Circular Seating Arrangement Questions and Answers

Answer: B

Correct answer: One

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix P; W is three to P’s left and Q three to P’s right. Trying each seat for T with S two to T’s right, only one choice keeps T away from Q, and of the two ways of then placing R and V, only one keeps U away from both T and W. Clockwise the table reads P → T → R → W → V → Q → U → S.

Keeping P where he is and running the alphabet clockwise puts Q, R, S, T, U, V, W in the seats after him. Comparing with the original table, only R lands on the seat he already occupies - two clockwise of P in both arrangements - so exactly one member keeps his place.

Answer: D

Correct answer: R, P

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix P; W is three to P’s left and Q three to P’s right. Trying each seat for T with S two to T’s right, only one choice keeps T away from Q, and of the two ways of then placing R and V, only one keeps U away from both T and W. Clockwise the table reads P → T → R → W → V → Q → U → S.

Going clockwise from P, the next seat is T’s and the one after that is R’s - so exactly one person sits between R and P. Between T and V sit two, V and Q are neighbours, and W and P have two on one side and four on the other.

Answer: E

Correct answer: P, Q

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix P; W is three to P’s left and Q three to P’s right. Trying each seat for T with S two to T’s right, only one choice keeps T away from Q, and of the two ways of then placing R and V, only one keeps U away from both T and W. Clockwise the table reads P → T → R → W → V → Q → U → S.

In W–T, P–U, S–Q and R–P the second person named sits second to the left of the first, two seats clockwise. P and Q are three seats apart, so that pair breaks the pattern.

Answer: A

Correct answer: F

Facing the centre, each friend’s left is the next seat clockwise and their right the next seat anticlockwise. Fix B; G takes the seat on B’s right, E sits three to G’s left, and A three to B’s right. Of the two ways to place F with H two seats to F’s right, only one keeps F away from E; and of the last two seats, D must take the one that does not touch B. Clockwise the circle reads B → C → E → D → H → A → F → G.

Counting two seats to B’s right - anticlockwise - gives G and then F.

Answer: D

Correct answer: HD

Facing the centre, each friend’s left is the next seat clockwise and their right the next seat anticlockwise. Fix B; G takes the seat on B’s right, E sits three to G’s left, and A three to B’s right. Of the two ways to place F with H two seats to F’s right, only one keeps F away from E; and of the last two seats, D must take the one that does not touch B. Clockwise the circle reads B → C → E → D → H → A → F → G.

To sit on someone’s immediate left is to occupy the next seat clockwise from them. H occupies exactly that seat with respect to D. In the other pairs the first person sits on the second’s right, or nowhere near.

Answer: C

Correct answer: Third to the right

Facing the centre, each friend’s left is the next seat clockwise and their right the next seat anticlockwise. Fix B; G takes the seat on B’s right, E sits three to G’s left, and A three to B’s right. Of the two ways to place F with H two seats to F’s right, only one keeps F away from E; and of the last two seats, D must take the one that does not touch B. Clockwise the circle reads B → C → E → D → H → A → F → G.

Counting three seats to D’s right - anticlockwise - gives E, C and then B. Counting the same distance to D’s left would reach F.

Answer: E

Correct answer: H

Facing the centre, each friend’s left is the next seat clockwise and their right the next seat anticlockwise. Fix B; G takes the seat on B’s right, E sits three to G’s left, and A three to B’s right. Of the two ways to place F with H two seats to F’s right, only one keeps F away from E; and of the last two seats, D must take the one that does not touch B. Clockwise the circle reads B → C → E → D → H → A → F → G.

A and D have exactly one seat between them, and H occupies it.

Answer: B

Correct answer: On the immediate left

Facing the centre, each friend’s left is the next seat clockwise and their right the next seat anticlockwise. Fix B; G takes the seat on B’s right, E sits three to G’s left, and A three to B’s right. Of the two ways to place F with H two seats to F’s right, only one keeps F away from E; and of the last two seats, D must take the one that does not touch B. Clockwise the circle reads B → C → E → D → H → A → F → G.

C’s left is the next seat clockwise, and E occupies it. The arrangement is fully determined, so the position is not in doubt.

Answer: A

Correct answer: R

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix P; V sits two to P’s left and W two beyond V. Of the two ways to place Q with T three seats to Q’s right, only one keeps T off V’s shoulder, and R and S then fit in one way only. Clockwise the circle reads P → Q → V → S → W → T → R.

Counting two seats to Q’s right - anticlockwise - gives P and then R.

Answer: D

Correct answer: W

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix P; V sits two to P’s left and W two beyond V. Of the two ways to place Q with T three seats to Q’s right, only one keeps T off V’s shoulder, and R and S then fit in one way only. Clockwise the circle reads P → Q → V → S → W → T → R.

S’s left is the next seat clockwise, and W occupies it. V is on S’s right.