Seven friends K, L, M, N, O, P and Q are sitting in a straight line all facing the same direction. N is sitting at one of the corners. O is fourth to the right of Q. Only three persons are sitting between M and L. Q is to the immediate left of P. O is second to the right of K. Only four persons are sitting between N and M. What is L’s position?
Second to the left of P
Solving the Seating Arrangement Puzzle
This question involves arranging seven friends, K, L, M, N, O, P, and Q, in a straight line based on given clues. All friends are facing the same direction. We need to determine the final arrangement to find L's position.
Step-by-Step Analysis of Clues
Let's break down the information given in the clues and build the seating arrangement step by step:
- Seven friends in a straight line facing the same direction. Total positions: 1 2 3 4 5 6 7.
- N is sitting at one of the corners. N is either at position 1 or position 7.
- Only four persons are sitting between N and M.
- If N is at position 1, there are 4 people between N and M. This places M at position 1 + 4 + 1 = 6. Arrangement looks like: N _ _ _ _ M _
- If N is at position 7, there are 4 people between N and M. This places M at position 7 - 4 - 1 = 2. Arrangement looks like: _ M _ _ _ _ N
- Only three persons are sitting between M and L.
- Using Framework 1 (N at 1, M at 6): N _ _ _ _ M _. M is at 6. Three people between M and L means L is 4 positions away. L can be at 6 - 4 = 2 (to the left) or 6 + 4 = 10 (to the right, impossible as there are only 7 positions). So, if N is at 1, L must be at 2. Framework 1 becomes: N L _ _ _ M _ (N=1, L=2, M=6).
- Using Framework 2 (N at 7, M at 2): _ M _ _ _ _ N. M is at 2. Three people between M and L means L is 4 positions away. L can be at 2 - 4 = -2 (to the left, impossible) or 2 + 4 = 6 (to the right). So, if N is at 7, L must be at 6. Framework 2 becomes: _ M _ _ L _ N (M=2, L=6, N=7).
- Q is to the immediate left of P. Q and P are adjacent, with Q before P (assuming facing right). This is a "QP" block.
- O is fourth to the right of Q. This means there are 3 people sitting between Q and O. The position difference between Q and O is 4 (e.g., if Q is at 1, O is at 5).
- O is second to the right of K. This means there is 1 person sitting between K and O. The position difference between K and O is 2 (e.g., if K is at 1, O is at 3).
Combining Clues for Q, P, K, O
From clues 5, 6, and 7, we can deduce the relative positions of Q, P, K, and O.
- Q is at position $x$, P is at $x+1$. (Q P)
- O is at $x+4$. (Q _ _ _ O)
- K is at O minus 2 positions = $(x+4)-2 = x+2$. (K _ O)
So, the relative order from left to right must be Q(x), P(x+1), K(x+2), \_(x+3), O(x+4). The sequence of these four people and one empty spot effectively takes up 5 positions, arranged as Q P K _ O.
Fitting the Pieces Together
Now let's try to fit the sequence Q P K _ O into our two possible frameworks:
Framework 1: N(1) L(2) \_(3) \_(4) \_(5) M(6) \_(7). The remaining spots are 3, 4, 5, 7. These are not 5 consecutive spots, nor can we place Q, P, K, O respecting their relative distances (Q at x, P at x+1, K at x+2, O at x+4) using only these specific, non-consecutive spots. For example, for O to be 4 positions right of Q using these spots, Q at 3 means O at 7 (3+4). This is possible. If Q is at 3 and O is at 7, P must be at 4 (immediate right of Q). K must be 2 positions left of O (at 7), so K must be at 5 (7-2). This gives the arrangement N L Q P K M O. Let's verify this arrangement with all clues:
- N at corner (Pos 1)? Yes.
- 4 between N and M (N at 1, M at 6)? Yes, 4 people (L, Q, P, K) are between them.
- 3 between M and L (M at 6, L at 2)? Yes, 3 people (Q, P, K) are between them.
- Q immediate left of P (Q at 3, P at 4)? Yes.
- O 4 right of Q (Q at 3, O at 7)? Yes, 3 people (P, K, M) are between them. (Position difference 7-3=4).
- O 2 right of K (K at 5, O at 7)? Yes, 1 person (M) is between them. (Position difference 7-5=2).
All clues are satisfied by the arrangement N L Q P K M O.
Framework 2: \_(1) M(2) \_(3) \_(4) \_(5) L(6) N(7). The remaining spots are 1, 3, 4, 5. Can we place Q, P, K, O respecting their relative distances (Q at x, P at x+1, K at x+2, O at x+4) using only these spots? Q and O must have a position difference of 4. The only pair in (1, 3, 4, 5) with a difference of 4 is (1, 5). So Q would be at 1 and O would be at 5. If Q is at 1, P must be at 2 (immediate right of Q). But M is already at position 2 in this framework. Since P and M are different people, this framework is not possible.
Final Seating Arrangement
Based on the analysis, the only valid arrangement is:
| Position | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|
| Friend | N | L | Q | P | K | M | O |
Determining L's Position
The question asks for L's position. From the final arrangement (N L Q P K M O), L is at position 2. Let's compare this to the options provided:
- Immediate right of Q? Q is at 3, L is at 2. L is to the left of Q. Incorrect.
- Third to the right of P? P is at 4, L is at 2. L is to the left of P. Incorrect.
- Immediate left of N? N is at 1, L is at 2. L is to the right of N. Incorrect.
- Second to the left of P? P is at 4, L is at 2. There is one person (Q) between P and L. So, L is second to the left of P. Correct.
Conclusion
The final arrangement is N L Q P K M O. L is at position 2, and P is at position 4. L is second to the left of P.
Seating Arrangement Puzzle Revision Table
| Clue | Interpretation / Deduction |
|---|---|
| 7 friends, straight line | 7 positions available |
| N at corner | N is at position 1 or 7 |
| 4 persons between N and M | If N=1, M=6. If N=7, M=2. |
| 3 persons between M and L | If M=6, L=2. If M=2, L=6. |
| Q immediate left of P | QP are adjacent |
| O fourth right of Q | Q _ _ _ O (3 people between, position difference 4) |
| O second right of K | K _ O (1 person between, position difference 2) |
| Combined Q, P, K, O clues | Relative order Q P K _ O |
| Final Arrangement | N L Q P K M O |
Additional Information on Linear Arrangements
Linear arrangement puzzles are common in logical reasoning sections of competitive exams. Here are some key points to remember when solving them:
- Always determine the total number of positions.
- Note if everyone is facing the same direction or different directions (though in this problem, direction doesn't affect relative left/right).
- Identify clues that involve corners or ends of the line.
- Look for clues that specify the number of people between two individuals – this helps calculate position differences.
- Identify immediate left/right clues – these describe adjacent positions.
- Combine clues to deduce relative positions of groups of people (like the Q P K _ O sequence here).
- If there are multiple possibilities early on (like N's position), keep track of each framework and see which one allows all subsequent clues to fit.
- Draw diagrams or write down the positions to help visualize the arrangement as you build it.
- Once a potential arrangement is complete, double-check it against every single clue to ensure validity.
Practice with different types of linear arrangement questions will improve your speed and accuracy in identifying and combining clues effectively.
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?
