from A: 7(B), 1(P), 2(M) are between them. (3 people). Correct.
- Clue 3 Check: L(3) is to the immediate right of M(2). Correct.
- Clue 4 Check: F(5) is next to E(4) and A(6). Correct.
This arrangement is consistent with all the clues.
Identifying Who Sits Second to the Left of B
According to the confirmed arrangement (clockwise P, M, L, E, F, A, B), B is at seat 7.
- The person immediately to the left of B (seat 7) is A (at seat 6).
- The person second to the left of B is F (at seat 5).
Final Conclusion
Based on the step-by-step deduction and verification, F sits second to the left of B.
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Important Questions from Seating arrangement
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2. E is seated next to A
3. D and C are separated by two seats
Select the correct answer using the code given below:
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