Six boys A, B, C, D, E, and F are sitting in a straight row facing north (not necessarily in the same order). B sits second to the right of D. A sits fourth to the left of F. F is not sitting on the extreme ends of the row. C sits second to the right of B. Who sits second to the right of A?
E
Solving the Six Boys Seating Arrangement Puzzle
This question is a classic example of a linear seating arrangement puzzle where we need to determine the exact position of six boys sitting in a straight row based on the given conditions. All boys are facing north, which means right is towards the right end of the row and left is towards the left end.
Analyzing the Given Conditions
Let's list down the conditions provided for the seating arrangement of boys A, B, C, D, E, and F:
- Condition 1: B sits second to the right of D. This implies there is one person sitting between D and B. We can represent this as D _ B.
- Condition 2: A sits fourth to the left of F. This means there are three people sitting between A and F. We can represent this as A _ _ _ F. This sequence takes up 5 consecutive positions.
- Condition 3: F is not sitting on the extreme ends of the row. Since there are 6 positions, F cannot be in position 1 or position 6.
- Condition 4: C sits second to the right of B. This implies there is one person sitting between B and C. We can represent this as B _ C.
Deducing the Seating Arrangement
We have 6 positions in the row. Let's try to combine the conditions to find the specific order.
From Condition 1 (D _ B) and Condition 4 (B _ C), we can combine them as B is common. Since both relationships are to the right, we can merge them sequentially: D is to the left of B, and B is to the left of C. Specifically, B is second right of D, and C is second right of B.
This gives us a block of 4 people: D _ B _ C. In this block, D is at position X, the person at X+1, B at X+2, the person at X+3, and C at X+4 relative to D. However, Condition 1 and 4 state "second to the right", meaning there is one person between them. So, D _ B means D (1st), person (2nd), B (3rd). B _ C means B (1st), person (2nd), C (3rd). Combining D _ B and B _ C implies D is to the left, then some gap, B, some gap, C. If B is second right of D, and C is second right of B, this means the arrangement is D, then one person, then B, then one person, then C. So the block is D _ B _ C.
Let's reconsider the spacing: D \xrightarrow{\text{2nd right}} B B \xrightarrow{\text{2nd right}} C This gives the relative order D (pos), (pos+1), B (pos+2), (pos+3), C (pos+4). This is a block of 5 positions for D, B, C and two intermediate people. So the pattern is D _ B _ C.
Let's re-read carefully: "B sits second to the right of D" (D, one person, B). "C sits second to the right of B" (B, one person, C). Combining these: D, one person, B, one person, C. This block D _ B _ C takes up 5 consecutive positions.
Now consider Condition 2: A sits fourth to the left of F. This means A, three people, F. A _ _ _ F. This block also takes up 5 consecutive positions.
We have 6 seats in total. Block 1: D _ B _ C (5 positions) Block 2: A _ _ _ F (5 positions)
Let's place the blocks within the 6 positions (1 to 6). If D _ B _ C takes positions 1-5: D at 1, person at 2, B at 3, person at 4, C at 5. Row looks like: D _ B _ C _. If D _ B _ C takes positions 2-6: D at 2, person at 3, B at 4, person at 5, C at 6. Row looks like: _ D _ B _ C.
Now let's integrate the A _ _ _ F block (A is 4th left of F, 3 people between them).
Case 1: D _ B _ C _ (Positions 1, 3, 5 filled by D, B, C). Positions 2, 4, 6 are empty. A _ _ _ F requires 5 consecutive spots. Can we fit A _ _ _ F into the empty spots (2, 4, 6) and the occupied spots, such that A is 4th left of F? If A is at 1, 4th left of F would be 1+4=5. F at 5. Row: A _ _ _ F _. But D is at 1. So A cannot be at 1. If A is at 2, 4th left of F would be 2+4=6. F at 6. Row: D A B _ C F. Check all conditions for D A B _ C F: D(1) A(2) B(3) _ (4) C(5) F(6). Conditions: 1. B (3) second right of D (1)? Yes. 2. A (2) fourth left of F (6)? Yes, 3 people (B, _, C) between. 3. F not at ends? F is at position 6, which IS an end. This case is invalid.
