Solving the Circular Table Seating Arrangement Puzzle

This question asks us to determine the seating positions of six friends around a circular table based on a set of clues and identify who is sitting between two specific individuals, A and E.

Understanding the Problem

We have six friends: A, B, C, D, E, and F. They are seated around a circular table. Circular arrangements are common in logical reasoning puzzles. In a circular arrangement, the positions are relative to each other, and there is no defined start or end point. We need to interpret clues involving 'left', 'right', and 'between'. For 'left' and 'right' in a circular arrangement, we usually assume the people are facing the center of the table.

Analyzing the Clues

Let's list the given clues:

• B is sitting to the immediate left of D.
• C is third to the right of E.
• A is between C and F.
• D is sitting to the immediate left of E.

Step-by-Step Solution

Let's build the arrangement step by step using the clues. It's often helpful to start with a clue that links two people directly or positions someone relative to a known point.

Step 1: Use Clue 4: D is sitting to the immediate left of E.
Let's place E first. In a circular arrangement of 6 people, 'immediate left' means the person is in the very next seat in the counter-clockwise direction (assuming they are facing the center). So, E and D are next to each other.

Step 2: Use Clue 1: B is sitting to the immediate left of D.
Since D is immediately left of E, B is immediately left of D. This places B, D, and E in a sequence around the table: B is followed by D, and D is followed by E (in the clockwise direction, or B-D-E in a counter-clockwise reading of immediate left). The sequence B, D, E occupies three adjacent seats.

Step 3: Use Clue 2: C is third to the right of E.
Starting from E, count three positions in the clockwise direction ('right'). If E is at position 1, the first right is position 2, second right is position 3, and the third right is position 4. So, C is at position 4 relative to E.

Let's visualize the arrangement based on the steps so far for 6 seats:

Seats: _ _ _ _ _ _ (1 to 6 clockwise)

From Step 1 & 2, we have a sequence B - D - E counter-clockwise (immediate left). Let's place E at a position, say position 1. D is immediate left (counter-clockwise), so D is at position 6. B is immediate left of D, so B is at position 5.

• Position 1: E
• Position 6: D
• Position 5: B

From Step 3, C is third right of E. E is at position 1. Right is clockwise. 1 > 2 (1st right) > 3 (2nd right) > 4 (3rd right). So, C is at position 4.

• Position 1: E
• Position 2: ?
• Position 3: ?
• Position 4: C
• Position 5: B
• Position 6: D

The remaining empty positions are 2 and 3. The remaining people are A and F.

Step 4: Use Clue 3: A is between C and F.
This means A is seated immediately next to C on one side and immediately next to F on the other side. C is at position 4. The adjacent seats are position 3 and position 5. Position 5 is occupied by B. So, A must be next to C at position 3. For A to be between C (at 4) and F, F must be in the remaining adjacent seat to A, which is position 2 (as position 3 is next to 4, and position 2 is next to 3). So, F is at position 2, and A is at position 3.

The final arrangement in clockwise order is:

• Position 1: E
• Position 2: F
• Position 3: A
• Position 4: C
• Position 5: B
• Position 6: D

Let's quickly verify all clues with this arrangement:

• B is immediate left of D: D is at 6, immediate left (counter-clockwise) is 5, which is B. Correct.
• C is third to the right of E: E is at 1, third right (clockwise) is 1>2>3>4, which is C. Correct.
• A is between C and F: C is at 4, F is at 2, A is at 3. Around the circle, A (3) is indeed between C (4) and F (2). Correct.
• D is sitting to the immediate left of E: E is at 1, immediate left (counter-clockwise) is 6, which is D. Correct.

All clues are satisfied by this arrangement.

Identifying Who Sits Between A and E

The question asks who is sitting between A and E. In our clockwise arrangement: E, F, A, C, B, D. Looking at A (at position 3) and E (at position 1), the person sitting immediately between them along one path around the circle is F (at position 2).

Conclusion

Based on the step-by-step deduction from the clues, the person sitting between A and E is F.

The final answer is F.

Revision Table: Key Concepts

Understanding terms like 'immediate left', 'immediate right', and 'between' in circular arrangements is crucial for solving these puzzles. 'Left' typically means counter-clockwise, and 'right' means clockwise when facing the center.

Additional Information: Circular Arrangement Strategies

Circular arrangement problems often involve relative positioning. Here are some tips:

• Start with clues that fix the positions of two or more people relative to each other.
• Visualize the table or draw a diagram to help place people.
• Be consistent with your direction for 'left' and 'right' (e.g., always counter-clockwise for left).
• Use clues to eliminate possibilities or confirm placements.
• Once you have a potential arrangement, verify all the given clues to ensure it is correct.