A, B, C, D and E are sitting around a circular table facing the centre. A don't have B and E as his neighbours. E is sitting to the immediate right of D. When seen in clockwise direction, which of the order of sitting is correct?
BEDAC
Understanding Circular Seating Arrangement Puzzles
This question involves a circular seating arrangement puzzle. Five individuals, A, B, C, D, and E, are seated around a circular table, all facing the center. We are given specific conditions about their seating positions, and we need to identify the correct arrangement from the given options when seen in the clockwise direction.
Analyzing the Rules for Sitting Order
Let's break down the given rules:
- Rule 1: A does not have B and E as his neighbours. This means the two people sitting immediately next to A must be from the remaining individuals, which are C and D. So, A's neighbours must be C and D.
- Rule 2: E is sitting to the immediate right of D. In a circular arrangement facing the center, "immediate right" corresponds to the next person in the clockwise direction. So, this rule means that if you move clockwise from D, the very next person you encounter is E. This can be represented as a sequence D \(\rightarrow\) E in the clockwise direction.
We are looking for a clockwise order of sitting that satisfies both of these conditions.
Evaluating the Sitting Order Options
Let's examine each provided option as a potential clockwise arrangement around the table.
Option 1: CBEAD
If the clockwise order is C, B, E, A, D, then:
- The sequence is C \(\rightarrow\) B \(\rightarrow\) E \(\rightarrow\) A \(\rightarrow\) D \(\rightarrow\) C (wrapping around).
- Let's check Rule 1: A's neighbours are the person before A (E) and the person after A (D) in the clockwise sequence. So, A's neighbours are E and D. Rule 1 states A does not have B and E as neighbours. Since E is a neighbour of A in this arrangement, this option violates Rule 1.
Option 1 is incorrect.
Option 2: ACBDE
If the clockwise order is A, C, B, D, E, then:
- The sequence is A \(\rightarrow\) C \(\rightarrow\) B \(\rightarrow\) D \(\rightarrow\) E \(\rightarrow\) A (wrapping around).
- Let's check Rule 1: A's neighbours are the person before A (E, due to wrap-around) and the person after A (C). So, A's neighbours are E and C. Rule 1 states A does not have B and E as neighbours. Since E is a neighbour of A in this arrangement, this option violates Rule 1.
Option 2 is incorrect.
Option 3: DACEB
If the clockwise order is D, A, C, E, B, then:
- The sequence is D \(\rightarrow\) A \(\rightarrow\) C \(\rightarrow\) E \(\rightarrow\) B \(\rightarrow\) D (wrapping around).
- Let's check Rule 1: A's neighbours are the person before A (D) and the person after A (C). So, A's neighbours are D and C. Rule 1 states A does not have B and E as neighbours. D and C are not B or E, so Rule 1 is satisfied by this arrangement.
- Let's check Rule 2: E is immediate right of D. This means D should be immediately followed by E in the clockwise sequence. In this arrangement, D is followed by A. So, A is immediate right of D, not E. This option violates Rule 2.
Option 3 is incorrect.
Option 4: BEDAC
Let's consider the order B, E, D, A, C as the clockwise arrangement.
- The sequence is B \(\rightarrow\) E \(\rightarrow\) D \(\rightarrow\) A \(\rightarrow\) C \(\rightarrow\) B (wrapping around).
- Let's check Rule 1: A's neighbours are the person before A (D) and the person after A (C). So, A's neighbours are D and C. Rule 1 states A does not have B and E as neighbours. D and C are not B or E, so Rule 1 is satisfied by this arrangement.
Considering all the conditions given in the question, the order BEDAC is the correct arrangement.
Final Correct Seating Arrangement
Based on the analysis of the options and the given conditions, the correct order of sitting in the clockwise direction is BEDAC.
| Option | Clockwise Order | A's Neighbours | Rule 1 (A \(\neq\) B, E neighbours) | Rule 2 (D \(\rightarrow\) E clockwise) | Correct? |
|---|---|---|---|---|---|
| 1. CBEAD | C \(\rightarrow\) B \(\rightarrow\) E \(\rightarrow\) A \(\rightarrow\) D \(\rightarrow\) C | E, D | Violated (E is neighbour) | Satisfied (D \(\rightarrow\) E) | No |
| 2. ACBDE | A \(\rightarrow\) C \(\rightarrow\) B \(\rightarrow\) D \(\rightarrow\) E \(\rightarrow\) A | E, C | Violated (E is neighbour) | Satisfied (D \(\rightarrow\) E) | No |
| 3. DACEB | D \(\rightarrow\) A \(\rightarrow\) C \(\rightarrow\) E \(\rightarrow\) B \(\rightarrow\) D | D, C | Satisfied | Violated (D \(\rightarrow\) A) | No |
| 4. BEDAC | B \(\rightarrow\) E \(\rightarrow\) D \(\rightarrow\) A \(\rightarrow\) C \(\rightarrow\) B | D, C | Satisfied | - | Yes |
Revision Table: Circular Seating Rules
| Rule | Description | Application Example (Clockwise P, Q, R, S...) |
|---|---|---|
| Neighbours | The two people sitting immediately next to a person in a circular arrangement. | In P, Q, R, S..., Q and S are neighbours of R. |
| Immediate Right | The person immediately next in the clockwise direction when facing the center. | In P, Q, R, S..., Q is to the immediate right of P; R is to the immediate right of Q. This corresponds to the sequence P \(\rightarrow\) Q \(\rightarrow\) R... |
Additional Information: Seating Arrangement Puzzle Tips
Seating arrangement questions are common in logical reasoning tests. Here are a few tips for solving them:
- Always start with the most restrictive conditions. Conditions about immediate neighbours or positions (like immediate right/left) facing a particular direction are usually good starting points.
- Draw a diagram! For circular arrangements, drawing a circle and placing individuals based on the rules is very helpful. For linear arrangements, drawing a line of slots works well.
- Identify fixed positions first. If a rule specifies a position relative to someone else whose position is known (or implied), place them first.
- Look for connections between rules. One rule might place person A relative to B, and another rule might place person C relative to A, allowing you to build a chain or block of people.
- Eliminate options. If an option violates even one rule, you can immediately discard it.
Circular arrangements facing the center mean "right" is always clockwise and "left" is always anti-clockwise from the perspective of the person at that seat.
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Who among the following is a neighbour of S and R?
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