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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 counterclockwise 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?

Entered answer:

Solution

✅ Correct Answer: 4
Slide 1/11

Seven chairs sit in a circle, numbered 11 to 77 clockwise.

Clockwise order: 1→2→3→4→5→6→7→11 \to 2 \to 3 \to 4 \to 5 \to 6 \to 7 \to 1.

Counterclockwise order: 1→7→6→5→4→3→2→11 \to 7 \to 6 \to 5 \to 4 \to 3 \to 2 \to 1.

A friend who moves stops at the first empty chair in the chosen direction.

We track the chair each friend sits on at the end of every turn.

The final column lists the set of occupied chairs, used to test clue 1: all four are adjacent (four consecutive chairs) only at the end of Turn 2 and Turn 6.

Who moves each turn: Aslam (T1, T5), Bashir (T2, T6), Chhavi (T3, T7), Davies (T4 only).

TurnAslamBashirChhaviDaviesOccupied
Start
T1 — Aslam
T2 — Bashir
T3 — Chhavi
T4 — Davies
T5 — Aslam
T6 — Bashir
T7 — Chhavi
TurnAslamBashirChhaviDaviesOccupied
Start72
T1 — Aslam
T2 — Bashir
T3 — Chhavi
T4 — Davies
T5 — Aslam
T6 — Bashir
T7 — Chhavi

Davies start =2= 2 and Chhavi start =7= 7 are filled from clue 2.

Davies first moves in Turn 4, so the statement that Davies is on chair 22 after Turn 1 means Davies begins on chair 22.

Chhavi first moves in Turn 3, so the statement that Chhavi is on chair 77 after Turn 2 means Chhavi begins on chair 77.


Davies is isolated (empty chairs on both sides), so chairs 11 and 33 are empty in the starting position.

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam
T2 — Bashir
T3 — Chhavi
T4 — Davies
T5 — Aslam
T6 — Bashir
T7 — Chhavi

Aslam start =6= 6 and Bashir start =4= 4 are filled.

Aslam sits next to Chhavi (chair 77); the neighbours of 77 are 66 and 11.

Chair 11 is empty, so Aslam =6= 6.


Bashir must be isolated and can only use a remaining chair.

Chair 55 has neighbour 66 (Aslam) occupied, so it is not isolated.

Chair 33 is empty.

Chair 44 has neighbours 33 and 55 both empty, so Bashir =4= 4.

Starting empty chairs: {1,3,5}\{1, 3, 5\}.

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir
T3 — Chhavi
T4 — Davies
T5 — Aslam
T6 — Bashir
T7 — Chhavi

Aslam moves from chair 66.

Clockwise: chair 77 is occupied, chair 11 is empty →1\to 1.

Counterclockwise: chair 55 is empty →5\to 5.


Clue 1 requires the four to be consecutive after Turn 2.

If Aslam →5\to 5: occupied {2,4,5,7}\{2,4,5,7\}, and Bashir (T2) from 44 can reach 33 giving {2,3,5,7}\{2,3,5,7\} or 66 giving {2,5,6,7}\{2,5,6,7\} — neither is four consecutive chairs.

So Aslam →1\to 1 (clockwise).

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir13721,2,3,7
T3 — Chhavi
T4 — Davies
T5 — Aslam
T6 — Bashir
T7 — Chhavi

Bashir moves from chair 44 (empty chairs now {3,5,6}\{3,5,6\}).

Clockwise: chair 55 empty →5\to 5, giving occupied {1,2,5,7}\{1,2,5,7\} — not consecutive.

Counterclockwise: chair 33 empty →3\to 3, giving occupied {1,2,3,7}\{1,2,3,7\}, i.e. chairs 7,1,2,37,1,2,3 — four consecutive.

Clue 1 requires consecutive chairs at Turn 2, so Bashir →3\to 3.

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir13721,2,3,7
T3 — Chhavi13621,2,3,6
T4 — Davies
T5 — Aslam
T6 — Bashir
T7 — Chhavi

Chhavi moves from chair 77 (empty chairs now {4,5,6}\{4,5,6\}).

Clockwise: chairs 1,2,31,2,3 occupied, chair 44 empty →4\to 4.

Counterclockwise: chair 66 empty →6\to 6.


If Chhavi →4\to 4: occupied {1,2,3,4}\{1,2,3,4\}, four consecutive — this would violate clue 1, since consecutive seating is allowed only at Turn 2 and Turn 6.

So Chhavi →6\to 6. This also keeps chair 44 free, which Davies will need next.