Case 2: _ D _ B _ C (Positions 2, 4, 6 filled by D, B, C). Positions 1, 3, 5 are empty. A _ _ _ F requires 5 consecutive spots. Can we fit A _ _ _ F? If A is at 1, 4th left of F would be 1+4=5. F at 5. Row: A D _ B F C. Let's check positions for A D _ B F C: A(1) D(2) _ (3) B(4) F(5) C(6). Conditions: 1. B (4) second right of D (2)? Yes, position 3 is between them. 2. A (1) fourth left of F (5)? Yes, 3 people (D, _, B) between them. 3. F not at ends? F is at position 5, which is not an end (1 or 6). Yes. 4. C (6) second right of B (4)? Yes, position 5 (F) is between them. This arrangement A D _ B F C satisfies all conditions.
Who is missing from A, B, C, D, F? E is missing. E must be in the empty spot, which is position 3.
The final confirmed seating arrangement is: Position 1: A Position 2: D Position 3: E Position 4: B Position 5: F Position 6: C
Arrangement: A D E B F C
Answering the Question
The question asks: Who sits second to the right of A?
- A is in Position 1.
- The person first to the right of A is at Position \(\text{1} + \text{1} = \text{2}\). This is D.
- The person second to the right of A is at Position \(\text{1} + \text{2} = \text{3}\). This is E.
Therefore, E sits second to the right of A.
Summary of the Seating Arrangement
| Position | Person |
|---|---|
| 1 | A |
| 2 | D |
| 3 | E |
| 4 | B |
| 5 | F |
| 6 | C |
Checking the arrangement: A(1) D(2) E(3) B(4) F(5) C(6)
- B(4) is second right of D(2). (D_B: D E B) Correct.
- A(1) is fourth left of F(5). (A___F: A D E B F) Correct.
- F(5) is not at ends (1 or 6). Correct.
- C(6) is second right of B(4). (B_C: B F C) Correct.
The arrangement is consistent with all conditions. Second to the right of A (at position 1) is the person at position 3, which is E.
Revision Table: Seating Arrangement Logic
| Condition | Interpretation | Inferred Pattern/Block |
|---|---|---|
| B is 2nd right of D | One person between D and B | D _ B |
| C is 2nd right of B | One person between B and C | B _ C |
| Combining D _ B and B _ C | D, one person, B, one person, C | D _ B _ C (5 positions) |
| A is 4th left of F | Three people between A and F | A _ _ _ F (5 positions) |
| F is not at ends | F is at position 2, 3, 4, or 5 (in a 6-person row) | |
| Fitting D _ B _ C and A _ _ _ F in 6 positions respecting F not at ends | Only A D E B F C works | A(1) D(2) E(3) B(4) F(5) C(6) |
Additional Information on Linear Arrangements
Linear arrangement puzzles are common in logical reasoning sections of various exams. They involve arranging people or objects in a line based on given clues about their relative positions.
- Facing North/South: When facing north, the right end is the viewer's right, and the left end is the viewer's left. When facing south, it's the opposite.
- "To the right/left of": Refers to the immediate neighbor unless a number is specified (e.g., "second to the right").
- "Between": "X is between Y and Z" means the order is Y X Z or Z X Y. "X is exactly between Y and Z" usually means X is the midpoint.
- "Second to the right/left": Means there is exactly one person between the two mentioned individuals.
- Strategy: Start with the most concrete clues (like someone being at an end or fixed relative positions that form a large block). Combine smaller blocks of relationships. Eliminate possibilities that contradict any condition.
Practice with different variations, such as people facing different directions or more complex relative positioning, can help improve speed and accuracy in solving these types of logical puzzles.
Important Questions from Linear Arrangement
M, N, L, O, Q and H are sitting in a row. Q and H are in the centre. M and N are at the ends. L is sitting to the immediate left of N. Who is to the right of M?
Five friends, Shruti, Shreya, Anup, Ankit and Kiran, are sitting in a row facing towards the south. Shruti is between Shreya and Anup. Kiran and Shreya are sitting at the extreme ends of the west and east, respectively. Who is sitting in the middle?
Five students are standing in a line. Suman is standing next to Pranav but not next to Deena. Kumar is standing next to Raju, who is standing on the extreme left, and Deena is not standing next to Kumar.
Who is standing in the middle?Eight friends, A, B, C, D, E, F, G and H, are sitting in a straight line, all facing the north. F is sitting between D and G. B is sitting between H and A. E is third to the left of G. G is sitting at one of the corners. H is third to the left of C. Who is sitting between A and E?
Five students are sitting in a row. Akbar is to the left of the person sitting in the middle, but to the right of Sekar. Prakash is to the right of Deva, and Ram is to the right of Prakash. Ram is second from the person sitting in the middle. Who is the person sitting in the middle?
