Five houses K, L, M, N and O are situated in a row, all facing the north. M is to the immediate left of L. K is between O and M. N is third to the right of K. Which house is exactly in the middle?
M
Solving the House Arrangement Puzzle
This question asks us to determine the position of five houses (K, L, M, N, and O) arranged in a row, all facing north. We are given specific clues about their relative positions, and we need to find the house exactly in the middle of the row.
Let's break down the clues provided and build the arrangement step by step:
- "M is to the immediate left of L." This tells us that M and L are next to each other in that specific order (M then L). We can represent this partial arrangement as:
... M L ... - "K is between O and M." This means O, K, and M are together in that sequence (O K M). Combining this with the first clue (M L), we see that the arrangement must be O K M L. We can represent this sequence as:
... O K M L ... - "N is third to the right of K." Starting from K, we count three positions to the right. In our current sequence (O K M L), K is followed by M (1st to the right) and then L (2nd to the right). This means the 3rd position to the right of K must be occupied by N. Adding N to the end of our current sequence gives us:
O K M L N
Now let's verify if this arrangement O K M L N satisfies all the given conditions:
- Five houses K, L, M, N, O: Yes, all five are present.
- Situated in a row, all facing the north: This is the setup assumption.
- M is to the immediate left of L: Yes, M is directly to the left of L in O K M L N.
- K is between O and M: Yes, K is positioned directly between O and M in O K M L N.
- N is third to the right of K: Starting from K, M is the 1st to the right, L is the 2nd to the right, and N is the 3rd to the right. Yes.
All conditions are met by the arrangement O K M L N. Since there are five houses in the row, the middle house will be the third house from either end.
Let's number the positions in the row:
Position 1: O
Position 2: K
Position 3: M
Position 4: L
Position 5: N
The house at the third position is M.
Therefore, the house exactly in the middle is M.
Revision Table: House Arrangement Clues
| Clue | Interpretation | Partial/Final Arrangement |
|---|---|---|
| M is immediate left of L | M and L are adjacent, in order M, then L | ... M L ... |
| K is between O and M | O, K, and M are adjacent, in order O, K, then M | ... O K M ... |
| Combine Clue 1 & 2 | O K M followed by L | O K M L ... |
| N is third to the right of K | From K, count 3 positions right to find N | O K M L N (M is 1st right, L is 2nd right, N is 3rd right) |
| Final Arrangement | All clues satisfied | O K M L N |
| Middle House (5 houses) | The 3rd house in the row | M |
Additional Information on Linear Arrangements
Linear arrangement puzzles involve arranging people or objects in a straight line based on given conditions. Key concepts include:
- Relative Position: Describing a position based on another object (e.g., "to the left of", "to the right of", "between").
- Immediate Position: Means directly next to, with no object in between (e.g., "immediate left", "immediate right").
- Counting Positions: "Nth to the right/left" means counting N positions away from the reference object in that direction. The reference object is position 0 for counting. So, 1st to the right is the very next object on the right.
- Facing Direction: In this case, all houses face North, which means their left and right are our standard left and right. If they faced South, their left and right would be opposite to ours.
- Total Number of Objects: Knowing the total number helps identify the middle position. For an odd number 'n', the middle position is \((\frac{n+1}{2})^{th}\). For 5 houses, the middle is \((\frac{5+1}{2})^{th} = 3^{rd}\) position.
Solving these puzzles often involves drawing diagrams or writing down sequences to visualize the relationships and piece together the full arrangement.
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Important Questions from Linear Arrangement
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5 boys A, B, C, D and E are sitting in a row. E is sitting between D and A, B is to the right of A, C is at one of the extreme ends and C and D are sitting next to each other. Which of the following statement is false?
Five friends Ram, Priya, Raunak, Aditya and Shyam are sitting in a row facing north. Raunak is to the right of Shyam and Priya is to the left of Shyam but to the right of Rama. Raunak is to the left of Aditya. Who is fourth from the left end?
Seven friends P, Q, R, S, T, U, and V are sitting in a straight line facing north. Q sits fifth to the right of T. Q does not sit at any of the extreme ends. Two people sit between U and R. S sits third to the left of V. S sits exactly in the middle. U is not an immediate neighbour of P.
How many people sit between R and V?
