Six friends – A, B, C, D, E and F are sitting in a circle facing center. F is to the immediate left of A and B is sitting opposite to F. E and D are sitting opposite to each other. Who is sitting third right to A?
C
Understanding the Seating Arrangement Puzzle
This question asks us to determine the position of six friends – A, B, C, D, E, and F – who are sitting in a circle facing the center. We are given specific clues about their positions relative to each other. Our goal is to use these clues to map out the seating arrangement and then identify who is sitting third to the right of A.
Step-by-Step Solution for the Circle Arrangement
Let's break down the clues and build the circular seating arrangement step by step:
- There are six people sitting in a circle. We can imagine six positions around the circle.
- The first clue states that F is to the immediate left of A. If we place A at a specific position, F will be in the position immediately counter-clockwise to A (since they are facing the center).
- The second clue says that B is sitting opposite to F. In a circle of six positions, the person opposite is three positions away in either direction. If we know where F is, we can find B's position directly opposite.
- The third clue tells us that E and D are sitting opposite to each other. This means E and D occupy a pair of positions directly across the circle from each other.
- We have six people: A, B, C, D, E, F. By placing A, F, B, D, and E, the last remaining person, C, must occupy the last empty spot.
Building the Seating Plan
Let's visualize or sketch the circle. Assume positions 1 through 6 are arranged clockwise around the circle.
- Place A at Position 1.
- According to clue 1, F is immediately left of A. Since they face the center, 'left' is counter-clockwise. So, F is at Position 6.
- According to clue 2, B is opposite F. If F is at Position 6, B is opposite at Position 3 (6 - 3 = 3, or 6 + 3 = 9 mod 6 = 3 for positions).
So far, we have:
| Position | Person |
|---|---|
| 1 | A |
| 2 | ? |
| 3 | B |
| 4 | ? |
| 5 | ? |
| 6 | F |
- According to clue 3, E and D are opposite each other. The remaining positions are 2, 4, and 5. The only remaining pair of opposite positions is Position 2 and Position 5. So, E and D occupy these two spots (either E at 2 and D at 5, or D at 2 and E at 5). The specific order of E and D doesn't affect the position of the remaining person or the person third right to A.
- The last person is C. The only remaining position is Position 4. Therefore, C must be at Position 4.
The final seating arrangement looks like this:
| Position | Person |
|---|---|
| 1 | A |
| 2 | E or D |
| 3 | B |
| 4 | C |
| 5 | D or E |
| 6 | F |
Finding the Person Third Right to A
Now that we have the complete arrangement, let's find the person sitting third right to A. 'Right' in a circle facing the center means moving clockwise.
- Starting from A (at Position 1):
- First person to the right of A is at Position 2 (either E or D).
- Second person to the right of A is at Position 3 (B).
- Third person to the right of A is at Position 4 (C).
Thus, C is sitting third right to A.
Conclusion of the Seating Puzzle
By carefully following each clue – F immediate left of A, B opposite F, and E/D opposite each other – we were able to deduce the position of every person in the circle. We found that C occupies the position third to the right of A in this six-person circular seating arrangement.
Revision Table: Key Clues and Deductions
| Clue | Deduction |
|---|---|
| Six friends in a circle facing center | Use a circular arrangement model. 'Left' is counter-clockwise, 'Right' is clockwise from person's perspective. |
| F is to the immediate left of A | A and F are adjacent; F is counter-clockwise from A. |
| B is sitting opposite to F | B is 3 positions away from F in a 6-person circle. |
| E and D are sitting opposite to each other | E and D occupy the remaining opposite pair of positions. |
| Who is sitting third right to A? | Count 3 positions clockwise starting from A. |
Additional Information: Circular Arrangements
Circular seating arrangement problems are common in logical reasoning tests. Here are some key points to remember when solving them:
- Facing Center: When people face the center, their left is the counter-clockwise direction and their right is the clockwise direction.
- Facing Away from Center: If people face away from the center, their left is the clockwise direction and their right is the counter-clockwise direction.
- Opposite Positions: In a circle with \(n\) positions, the position opposite to position \(p\) is \(p + n/2\) (if \(n\) is even). For a 6-person circle, positions opposite are 1-4, 2-5, 3-6.
- Relative Positions: "Immediate left/right" means the very next seat in that direction. "Second left/right" means skipping one seat, and so on.
- Starting Point: You can start placing the first person in any position, but consistency is key. The relative positions of everyone else will fall into place based on the clues.
Solving these puzzles involves carefully reading each statement and building the arrangement step by step, eliminating possibilities as you go. Visualizing or drawing the circle can be very helpful.
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