Seven people, A, B, C, D, E, F and G are sitting in a row, facing north. Only five people sit between F and D. G sits third to the right of F. E is the immediate neighbour of C and D. B is not the immediate neighbour of G. How many people sit between A and F?
One
Analyzing the Seating Arrangement Puzzle
This problem requires us to figure out the exact positions of seven people (A, B, C, D, E, F, G) sitting in a single row. They are all facing north. Our main goal is to determine the final seating order and then count how many people are seated between individuals A and F.
Breaking Down the Clues
Let's list all the pieces of information given:
- There are a total of 7 people arranged in a row.
- Everyone is facing the North direction.
- Exactly five people are sitting between person F and person D.
- Person G is positioned third to the right of person F.
- Person E is sitting immediately next to both person C and person D.
- Person B is not sitting immediately next to person G.
Deducing the Arrangement Step-by-Step
Step 1: Determine the positions of F and D
With 7 seats in total, the condition "Only five people sit between F and D" strongly suggests that F and D must be occupying the two end seats. This creates a gap of 5 seats between them. There are two possibilities:
- F is in the first seat (leftmost) and D is in the seventh seat (rightmost): F _ _ _ _ _ D.
- D is in the first seat and F is in the seventh seat: D _ _ _ _ _ F.
Step 2: Position G relative to F
We are told that "G sits third to the right of F". Since they face North, "right" means moving towards the higher seat numbers.
- Let's examine the case D _ _ _ _ _ F. Here, F is in the 7th seat. There's no space to the right of F for G to sit. So, this case is not possible.
- Now, let's consider the case F _ _ _ _ _ D. F is in the 1st seat and D is in the 7th seat. G is third to the right of F. Counting from F (seat 1), the third seat to the right is seat 1 + 3 = 4. So, G is in the 4th seat. The arrangement now is: F _ _ G _ _ D.
Step 3: Place E and C based on adjacency
The clue "E is the immediate neighbour of C and D" is key here.
- We know D is in the 7th seat. Since E is D's immediate neighbour and it's a row, E must be in the 6th seat.
- E is also C's immediate neighbour. With E in the 6th seat, C must be in the 5th seat.
- The row now looks like this: F _ _ G C E D. We have filled seats 1, 4, 5, 6, and 7.
Step 4: Position the remaining people, A and B
The only people left to place are A and B. The empty seats are the 2nd and 3rd positions. This means A and B must occupy these two seats. There are two possible ways to arrange them:
- Arrangement 1: F A B G C E D
- Arrangement 2: F B A G C E D
Step 5: Use the final clue to finalize the order
The last condition is "B is not the immediate neighbour of G". G is in the 4th seat. The seats immediately next to G are the 3rd and 5th seats.
- In Arrangement 1 (F A B G C E D), B is in the 3rd seat. This seat is adjacent to G (4th seat). This arrangement violates the condition.
- In Arrangement 2 (F B A G C E D), B is in the 2nd seat. This seat is not next to G (4th seat). This arrangement satisfies all the given conditions.
Thus, the definitive seating arrangement from left to right (West to East, or position 1 to 7) is: F B A G C E D.
Calculating People Between A and F
We need to find how many people sit between A and F in the confirmed arrangement: F B A G C E D.
- F is located at the 1st position.
- A is located at the 3rd position.
- Looking at the positions between 1 and 3, we find only position 2.
- The person in position 2 is B.
- Therefore, there is exactly one person (B) sitting between A and F.
Similar Questions
Seven people, A, B, C, D, E, F and G, are sitting in a row, facing north. A sits fifth from the right end. Only two people sit between E and A. C is an immediate neighbour of G and E. B sits to the immediate right of F. How many people sit between D and B?
Seven people, B, C, D, E, F, G, and K, are sitting in a straight line, facing north. Only K sits to the left of G. Only four people sit between K and C. Only E sits between F and D and F is not an immediate neighbour of C. Who sits at the extreme right of the line?
I, J, K and L are sitting in a row. L and I are sitting next to each other and I and K are the ends. Who is sitting next to J?
E, F, G. and H are sitting in a row. F and H are adjacent. E and G are adjacent. G does not want to sit next to either H or F, and H does not want to sit next to E. Which two are sitting at the ends?
- Read the following question and decide which of the given statements is/are sufficient.
If X is a natural number, is X+6 odd?
Statements:
1. X−15 is a whole number.
2. X−6 is an odd number. - Seven people, A, B, C, D, E, F and G, are sitting in a row, facing north. No one sits to the right of E. Only three people sit between E and D. Only two people sit between D and A. F sits third to the left of B. G sits to the immediate right of B. How many people sit between B and E?
- Consider the given question and decide which of the following statements is sufficient to answer the question.
Five people, P, Q, R, S and T, are standing in a line; who is in the middle?
Statements:
1. Q is to the left of T.
2. S is in between P and T.
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?
