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
What is the number of the chair initially occupied by Bashir?
Correct Answer :
Solution :
The correct answer is 4.
To solve this problem, we need to determine the initial positions of the four friends based on the given clues about their starting conditions and their positions after certain turns. Let's break down the logic step-by-step.
Step 1: Understand the initial constraints
We are told that initially:
1. Aslam and Chhavi are sitting next to each other.
2. Davies has empty chairs on either side of him.
3. Bashir has empty chairs on either side of him.
Step 2: Determine Davies's and Chhavi's initial positions
The clues state that Aslam moves in Turn 1, Bashir in Turn 2, Chhavi in Turn 3, and Davies in Turn 4.
We are given that "Davies occupies Chair 2 after Turn 1". Since Davies does not take his turn to move until Turn 4, his position after Turn 1 must be the exact same as his initial position. Therefore, Davies initially occupied Chair 2.
Similarly, we are given that "Chhavi occupies Chair 7 after Turn 2". Since Chhavi does not take her turn to move until Turn 3, her position after Turn 2 is also the same as her initial position. Therefore, Chhavi initially occupied Chair 7.
Step 3: Determine Aslam's initial position
We know that initially, Aslam and Chhavi are sitting next to each other. Since Chhavi is at Chair 7, Aslam must be adjacent to her, meaning Aslam is at either Chair 1 or Chair 6.
We also know that Davies, who is sitting at Chair 2, must have empty chairs on either side of him. This means both Chair 1 and Chair 3 must be empty.
Because Chair 1 must be empty, Aslam cannot sit there. Thus, Aslam initially occupied Chair 6.
Step 4: Determine Bashir's initial position
At this point, we know the status of most chairs in the starting position:
- Chair 1: Empty (adjacent to Davies)
- Chair 2: Davies
- Chair 3: Empty (adjacent to Davies)
- Chair 6: Aslam
- Chair 7: Chhavi
This leaves only Chairs 4 and 5 available for Bashir. The rules state that Bashir must also have empty chairs on either side of him in the initial arrangement.
- If Bashir were to sit in Chair 5, his adjacent chairs would be Chair 4 and Chair 6. However, Chair 6 is occupied by Aslam, which violates the condition.
- If Bashir sits in Chair 4, his adjacent chairs are Chair 3 and Chair 5. We already know Chair 3 is empty, and placing him in Chair 4 leaves Chair 5 empty. This perfectly satisfies the condition that Bashir has empty chairs on both sides.
Therefore, Bashir must have initially occupied Chair 4.
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