Seating Arrangement questions with answers and concepts

Eight persons A, B, C, D, E, F, G, and H are sitting in a row facing North. Given: (1) B sits third to the left of A. (2) D sits second to the right of A. (3) E sits at one of the extreme ends. (4) C sits to the immediate left of E. (5) F is not adjacent to A. (6) G sits somewhere to the left of D. Who sits at the extreme right end?

Step 1: From condition (3), E is at an extreme end. Let's try E at the left end (position 1).
Step 2: From condition (4), C sits immediately left of E. But if E is at position 1, C cannot be to its left (position 0 doesn't exist).
Step 3: Therefore, E must be at the right end (position 8).
Step 4: From condition (4), C sits immediately left of E, so C is at position 7.
Step 5: From condition (1), B is third to the left of A. Possible arrangements: B at 1, A at 4; B at 2, A at 5; B at 3, A at 6; B at 4, A at 7; B at 5, A at 8.
Step 6: Since E is at position 8, A cannot be at position 8.
Step 7: From condition (2), D is second to the right of A. If A is at 4, D is at 6; If A is at 5, D is at 7; If A is at 6, D is at 8 (but E is at 8); If A is at 7, D is at 9 (doesn't exist).
Step 8: Since C is at position 7, A cannot be at position 5 (would make D at $7=C$).
Step 9: Try A at position 4, then B is at position 1, and D is at position 6.
Step 10: Current arrangement: B(1), _, _, A(4), _, D(6), C(7), E(8).
Step 11: From condition (6), G sits left of D. Available positions for G: 2, 3, or 5.
Step 12: From condition (5), F is not adjacent to A (position 4), so F cannot be at 3 or 5.
Step 13: We have positions 2, 3, 5 for F, G, H.
Step 14: F cannot be at 3 or 5 (adjacent to A), so F must be at position 2.
Step 15: G is left of D, so G can be at 3 or 5. H takes the remaining position.
Step 16: Final arrangement: B(1), F(2), G(3), A(4), H(5), D(6), C(7), E(8) or B(1), F(2), H(3), A(4), G(5), D(6), C(7), E(8).
Step 17: In both valid arrangements, E is at the extreme right end.
Answer: E sits at the extreme right end.

Six friends P, Q, R, S, T, and U are sitting around a circular table facing the centre. Given: (1) P sits second to the left of Q. (2) R sits opposite to Q. (3) S sits to the immediate right of Q. (4) T does not sit adjacent to P. Who sits opposite to U?

Step 1: Set up a circular table with 6 equidistant positions numbered 1 to 6 clockwise.
Step 2: When facing the centre, moving clockwise corresponds to moving left, and moving anticlockwise corresponds to moving right.
Step 3: Fix Q at position 1 without loss of generality.
Step 4: From condition (1), P sits second to the left of Q (2 positions clockwise from 1): 1 → 2 → 3. So P is at position 3.
Step 5: From condition (2), R sits opposite to Q. In a 6-person circle, the opposite seat is 3 positions away: $1+3=4$. So R is at position 4.
Step 6: From condition (3), S sits to the immediate right of Q (1 position anticlockwise from 1): 1 → 6. So S is at position 6.
Step 7: The seats currently occupied are: Q(1), P(3), R(4), and S(6). The remaining unoccupied seats are positions 2 and 5 for T and U.
Step 8: From condition (4), T cannot sit adjacent to P (position 3). Position 2 is adjacent to position 3, while position 5 is not adjacent to position 3.
Step 9: Therefore, T must occupy position 5.
Step 10: Consequently, U occupies the remaining position 2.
Step 11: The question asks who sits opposite to U (position 2). The seat opposite position 2 is position $2+3=5$, which is occupied by T.
Answer: T sits opposite to U.

In two parallel rows with 4 people each: Row 1 (A, B, C, D) faces North; Row 2 (P, Q, R, S) faces South. Given: (1) A sits at the extreme left end of Row 1. (2) Q faces the person who is second to the right of A. (3) R sits to the immediate left of Q. (4) B faces S. (5) C is not at any extreme end. Who faces D?

