Six friends – A, B, C, D, E and F are sitting in a circle facing centre. F is sitting immediate left of A and B is sitting opposite to E. A and D is sitting opposite to each other. Who is sitting opposite to F?
C
Solving the Circular Seating Arrangement Puzzle
This question involves a common type of logical reasoning puzzle: a circular seating arrangement. Six friends are sitting in a circle, all facing the centre. We are given specific conditions about their positions relative to each other. Our goal is to deduce the full arrangement and find who is sitting opposite to F.
Given Conditions for the Seating Arrangement
- Six friends: A, B, C, D, E, F.
- Sitting in a circle facing the centre.
- Condition 1: F is sitting immediate left of A.
- Condition 2: B is sitting opposite to E.
- Condition 3: A is sitting opposite to D.
Step-by-Step Deduction of the Seating Arrangement
Let's build the arrangement step by step based on the given conditions. In a circle with six people, positions are directly opposite when there are two people between them on either side.
- Place A and D: The easiest condition to start with is the opposite relationship. A and D are opposite to each other. Let's place A at any position, say the top. Then D must be directly opposite A.
- Place F immediate left of A: When facing the centre, "immediate left" means the person is sitting clockwise relative to A. So, place F in the position immediately clockwise to A.
- Consider the remaining positions: We have placed A, D, and F. The remaining three friends are B, C, and E. There are three empty seats left.
- Place B and E: We know B is opposite to E. Among the three remaining seats, only two can be opposite each other. These two opposite seats must be occupied by B and E. The remaining single seat is where the last person sits.
- Place C: The only friend left is C. The only seat left is the one that is not part of the B-E opposite pair. This seat must be occupied by C.
- Final Arrangement Check: Now let's look at the positions. We have A opposite D, and B opposite E. This leaves C in the final spot. Let's verify the position of F relative to A. F is immediately left (clockwise) of A. With A and D opposite, and F next to A, who is opposite to F?
Determining Who is Opposite to F
Based on our arrangement:
We have the opposite pairs:
- A is opposite D.
- B is opposite E.
This accounts for 4 friends. The remaining two friends are C and F. Since A is opposite D and B is opposite E, the only remaining pair of opposite positions must be occupied by C and F. Therefore, C must be sitting opposite to F.
| Friend | Opposite Friend |
|---|---|
| A | D |
| B | E |
| F | C |
The arrangement confirms that C is opposite to F.
Conclusion
Following the conditions for the circular seating arrangement, we determined the positions of all six friends. The friend sitting opposite to F is C.
Revision Table: Key Concepts in Seating Arrangements
| Concept | Description |
|---|---|
| Circular Arrangement | People are seated around a circle. Relative positions (left/right) depend on whether they face the centre or away. |
| Facing Centre | Left is clockwise movement, Right is anti-clockwise movement relative to the person. |
| Opposite Positions | In a circle of N people, two people are opposite if N/2 - 1 people are between them on each side. For 6 people, 6/2 - 1 = 2 people are between opposite friends. |
| Immediate Left/Right | The person directly next to someone on their left or right side. |
Additional Information: Types of Arrangement Puzzles
Seating arrangement puzzles are common in logical reasoning sections of exams. They can involve:
- Linear Arrangement: People in a straight line (single row or double rows). Directions are typically left, right, north, south, etc.
- Circular Arrangement: People in a circle, often facing inwards or outwards.
- Rectangular/Square Arrangement: People around a table, often at corners and sides.
- Combination: Sometimes arrangements combined with other attributes like profession, city, etc.
Solving these puzzles requires careful reading of conditions, drawing diagrams, and step-by-step deduction.
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