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 following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
Correct Answer :
Davies only
Solution :
The correct answer is Davies only.
Let's break down the puzzle step-by-step to track the positions of the four friends around the circular table of 7 chairs.
Step 1: Determine the Initial Positions
We know Davies (D) takes his first move on Turn 4. The problem states he occupies Chair 2 after Turn 1. Since he hasn't moved yet, he must have started on Chair 2.
Initially, D has empty chairs on either side. Therefore, Chair 1 and Chair 3 are empty.
Bashir (B) also needs empty chairs on both sides. He cannot be on Chair 1 or 3. If B is on Chair 7, then Chairs 6 and 1 are empty, leaving Chairs 4 and 5 for Aslam (A) and Chhavi (C). But we know C occupies Chair 7 after Turn 2 (and hasn't moved yet), so C must start on Chair 7. This contradicts B being on Chair 7. Thus, B must start on Chair 4, leaving Chairs 3 and 5 empty.
This leaves Chairs 6 and 7 for A and C. Since C must be on Chair 7, A starts on Chair 6.
Initial Setup: Aslam = 6, Bashir = 4, Chhavi = 7, Davies = 2. The empty chairs are 1, 3, and 5.
Step 2: Track Turns 1 and 2
Turn 1: Aslam moves from Chair 6 to the first empty chair, either Chair 1 (clockwise) or Chair 5 (counter-clockwise).
Turn 2: Bashir moves from Chair 4. After this turn, all four friends must occupy adjacent chairs. Currently, Davies is on Chair 2 and Chhavi is on Chair 7. To form a continuous block of four chairs that includes 2 and 7 on a 7-chair circular table, the occupied chairs must be 7, 1, 2, and 3.
For this to happen, Aslam must have moved to Chair 1 (in Turn 1), and Bashir must move to Chair 3 (in Turn 2).
Positions after Turn 2: Aslam = 1, Davies = 2, Bashir = 3, Chhavi = 7.
Step 3: Track Turns 3, 4, and 5
Turn 3: Chhavi moves from Chair 7. She can move to Chair 4 or 6. If she moves to Chair 4, the friends would occupy Chairs 1, 2, 3, and 4 (which are adjacent). But the rules state they are adjacent only after Turns 2 and 6. Therefore, she must move to Chair 6.
Positions after Turn 3: Aslam = 1, Davies = 2, Bashir = 3, Chhavi = 6.
Turn 4: Davies moves from Chair 2. We are given that Davies occupies Chair 4 after Turn 5. Since he doesn't move in Turn 5, he must move to Chair 4 during Turn 4.
Positions after Turn 4: Aslam = 1, Bashir = 3, Davies = 4, Chhavi = 6.
Turn 5: Aslam moves from Chair 1 to either Chair 2 or Chair 7.
Step 4: Track Turn 6
Turn 6: Bashir moves from Chair 3. After this turn, the friends must again occupy adjacent chairs.
Currently, Davies is on Chair 4 and Chhavi is on Chair 6. To form a continuous block of four chairs that includes 4 and 6, the group must occupy Chairs 4, 5, 6, and 7.
For this to happen, Aslam must have moved to Chair 7 in Turn 5, and Bashir must move to Chair 5 in Turn 6.
Positions after Turn 6: Davies = 4, Bashir = 5, Chhavi = 6, Aslam = 7.
Step 5: Track Turn 7 and Find the Final Answer
Turn 7: Chhavi moves from Chair 6. She will move to the first empty chair available (either Chair 1 or 3). By leaving her current seat, Chair 6 becomes empty.
The question asks who is sitting adjacent to Bashir after Turn 7.
Bashir is sitting on Chair 5. The chairs directly adjacent to Chair 5 are Chair 4 and Chair 6.
Looking at our final positions, Chair 4 is occupied by Davies, and Chair 6 is empty (since Chhavi just left it to move to an empty seat).
Therefore, Davies is the only person sitting on a chair adjacent to Bashir.
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