Step 1: Map the row positions from our viewpoint (looking North):
- Row 1 (faces North): positions 1 (left) to 4 (right). For people facing North, right is East (1 → 4) and left is West.
- Row 2 (faces South): positioned directly opposite Row 1 at positions 1 to 4. For people facing South, right is West (4 → 1) and left is East (1 → 4).
Step 2: From condition (1), A sits at the extreme left end of Row 1, so A is at Row 1, Position 1.
Step 3: From condition (2), Q faces the person second to the right of A. Since A is at Position 1, the person second to A's right is at Position $1+2=3$. Therefore, Q is in Row 2 at Position 3.
Step 4: From condition (3), R sits to the immediate left of Q. In Row 2 facing South, moving left means moving East toward higher position numbers (3 → 4). Thus, R is at Position 4 of Row 2.
Step 5: Row 2 now has:\log_{Pos1} ,\log_{Pos2} , Q (Pos 3), R (Pos 4). The remaining members P and S must occupy Positions 1 and 2.
Step 6: From condition (5), C in Row 1 cannot sit at an extreme end (Positions 1 or 4). With A at Position 1, C must be at Position 2 or Position 3.
Step 7: From condition (4), B faces S. If C were at Position 3, then Position 3 of Row 1 would face Q (Position 3 of Row 2), leaving Positions 2 and 4 for B and D. If B is at Position 2, B faces S at Row 2 Position 2 (consistent!). This leaves D at Row 1 Position 4, facing R at Row 2 Position 4.
Step 8: Verify all conditions:
- Row 1: A(1), B(2), C(3), D(4)
- Row 2: P(1), S(2), Q(3), R(4)
- A is at left end of Row 1.
- Q(3) faces C(3), who is second right of A(1).
- R(4) is immediately left of Q(3).
- B(2) faces S(2).
- C(3) is not at any extreme end.
- D(4) faces R(4).
Answer: R faces D.

Five people A, B, C, D, and E are sitting in a row facing North. Given: (1) A is at the left end. (2) B is to the immediate right of C. (3) D is between B and E. (4) E is not at the right end. Who is at the right end?

Step 1: Set up 5 seats numbered 1 (extreme left) to 5 (extreme right).
Step 2: From condition (1), A sits at the left end, so A is at position 1.
Step 3: The remaining seats 2, 3, 4, 5 must be filled by B, C, D, E.
Step 4: From condition (2), B is to the immediate right of C, so C and B must appear as the contiguous block [C, B].
Step 5: From condition (3), D is between B and E. This means D lies strictly between B and E in linear order (either E ... D ... B or B ... D ... E).
Step 6: Consider Case 1: [C, B, D, E]. Then seats 2 to 5 would be occupied as C(2), B(3), D(4), E(5). But condition (4) explicitly states that E is not at the right end (seat 5). Therefore, Case 1 is impossible.
Step 7: Consider Case 2: E lies to the left of D, and D lies to the left of the [C, B] block, giving the linear order E followed by D followed by C then B.
Step 8: Placing this into seats 2 to 5 gives: Position 1: A, Position 2: E, Position 3: D, Position 4: C, Position 5: B.
Step 9: Verify all conditions for arrangement A - E - D - C - B:
- A is at the left end (seat 1): Satisfied.
- B is immediately right of C (seats 4 and 5): Satisfied.
- D is between B and E (D is at seat 3, between E at seat 2 and B at seat 5): Satisfied.
- E is not at the right end (E is at seat 2, not seat 5): Satisfied.
Step 10: Position 5 (the extreme right end) is occupied by B.
Answer: B is at the right end.

Six boys A, B, C, D, E and F are sitting in a row facing North. B sits immediately between A and C. C is to the immediate left of D. If A is at the extreme left, who is second from the left?

With A at the extreme left (seat 1) and B between “B” and “D”, the sequence is A - B - C. Person B occupies seat 2 (second from left).

Seven persons P, Q, R, S, T, U and V sit in a row facing North. P sits third from the left. Q sits second to the right of P. R sits immediately left of Q. Who sits immediately right of P?

Step 1: P is third from the left, so P is in seat 3.
Step 2: Q is second to the right of P, so Q is in seat 5.
Step 3: R is immediately left of Q, so R is in seat 4.
Step 4: Seat 4 is immediately right of P.
Answer: R

Eight persons sit in a row facing North. A is fourth from the left and B is third from the right. How many persons sit between A and B?

Step 1: A is fourth from the left, so, “0” is in seat 4.
Step 2: B is third from the right in a row of 8, so, “1” is in seat 6.
Step 3: Only seat 5 lies between seat 4 and seat 6.
Answer: 1