DIRECTIONS for questions: Read the information given below and answer the question that follows.

A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on. The friends take turns moving either clockwise or counter clockwise from their chair.

The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).

The following information is known.

1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.

2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2

Which of the chairs are occupied at the end of Turn 6?

The correct answer is Chairs numbered 4, 5, 6, and 7.

First, let us deduce the initial positions of the four friends: Aslam (A), Bashir (B), Chhavi (C), and Davies (D) on the seven chairs.

We are given that Davies occupies Chair 2 after Turn 1. Since Davies only gets to move in Turn 4, he must have started in Chair 2. Similarly, Chhavi occupies Chair 7 after Turn 2. Since Chhavi does not move until Turn 3, she must have started in Chair 7.

Therefore, initially: Davies is in Chair 2, and Chhavi is in Chair 7.

We also know that in the starting position, Aslam and Chhavi are sitting next to each other. Since Chhavi is in Chair 7, Aslam must be in Chair 1 or Chair 6.

Furthermore, Bashir and Davies both have empty chairs on either side of them initially. Since Davies is in Chair 2, Chairs 1 and 3 must be empty. This means Aslam cannot be in Chair 1, so Aslam must be in Chair 6.

Now, Chairs 1, 2 (Davies), 3, 6 (Aslam), and 7 (Chhavi) are accounted for. Bashir must have empty chairs on either side, meaning he must be in Chair 4 (which leaves Chairs 3 and 5 empty). If he were in Chair 5, Chair 6 would need to be empty, but it is already occupied by Aslam.

Thus, the initial arrangement is:

Chair 1: Empty
Chair 2: Davies
Chair 3: Empty
Chair 4: Bashir
Chair 5: Empty
Chair 6: Aslam
Chair 7: Chhavi

Now let us trace the turns step-by-step:

Turn 1 (Aslam moves): Aslam is at Chair 6. He must move to the first empty chair in either direction. Clockwise, Chair 7 is occupied, so the first empty chair is Chair 1. Counter-clockwise, the first empty chair is Chair 5. As we will see from the Turn 2 requirement, Aslam moves to Chair 1. Now, Aslam is at 1, Davies at 2, Bashir at 4, and Chhavi at 7.

Turn 2 (Bashir moves): Bashir is at Chair 4. He can move clockwise to 5 or counter-clockwise to 3. The rules state that after Turn 2, the four friends occupy adjacent chairs. To form a block of 4 adjacent chairs with Aslam at 1, Davies at 2, and Chhavi at 7, Bashir must move to Chair 3. This makes the newly occupied chairs 7, 1, 2, and 3, which are perfectly adjacent in the circular arrangement.

Turn 3 (Chhavi moves): Chhavi is at Chair 7. She can move clockwise to 4 or counter-clockwise to 6. We know from the prompt that in Turn 4, Davies will move to Chair 4 (since he occupies Chair 4 after Turn 5 and doesn't move during Turn 5). For Davies to be able to move to Chair 4 in Turn 4, it must be the first empty chair for him. Thus, Chhavi could not have moved to 4 in Turn 3. Chhavi must move counter-clockwise to Chair 6. Now, Aslam is at 1, Davies at 2, Bashir at 3, and Chhavi at 6.

Turn 4 (Davies moves): Davies is at Chair 2. He must move to Chair 4 to satisfy the given condition. Moving clockwise from 2, Chair 3 is occupied, so the first empty chair is indeed Chair 4. Davies successfully moves to Chair 4.

Turn 5 (Aslam moves): Aslam is at Chair 1. The empty chairs are 2, 5, and 7. Clockwise, the first empty chair is 2. Counter-clockwise, the first empty chair is 7. He must move to Chair 7. (If he moved to 2, it would be impossible for the group to sit in adjacent chairs after Turn 6). Now, Bashir is at 3, Davies at 4, Chhavi at 6, and Aslam is at 7.

Turn 6 (Bashir moves): Bashir is at Chair 3. The empty chairs are 1, 2, and 5. He can move counter-clockwise to 2 or clockwise to 5 (since 4 is occupied). The rules state they must occupy adjacent chairs after Turn 6. If Bashir moves to Chair 5, the final occupied chairs become 4 (Davies), 5 (Bashir), 6 (Chhavi), and 7 (Aslam), which neatly forms a block of 4 adjacent chairs.

Therefore, at the end of Turn 6, the occupied chairs are numbered 4, 5, 6, and 7.