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
Eight friends, A, B, C, D, E, F, G and H, are sitting in two lines of four persons each. Both the lines are facing each other. A is facing D. E is to the immediate left of G. H is to the immediate right of B. C is facing G. F is facing H. B is to the immediate right of the person who is facing G. D is to the immediate left of F. Which four persons are sitting in the same line?
Nine employees, K, L, M, N, O, P, Q, R and S, are sitting in the office in a straight line, all facing the east. O is third to the right of M. K is third to the left of P. Q is between P and S. N is fourth to the right of M. P is to the immediate right of N. R is fourth to the left of O. Which of the following statements is NOT correct?
Eight north-facing restaurants named P, Q, R, S, T, U, V and W are located in a straight line. S is second to the left of T. W is third to the left of P. T is between P and V. S is third to the left of V. W is to the immediate right of U. R is third to the right of P. Who is sitting fourth to the right of S?
Anamika, Gopal, Nischal, Vanmayi, Shresta and Sripad are sitting in a straight line facing the north. Nischal is to the immediate left of Gopal. Shresta is between Anamika and Sripad. Sripad is at the second place from the right end. Four persons are sitting between Nischal and Vanmayi. If Gopal and Sripad interchange their positions, then who will be sitting between Vanmayi and Shresta?
A question is given, followed by two statements numbered (I) and (II). You have to decide whether the data provided in the statements is sufficient to answer the question. Read both the statements and select the appropriate answer.
Question: How many people are standing in the row where all people are facing north?
Statements:
(I) A is fourth from the left end; M is second to the right of A; and R is second from the left end.
(II) M is fourth from the right end; only two people Stand between M and B.
