Six persons P, Q, R, S, T and U are sitting around a circular table facing the center not necessarily in the same order. Consider the following statements:
• P sits next to S and T.
• Q sits diametrically opposite to P.
• The shortest distance between S and R is equal to the shortest distance between T and U.
Based on the above statements, Q is a neighbor of
Seating Arrangement Logic
Six people (P, Q, R, S, T, U) are seated around a circular table facing the center. The goal is to determine Q's neighbors based on the provided statements.
Analyzing Seating Statements
- Statement 1: P sits next to S and T. This means the sequence is either S-P-T or T-P-S.
- Statement 2: Q sits diametrically opposite to P. In a circle of 6 people, this means there are two people between P and Q on either side.
- Statement 3: The shortest distance between S and R is equal to the shortest distance between T and U. The "distance" here refers to the number of people sitting between them along the shorter arc. Adjacent means 0 people between.
Deducing the Arrangement
Visualize the table with 6 positions (1 to 6 clockwise).
1. Place P at position 1. From Statement 2, Q is at position 4.
2. From Statement 1, S and T must be neighbors of P. This leads to two possible scenarios:
- Scenario A: S is at position 2 and T is at position 6. (Positions occupied: P(1), S(2), Q(4), T(6))
- Scenario B: T is at position 2 and S is at position 6. (Positions occupied: P(1), T(2), Q(4), S(6))
3. The remaining people are R and U. The remaining positions are 3 and 5.
Testing Scenario A (P-S-?-Q-?-T)
Positions: 1(P), 2(S), 3(?), 4(Q), 5(?), 6(T)
- Possibility A1: R at 3, U at 5. Arrangement: P, S, R, Q, U, T.
- Distance(S, R): S(2) and R(3) are adjacent. 0 people between. Distance = 0.
- Distance(T, U): T(6) and U(5) are adjacent. 0 people between. Distance = 0.
- Statement 3 (0 = 0) is satisfied.
- In this arrangement, Q(4)'s neighbors are R(3) and U(5).
- Possibility A2: U at 3, R at 5. Arrangement: P, S, U, Q, R, T.
- Distance(S, R): S(2) to R(5). People between: U(3), Q(4) (2 people). Distance = 2.
- Distance(T, U): T(6) to U(3). People between: P(1), S(2) or R(5), Q(4) (2 people). Distance = 2.
- Statement 3 (2 = 2) is satisfied.
- In this arrangement, Q(4)'s neighbors are U(3) and R(5).
Testing Scenario B (P-T-?-Q-?-S)
Positions: 1(P), 2(T), 3(?), 4(Q), 5(?), 6(S)
- Possibility B1: R at 3, U at 5. Arrangement: P, T, R, Q, U, S.
- Distance(S, R): S(6) to R(3). People between: P(1), T(2) or Q(4), U(5) (2 people). Distance = 2.
- Distance(T, U): T(2) to U(5). People between: R(3), Q(4) or P(1), S(6) (2 people). Distance = 2.
- Statement 3 (2 = 2) is satisfied.
- In this arrangement, Q(4)'s neighbors are R(3) and U(5).
- Possibility B2: U at 3, R at 5. Arrangement: P, T, U, Q, R, S.
- Distance(S, R): S(6) and R(5) are adjacent. 0 people between. Distance = 0.
- Distance(T, U): T(2) and U(3) are adjacent. 0 people between. Distance = 0.
- Statement 3 (0 = 0) is satisfied.
- In this arrangement, Q(4)'s neighbors are U(3) and R(5).
Final Conclusion
In all valid seating arrangements derived from the statements (A1, A2, B1, B2), Q is consistently found to be sitting between R and U.
Important Questions from Seating Arrangement
- P and Q have been allotted a hostel room with two beds, a study table, and an almirah. P is an avid bird-watcher and wants to sit at the table and watch birds outside the window. Q does not mind that as long as his bed is close to the ceiling fan.
Which one of the following arrangements suits them the most? Seven cars P, Q, R, S, T, U and V are parked in a row not necessarily in that order. The cars T and U should be parked next to each other. The cars S and V also should be parked next to each other, whereas P and Q cannot be parked next to each other. Q and S must be parked next to each other. R is parked to the immediate right of V. T is parked to the left of U.
Based on the above statements, the only INCORRECT option given below is:- Four persons P, Q, R and S are to be seated in a row, all facing the same direction, but not necessarily in the same order. P and R cannot sit adjacent to each other. S should be seated to the right of Q. The number of distinct seating arrangements possible is:
- P, Q, R, S, T and U are seated around a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and U now switch seats, which of the following must necessarily be true?
Five persons P, Q, R, S and T are sitting in a row not necessarily in the same order. Q and R are separated by one person, and S should not be seated adjacent to Q.
The number of distinct seating arrangements possible is:
