B is seated third from the extreme right end of the line.
Only two people are seated between B and E.
C is sitting second from the right of B.
F is an immediate neighbour of B and C.
A is sitting to the immediate right of D.
How many people are seated between D and F?
Solving the Seating Arrangement Puzzle
This problem involves determining the exact seating positions of six people (A, B, C, D, E, F) based on given clues and then finding the number of people between two specific individuals, D and F.
Step 1: Visualizing the Setup
We have six positions in a straight line, and everyone is facing North. We can represent the seats from left to right:
$[Seat 1] [Seat 2] [Seat 3] [Seat 4] [Seat 5] [Seat 6]$
Step 2: Placing B
Clue: "B is seated third from the extreme right end of the line."
The extreme right is Seat 6. Third from the right means Seat 6 - 2 = Seat 4.
Arrangement after Step 2:
$[ _ ] [ _ ] [ _ ] [ B ] [ _ ] [ _ ]$
Step 3: Placing E
Clue: "Only two people are seated between B and E."
B is at Seat 4. If two people are between them, E could be at Seat 1 ($E _ _ B ...$) or Seat 7 (not possible). Therefore, E must be at Seat 1.
Arrangement after Step 3:
$[ E ] [ _ ] [ _ ] [ B ] [ _ ] [ _ ]$
Step 4: Placing C
Clue: "C is sitting second from the right of B."
B is at Seat 4. The seat immediately to the right is Seat 5. The second seat to the right is Seat 6.
Arrangement after Step 4:
$[ E ] [ _ ] [ _ ] [ B ] [ _ ] [ C ]$
Step 5: Placing F
Clue: "F is an immediate neighbour of B and C."
F must be next to B (Seat 4) and next to C (Seat 6). The only seat that satisfies both conditions is Seat 5.
Arrangement after Step 5:
$[ E ] [ _ ] [ _ ] [ B ] [ F ] [ C ]$
Step 6: Placing A and D
Clue: "A is sitting to the immediate right of D."
The remaining seats are Seat 2 and Seat 3. The remaining people are A and D.
To satisfy the condition that A is to the immediate right of D, D must be in Seat 2, and A must be in Seat 3.
Final Arrangement:
$[ E ] [ D ] [ A ] [ B ] [ F ] [ C ]$
Positions: 1 2 3 4 5 6
Step 7: Answering the Question
Question: "How many people are seated between D and F?"
D is at Seat 2. F is at Seat 5.
The people seated between Seat 2 and Seat 5 are those in Seat 3 (A) and Seat 4 (B).
Therefore, there are Two people seated between D and F.
Final Conclusion
Based on the step-by-step deduction from the given clues, the final seating arrangement is E, D, A, B, F, C from left to right. The number of people seated between D and F is two.
Important Questions from Linear Arrangement
- Five people (A, B, C, D and E) are sitting in a straight line. They all are facing towards the north. B is sitting immediately between C and E. A is sitting third to the left of E. C is sitting second to the right of D. Who is sitting at the extreme left end of line?
- Seven people A, B, C, D, E, F and G are sitting in a row, facing the north. Only three people sit to the left of D. B sits third to the left of D. F sits to the right of A but left of D. E sits to the right of C but left of G. How many people sit to the right of F?
- Seven people, I, J, K, L, M, N and O, are sitting in a row, facing north. Only three people sit to the left of M. Only I sits to the right of O. Only three people sit between O and N. J sits at some place to the left of K but at some place to the right of L. How many people sit between L and K?
- Seven people A, B, C, D, E, F and G are sitting in a row, facing north. Only two people sit between D and C. Only G sits to the right of E. Only one person sits between C and E. A sits at some place to the right of F but at some place to the left of B. How many people sit to the right of A?
- Seven people, A, B, C, D, P, Q and R, are sitting in a row, facing north. Only two people sit between Q and R. Only D sits to the right of A. Only one person sits between R and A. B sits at some place to the right of P but at some place to the left of C. How many people sit between C and P?
