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
Seven people, A, B, C, D, E, F and G, are sitting in a straight row facing the north. Only two people sit to the left of C. Only two people sit between A and B. B sits to the left of A. E is an immediate neighbour of A to the right. Only one person sits to the right of D. F is not an immediate neighbour of B. Who sits at the centre?
P, Q, R and S are sitting on a bench and facing in the same direction. P sits next to Q but not next to R. S, who is sitting on the extreme right, does not sit next to either Q or R. How many of them each have two neighbors?
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?
