Question

What is the number of the chair initially occupied by Bashir?

• A. Bashir
• B. Chhavi
• C. Davies
• D. No one
• A. Chairs numbered 4, 5, 6, and 7
• B. Chairs numbered 1, 2, 3, and 4
• C. Chairs numbered 2, 3, 4, and 5
• D. Chairs numbered 1, 2, 6, and 7
• A. Chhavi only
• B. Davies only
• C. Chhavi and Davies
• D. Aslam and Chhavi

Answer 1

Correct Answer: 4

Let's analyze the seating arrangement and identify the initial position of Bashir: Number the chairs clockwise from 1 to 7. Since Aslam and Chhavi sit next to each other, assume Aslam is in chair 1 and Chhavi in chair 2 initially (or vice versa, but both together). Bashir and Davies must be on chairs with empty spaces on either side. Given Davies moves to chair 2 after Turn 1, this implies Aslam initially moves from chair 1 to chair 3, placing Davies in chair 2 (as it's specified that Davies occupies chair 2 after Turn 1). This means Bashir must have been on chair 6 or 7 with empty chairs (1 and 6 or 7 and 1 around them) in their initial positions. Given Chhavi ends up on chair 7 after Turn 2 and friends are adjacent after Turn 2, Bashir must initially be on chair 4 moving to chair 5 after Turn 2. The adjacency after turn 2 aligns: Aslam (3), Davies (2), Bashir (5), Chhavi (7). Given Davies ends at chair 4 after Turn 5 confirms Bashir's movement pattern and positions. Thus, Bashir initially occupied chair 4.

Answer 2

Step 1: Fix Davies' initial chair. & nbsp;

Davies occupies Chair 2 after Turn 1. Since he does not move in Turn 1, he must already be in Chair 2 initially.

He must have empty chairs on both sides initially; hence Chairs 1 and 3 were empty at the start.

\[ D \text{ at } 2,\quad \text{so Chairs } 1 \text{ and } 3 \text{ are empty.} \]

Step 2: Fix Chhavi and Aslam initially.

Chhavi occupies Chair 7 after Turn 2. She does not move until Turn 3; therefore, she must have been at Chair 7 initially.

\[ C \text{ at } 7. \]

Aslam and Chhavi are adjacent initially. The chairs adjacent to 7 are 6 and 1. Since Chair 1 must be empty, Aslam must be at Chair 6.

\[ A \text{ at } 6. \]

So far:

\[ D(2),\ A(6),\ C(7),\ \text{empty: } 1,3,\text{ and two of } \{4,5\}. \]

Step 3: Determine Bashir's initial position.

Remaining chairs: 4 and 5. Bashir must have empty chairs on both sides initially.

Case 1: Bashir at Chair 5.

Neighbors: 4 and 6. Chair 6 is occupied → invalid.

Case 2: Bashir at Chair 4.

Neighbors: 3 and 5. Both are empty → valid.

\[ B \text{ at } 4. \]

Initial configuration:

\[ A(6),\ B(4),\ C(7),\ D(2). \]

Step 4: Verification.

Empty chairs: 1, 3, 5.

Turn 1 (Aslam moves):

From 6, the first empty clockwise is 1 → Aslam moves to 1.

\[ A(1), D(2), B(4), C(7) \]

Turn 2 (Bashir moves from 4):

Nearest empty counterclockwise is 3 → Bashir moves to 3.

Occupied chairs are \(7, 1, 2, 3\): a block of four adjacent chairs, satisfying the condition.

Conclusion:

Bashir initially occupied \(\boxed{4}\).

Answer 3

To solve the problem, we will carefully follow the details provided in the comprehension building block, using the rules and movements described:

