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?
C
Solving the Linear Seating Arrangement Puzzle
This question asks us to determine the seating arrangement of eight friends, A, B, C, D, E, F, G, and H, sitting in a straight line, all facing North. We are given several clues that help us deduce their positions. Since everyone is facing North, 'left' and 'right' are standard left and right as we look at the line.
Analyzing the Clues
Let's break down the information provided:
- F is sitting between D and G. This means they are in sequence like D-F-G or G-F-D.
- B is sitting between H and A. This means they are in sequence like H-B-A or A-B-H.
- E is third to the left of G.
- G is sitting at one of the corners. There are two corners in a straight line: the left end and the right end.
- H is third to the left of C.
Step-by-Step Deduction
Let's use the clues to build the arrangement. There are 8 positions in the line. Let's number them 1 to 8 from left to right.
Clue 1: G is sitting at one of the corners.
G is either at position 1 (left corner) or position 8 (right corner).
Clue 2: E is third to the left of G.
- If G is at position 1 (left corner), E would need to be at a position 3 steps to its left. However, there are no positions to the left of the left corner. So, G cannot be at position 1.
- Therefore, G must be at position 8 (right corner).
Now, let's find E's position. E is third to the left of G (at position 8). Moving left from 8:
- Position 7 is 1st to the left of 8.
- Position 6 is 2nd to the left of 8.
- Position 5 is 3rd to the left of 8.
So, E is at position 5.
Current arrangement snapshot:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|
| E | G |
Clue 3: F is sitting between D and G.
G is at position 8. The arrangement must be D-F-G or G-F-D. Since G is at the end (position 8), the only possibility is D-F-G, reading from left to right towards G. So, F must be at position 7 and D at position 6.
Updated arrangement snapshot:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|
| E | D | F | G |
Clue 4: H is third to the left of C.
Let's consider the remaining open positions: 1, 2, 3, and 4. We need to place H and C such that H is 3 positions to the left of C.
- If C is at position 4, H is at position \(4 - 3 = 1\). This is a valid position.
- If C is at position 3, H would be at position \(3 - 3 = 0\), which is not possible.
- If C is at position 2, H would be at position \(2 - 3\), which is not possible (negative position).
- If C is at position 1, H would be at position \(1 - 3\), which is not possible (negative position).
So, C must be at position 4, and H must be at position 1.
Updated arrangement snapshot:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|
| H | C | E | D | F | G |
Clue 5: B is sitting between H and A.
H is at position 1. The remaining open positions are 2 and 3. For B to be between H (at 1) and A, A must be at position 3, and B must be at position 2. This forms the sequence H-B-A.
Final arrangement:
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|
| H | B | A | C | E | D | F | G |
Verifying the Arrangement
Let's quickly check if the final arrangement H B A C E D F G satisfies all conditions:
- F is between D and G (positions 6, 7, 8 - D-F-G) - Yes.
- B is between H and A (positions 1, 2, 3 - H-B-A) - Yes.
- E is third to the left of G (G at 8, E at 5; \(8-5=3\)) - Yes.
- G is sitting at one of the corners (position 8) - Yes.
- H is third to the left of C (C at 4, H at 1; \(4-1=3\)) - Yes.
All conditions are met by the arrangement H B A C E D F G.
Answering the Question
The question asks: Who is sitting between A and E?
Looking at the final arrangement H B A C E D F G:
- A is at position 3.
- E is at position 5.
- The person at position 4, between A and E, is C.
Therefore, C is sitting between A and E.
Revision Table: Key Steps
| Step | Clue Used | Deduction | Partial/Final Arrangement |
|---|---|---|---|
| 1 | G is at a corner; E is 3rd left of G | G must be at the right corner (Pos 8). E is at Pos 5. | \_ \_ \_ \_ E \_ \_ G |
| 2 | F is between D and G | D-F-G sequence ending at Pos 8. D at Pos 6, F at Pos 7. | \_ \_ \_ \_ E D F G |
| 3 | H is 3rd left of C | Only possible placement in remaining spots: C at Pos 4, H at Pos 1. | H \_ \_ C E D F G |
| 4 | B is between H and A | Only possible placement in remaining spots: H-B-A sequence starting at Pos 1. A at Pos 3, B at Pos 2. | H B A C E D F G |
| 5 | Final Check & Answer | Verify all clues. Identify person between A (Pos 3) and E (Pos 5). | C is between A and E. |
Additional Information on Linear Arrangements
Linear seating arrangement puzzles are a common type of logical reasoning problem. The key to solving them is carefully reading each clue and using it to narrow down the possibilities for each person's position. When people are facing North, 'left' is towards position 1 and 'right' is towards position 8 (in an 8-person line numbered 1 to 8 from left to right). If they were facing South, the directions would be reversed.
Common clue types include:
- Relative positions (e.g., X is to the left/right of Y).
- Positions from ends (e.g., X is at an end, X is 3rd from the left end).
- Betweenness (e.g., X is between Y and Z).
- Fixed positions (less common in abstract puzzles, but possible).
It is often helpful to draw a diagram or use placeholders (like blanks or numbered spots) to keep track of the arrangement as you deduce it step by step.
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?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?
Five friends, R, S, V, P and Q, are sitting in a row facing north. Q is sitting to the right of R and left of S. If V is the only one sitting to the left of R, then who is sitting in the left most position?