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir13721,2,3,7
T3 — Chhavi13621,2,3,6
T4 — Davies13641,3,4,6
T5 — Aslam
T6 — Bashir
T7 — Chhavi

Davies moves from chair 22 (empty chairs now {4,5,7}\{4,5,7\}).

From clue 2, Davies is on chair 44 after Turn 5; since Davies moves only in Turn 4, Davies must reach chair 44 now.

Clockwise from 22: chair 33 occupied, chair 44 empty →4\to 4.

So Davies →4\to 4. Occupied {1,3,4,6}\{1,3,4,6\} is not consecutive, consistent with clue 1.

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir13721,2,3,7
T3 — Chhavi13621,2,3,6
T4 — Davies13641,3,4,6
T5 — Aslam73643,4,6,7
T6 — Bashir
T7 — Chhavi

Aslam moves from chair 11 (empty chairs now {2,5,7}\{2,5,7\}).

Clockwise: chair 22 empty →2\to 2.

Counterclockwise: chair 77 empty →7\to 7.


Clue 1 requires the four to be consecutive after Turn 6.

If Aslam →2\to 2: occupied {2,3,4,6}\{2,3,4,6\}, and Bashir (T6) from 33 reaches 55 giving {2,4,5,6}\{2,4,5,6\} or 11 giving {1,2,4,6}\{1,2,4,6\} — neither consecutive.

If Aslam →7\to 7: occupied {3,4,6,7}\{3,4,6,7\}, and Bashir (T6) from 33 can reach 55 giving {4,5,6,7}\{4,5,6,7\} — consecutive.

So Aslam →7\to 7. (Davies remains on 44, matching clue 2.)

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir13721,2,3,7
T3 — Chhavi13621,2,3,6
T4 — Davies13641,3,4,6
T5 — Aslam73643,4,6,7
T6 — Bashir75644,5,6,7
T7 — Chhavi

Bashir moves from chair 33 (empty chairs now {1,2,5}\{1,2,5\}).

Clockwise: chair 44 occupied, chair 55 empty →5\to 5, giving occupied {4,5,6,7}\{4,5,6,7\} — four consecutive.

Counterclockwise: chair 22 empty →2\to 2, giving {2,4,6,7}\{2,4,6,7\} — not consecutive.

Clue 1 requires consecutive chairs at Turn 6, so Bashir →5\to 5.

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir13721,2,3,7
T3 — Chhavi13621,2,3,6
T4 — Davies13641,3,4,6
T5 — Aslam73643,4,6,7
T6 — Bashir75644,5,6,7
T7 — Chhavi751/341,4,5,7 / 3,4,5,7

Chhavi moves from chair 66 (empty chairs now {1,2,3}\{1,2,3\}).

Clockwise: chair 77 occupied, chair 11 empty →1\to 1, giving occupied {1,4,5,7}\{1,4,5,7\}.

Counterclockwise: chairs 5,45,4 occupied, chair 33 empty →3\to 3, giving occupied {3,4,5,7}\{3,4,5,7\}.

Neither set is four consecutive chairs, so both directions satisfy clue 1; Chhavi's Turn 7 destination is not pinned down.


Either way, Chhavi leaves chair 66, so chair 66 becomes empty.

Bashir stays on chair 55; its neighbours are chair 44 (Davies) and chair 66 (empty).

TurnAslamBashirChhaviDaviesOccupied
Start64722,4,6,7
T1 — Aslam14721,2,4,7
T2 — Bashir13721,2,3,7
T3 — Chhavi13621,2,3,6
T4 — Davies13641,3,4,6
T5 — Aslam73643,4,6,7
T6 — Bashir75644,5,6,7
T7 — Chhavi751/341,4,5,7 / 3,4,5,7

The table is complete.

All positions are uniquely determined except Chhavi's destination at Turn 7, which can be chair 11 or chair 33; both satisfy every clue.

This ambiguity does not affect Bashir, who ends on chair 55 with neighbours chair 44 (Davies) and chair 66 (empty) in either case.


From the Start row of the table, Bashir begins on chair 44.

Davies starts on chair 22 (he is on 22 after Turn 1 but moves only at Turn 4) and is isolated, so chairs 11 and 33 are empty. Chhavi starts on chair 77 (she is on 77 after Turn 2 but moves only at Turn 3). Aslam, adjacent to Chhavi, must take chair 66 (chair 11 is empty). Bashir must be isolated: chair 55 touches Aslam at 66, so the only isolated remaining seat is chair 44.

Answer: chair 4 (the entered answer 4 is correct).

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