1. Initially, four friends - Aslam (A), Bashir (B), Chhavi (C), and Davies (D) - occupy 4 chairs among the 7 chairs. Let the initial configuration of friends be: 
   • Aslam and Chhavi are sitting next to each other.
   • Bashir and Davies have an empty chair on either side of them.
2. Turn 1: Aslam moves first. If Davies is to occupy Chair 2 after this turn, Aslam must move to Chair 3, assuming Davies initially occupies a chair that allows for this continuity.
3. Configuration after Turn 1:
   • Davies occupies Chair 2.
   • Aslam takes the next empty chair in the direction chosen by Aslam - assumed to be Chair 3 for continuity with Turn 2 requirements.
4. Turn 2: Bashir moves and the condition is that "the four friends occupy adjacent chairs only at the end of Turn 2." Let's assume:
   • Bashir moves to Chair 1. The configuration now aligns like Chair 1: Bashir, Chair 2: Davies, Chair 3: Aslam, and Chair 7: Chhavi.
5. Turn 3: Chhavi moves next. Given that Chair 4 was initially empty, and Chhavi was next to Aslam at the start:
   • Chhavi can move to Chair 5 since Chair 4 is empty right after Turn 1 and Turn 2 positions.
6. Position after Turn 3:
   • Chair 4 remains empty since Chhavi moves to Chair 5 after occupying Chair 7 by moving one position clockwise.
7. The question asks who sits on Chair 4 at the end of Turn 3, as explained above, Chair 4 is empty.

Therefore, the correct answer is:

No one

Answer 4

Step 1: Turn 1 (Aslam moves). & nbsp;

Aslam moves first from Chair 6. To allow the adjacency of all four friends at the end of Turn 2 (a required condition), Aslam must move to Chair 1.

\[ A(1),\ D(2),\ B(4),\ C(7) \]

Step 2: Turn 2 (Bashir moves).

Bashir moves from Chair 4. To make all four friends adjacent at the end of Turn 2, Bashir must move to the empty Chair 3.

\[ A(1),\ D(2),\ B(3),\ C(7) \]

The chairs \(7,1,2,3\) form a consecutive block — satisfying the condition.

Step 3: Turn 3 (Chhavi moves).

Chhavi is at Chair 7. Empty chairs are 4, 5, and 6.

If Chhavi moved to Chair 4, the occupied chairs would be \(1,2,3,4\): This forms another block of four adjacent friends.

But the problem states they are adjacent only at the end of Turn 2 and Turn 6. Thus Chhavi cannot move to Chair 4.

She must move in the other direction, reaching Chair 6 (the first empty chair counterclockwise).

\[ A(1),\ D(2),\ B(3),\ C(6) \]

Conclusion:

Chair 4 remains empty at the end of Turn 3.

\[ \boxed{\text{No one sits on Chair 4}} \]

Answer 5

To determine which chairs are occupied at the end of Turn 6, let's analyze the problem step by step based on the information given:

1. Initial Setup: The table has 7 chairs, numbered 1 through 7 in a clockwise order. We know:
   • Aslam (A) and Chhavi (C) are sitting next to each other. 
   • Bashir (B) and Davies (D) have empty chairs on either side of them.
2. Davies's Chair after specific Turns:
   • Davies occupies Chair 2 after Turn 1.
   • Davies occupies Chair 4 after Turn 5.
3. Chhavi's position after Turn 2:
   • Chhavi occupies Chair 7 after Turn 2.
4. Turns Explained:
   • Turn 1 (Aslam): Aslam moves to the first available empty chair. We assume Aslam moves clockwise.
   • Turn 2 (Bashir): Bashir moves to the first available empty chair.
   • Turn 3 (Chhavi): Chhavi moves to occupy Chair 7 as given.
   • Turn 4 (Davies): Davies is already on Chair 2 and stays until end of Turn 5.
   • Turn 5 (Aslam): Aslam's move results in Davies occupying Chair 4 at the end, so Aslam and others rearrange accordingly.
   • Turn 6 (Bashir): They are adjacent, validating configuration of Chairs 4, 5, 6, and 7 being occupied.
5. Conclusion: At the end of Turn 6, the friends occupy Chairs 4, 5, 6, and 7. Thus, the correct answer is: Chairs numbered 4, 5, 6, and 7.

Answer 6

Step 1: Recall the positions at the end of Turn 3. & nbsp;

From the previous analysis:

\[ A(1),\ D(2),\ B(3),\ C(6) \]

Chairs 4, 5, and 7 are empty.

Step 2: Turn 4 (Davies moves).

Davies is currently at Chair 2. We are told that Davies must be at Chair 4 after Turn 5. Since Davies does not move in Turn 5, he must move to Chair 4 now in Turn 4.

\[ A(1),\ B(3),\ D(4),\ C(6) \]

Step 3: Turn 5 (Aslam moves).

Aslam is at Chair 1. We know that at the end of Turn 6, all four friends must again occupy adjacent chairs. To make that possible, Aslam should move from Chair 1 to Chair 7 (the first empty chair clockwise or counterclockwise chosen suitably).

\[ B(3),\ D(4),\ C(6),\ A(7) \]

Empty chair is 5.

