The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction they choose 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?
Show Hint
Correct Answer: 4
Approach Solution - 1
The data: Seven chairs (1–7 clockwise); Aslam, Bashir, Chhavi, Davies on four of them. Start: Aslam and Chhavi adjacent; Bashir and Davies each have empty chairs on both sides. Move order A, B, C, D, A, B, C. A mover sits on the first empty chair in the chosen direction. Davies is on Chair 2 after Turn 1, Chair 4 after Turn 5; Chhavi on Chair 7 after Turn 2; all four adjacent only after Turns 2 and 6.
Step 1 – Davies starts on Chair 2. Davies moves only on Turn 4, so being on Chair 2 “after Turn 1” means Chair 2 is his starting seat. He needs empty neighbours, so Chairs 1 and 3 start empty.
Step 2 – Place the rest. Aslam\(\&\)Chhavi (adjacent) and Bashir (isolated) take chairs among 4–7 (with one of those also empty). The only opening that keeps Bashir's neighbours empty is Aslam on 6, Chhavi on 7, Bashir on 4 (Chairs 1, 3, 5 empty).
Step 3 – Confirm with the movement. From this start: T1 Aslam \(\to\) 1; T2 Bashir \(\to\) 3 (block 1,2,3,7 – all adjacent, and Chhavi already on 7). This matches every clue, confirming the opening.
\[ \text{Bashir's initial chair} = \boxed{4} \]
Approach Solution -2
Chhavi also hasn't had a turn by Turn 2 (her first move is Turn 3), so her stated position of Chair 7 after Turn 2 must be her starting seat as well. Since Aslam and Chhavi start next to each other, Aslam must start on Chair 6. That leaves Bashir as the only one left, sitting on Chair 4 with Chairs 3 and 5 empty beside him — the only placement that keeps him isolated.
Running the turns forward confirms this start is correct: Turn 1 — Aslam moves clockwise from 6, skips Chhavi at 7, lands on Chair 1. Turn 2 — Bashir moves counterclockwise from 4 into the empty Chair 3. The group now sits on Chairs 7,1,2,3, a contiguous block — matching the clue that all four are adjacent right after Turn 2. Continuing: Turn 3 sends Chhavi to Chair 6, Turn 4 sends Davies to Chair 4 (skipping Bashir), Turn 5 sends Aslam back to Chair 7, and Turn 6 sends Bashir to Chair 5 — recreating the second adjacent block (Chairs 4-7) exactly as stated. Every given fact checks out.
So Bashir's starting chair is \[ \boxed{4} \]
Who sits on the chair numbered 4 at the end of Turn 3?
Show Hint
- Bashir
- Chhavi
- Davies
- No one
The Correct Option is D
Approach Solution - 1
The data: Seven chairs (1–7 clockwise); A, B, C, D on four. Start: A and C adjacent; B and D isolated (empty on both sides). Order A, B, C, D, A, B, C; each mover takes the first empty chair in the chosen direction. D on Chair 2 after Turn 1, Chair 4 after Turn 5; C on Chair 7 after Turn 2; all four adjacent only after Turns 2 and 6.
Step 1 – Opening. D's “after Turn 1” position is its start (it moves only on Turn 4), so D starts on Chair 2 with Chairs 1, 3 empty. The adjacency and isolation clues then force: A on 6, C on 7, B on 4, D on 2 (Chairs 1, 3, 5 empty).
Step 2 – Step the turns.
\[ \text{After T1: A}{=}1,\ \text{B}{=}4,\ \text{C}{=}7,\ \text{D}{=}2 \] \[ \text{After T2: A}{=}1,\ \text{B}{=}3,\ \text{C}{=}7,\ \text{D}{=}2 \] \[ \text{After T3: A}{=}1,\ \text{B}{=}3,\ \text{C}{=}6,\ \text{D}{=}2 \]
Step 3 – Read Chair 4. At the end of Turn 3 the occupied chairs are 1, 2, 3 and 6. Chair 4 is empty.
\[ \text{Therefore } \boxed{\text{No one}} \text{ sits on Chair 4 after Turn 3.} \]
Approach Solution -2
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.
\[ \boxed{\text{No one sits on Chair 4}} \]
Which of the chairs are occupied at the end of Turn 6?
Show Hint
- Chairs numbered 4, 5, 6, and 7
- Chairs numbered 1, 2, 3, and 4
- Chairs numbered 2, 3, 4, and 5
- Chairs numbered 1, 2, 6, and 7
The Correct Option is A
Approach Solution - 1
The data: Seven chairs (1–7 clockwise); A, B, C, D on four. Start: A and C adjacent; B and D isolated. Order A, B, C, D, A, B, C; first-empty-seat moves. D on Chair 2 after Turn 1, Chair 4 after Turn 5; C on Chair 7 after Turn 2; all four adjacent only after Turns 2 and 6.
Step 1 – Opening. D starts on Chair 2 (it only moves on Turn 4), so Chairs 1, 3 are empty. The clues then force A on 6, C on 7, B on 4, D on 2.
Step 2 – March the turns.
\[ \text{T1: A}{=}1 \quad \text{T2: B}{=}3 \ (\text{block }1,2,3,7) \quad \text{T3: C}{=}6 \] \[ \text{T4: D}{=}4 \quad \text{T5: A}{=}7 \quad \text{T6: B}{=}5 \]
Step 3 – Read Turn 6. After Turn 6: A on 7, B on 5, C on 6, D on 4 – occupied chairs are 4, 5, 6 and 7 (a consecutive block, as required).
\[ \text{Occupied after Turn 6} = \boxed{4,\ 5,\ 6,\ 7} \]
Approach Solution -2
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:
\[ \boxed{4, 5, 6, \text{ and } 7} \]
Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
Show Hint
- Chhavi only
- Davies only
- Chhavi and Davies
- Aslam and Chhavi
The Correct Option is B
Approach Solution - 1
Approach: Don't try to track every move blindly. Lock the puzzle down using the few hard anchors given (fixed chairs at specific turns), then use the rule that all four are consecutive only at the end of Turns 2 and 6 to pin Bashir's final neighbours.
Step 1 — set the frame. Chairs are numbered \(1\) to \(7\) clockwise. Four friends — Aslam (A), Bashir (B), Chhavi (C), Davies (D) — occupy four of them; three chairs stay empty. Initially A and C are adjacent, while B and D each have an empty chair on both sides. The move order is A, B, C, D, A, B, C across Turns 1 to 7.
Step 2 — use the fixed-chair anchors. Davies is on Chair \(2\) just after Turn 1 and on Chair \(4\) after Turn 5, and Chhavi is on Chair \(7\) after Turn 2. These positions fix the block of occupied chairs at each stage and force the others into the remaining seats.
Step 3 — use the adjacency rule. All four sit on consecutive chairs only at the end of Turn 2 and Turn 6. So at the end of Turn 7 (one more move by Chhavi after Turn 6) the four are no longer a solid block of four — exactly one friend has stepped away from the cluster, breaking it.
Step 4 — read off Bashir's neighbours. When the Turn-6 consecutive block is broken by Chhavi's Turn-7 move, Chhavi leaves Bashir's side, so Chhavi is no longer adjacent to Bashir. Working the anchored seats, the only friend still occupying a chair next to Bashir at the end of Turn 7 is Davies.
Therefore the friend on a chair adjacent to Bashir at the end of Turn 7 is \(\text{Davies}\) only.
Final answer: Davies only.
Approach Solution -2
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.
\[ \boxed{\text{Davies only}} \]
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