Step 4: Turn 6 (Bashir moves).

Bashir is at Chair 3. The empty chair is 5. Moving from 3 to 5 (via the first empty in a suitable direction) gives:

\[ D(4),\ B(5),\ C(6),\ A(7) \]

Now the occupied chairs are \(4, 5, 6, 7\) — a block of four adjacent chairs, satisfying the condition that they are all adjacent at the end of Turn 6.

Conclusion:

At the end of Turn 6, the occupied chairs are:

\[ \boxed{4, 5, 6, \text{ and } 7} \]

Answer 7

To solve this question about seating arrangements at the end of different turns, let's follow the given data and rules systematically.

Understanding Initial Conditions and Moves: 

• The chairs are numbered 1 through 7 clockwise. Four friends are sitting on the chairs: Aslam (A), Bashir (B), Chhavi (C), and Davies (D).
• Initially, Aslam and Chhavi are sitting next to each other, which means they occupy consecutive chairs. For Bashir and Davies, there are empty chairs on either side of the chairs they sit on.

Let's analyze this further based on the given conditions:

• Aslam moves first (Turn 1), followed by Bashir, Chhavi, Davies (Turns 2, 3, and 4, respectively). Then Aslam, Bashir, and Chhavi move again (Turns 5, 6, and 7).
• According to Additional Information:
  1. All four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
  2. Davies occupies Chair 2 after Turn 1, implying Aslam must have moved to Chair 1.
  3. Davies then occupies Chair 4 after Turn 5, which indicates the order of movement.
  4. Chhavi occupies Chair 7 after Turn 2, showing his movement strategy as well.

Step-by-step seating position after each turn:

1. Turn 1: Aslam moves and occupies the first empty chair. Let's assume Aslam moves clockwise to Chair 1. Davies moves to Chair 2.
2. Turn 2: Bashir makes his move. Given that Bashir has empty chairs on either side initially, he can only move to achieve end adjacency as mentioned. Let's assume Bashir moves to Chair 3, making Chairs 1, 2, 3, and Bashir at 4 are adjacent. Chhavi will then move to Chair 5. At the end of this turn, chairs 1 to 4 are occupied consecutively: [D (2), B(3), C (5)].
3. After Turn 2: Chhavi is on Chair 5, completing this sequence.
4. Turns 3 to 5: Keeping the rule that Bashir should move only in available chairs, and based on the condition, Davies ends at chair 4 after turn 5. Thus, Bashir moves for achieving such continuity. Aslam returns to his initial chair position, and Bashir lands on a chair with an even cycle of moves.
5. End of Turn 6: All are again adjacent.
6. Final positions:
   • Chhavi at Chair 7, Davies at Chair 6, and Aslam and Bashir are still adjacent but positioned maintaining rules.

As a result, at the end of Turn 7, Bashir is not adjacent to Chhavi anymore but possibly remains alongside due to the arrangement, where Davies is the only neighbor of Bashir.

Conclusion: Thus, the friend sitting adjacent to Bashir at the end of Turn 7 is \(Davies\) only, which corresponds to option (b).

Answer 8

From the previous turns, we know that at the end of Turn 6 the configuration was:

\[ D(4),\ B(5),\ C(6),\ A(7) \] & nbsp;

All four are on adjacent chairs \(4, 5, 6, 7\).

Step 1: Turn 7 (Chhavi moves).

At the start of Turn 7:

\[ B(5),\ D(4),\ C(6),\ A(7) \]

Chhavi is at Chair 6. She must move in Turn 7 to the first empty chair in either clockwise or counterclockwise direction.

At this moment, the only empty chairs are 1, 2, and 3. Wherever Chhavi moves, she vacates Chair 6, so after her move:

• Bashir remains at Chair 5.
• Chair 6 becomes empty.
• Davies remains at Chair 4.
• Aslam remains at Chair 7.

Step 2: Identify who is adjacent to Bashir.

Bashir is at Chair 5. The chairs adjacent to Chair 5 are:

• Chair 4
• Chair 6

After Turn 7:

• Chair 4 is occupied by Davies.
• Chair 6 is empty (Chhavi has moved away).

So, the only friend adjacent to Bashir is Davies.

Conclusion:

At the end of Turn 7, only Davies sits adjacent to Bashir.

\[ \boxed{\text{Davies only}} \]