Circular Seating Arrangement Questions and Answers

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: C

Correct answer: U

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.

Two seats to V’s left - clockwise - gives Q and then U.

Answer: A

Correct answer: S

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.

U and P have exactly one seat between them, and S occupies it.

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: C

Correct answer: M

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix K, put P three seats to K’s right and D two to P’s right. Of the ways of placing W with T three seats to W’s right, only one keeps W away from D’s side, and M three to R’s left then falls into place. Clockwise the circle reads K → M → D → T → P → R → W.

Counting two seats to T’s right - anticlockwise - gives D and then M. The arrangement is fully determined, so the data are not inadequate.

Answer: D

Correct answer: KW

Facing the centre, each person’s left is the next seat clockwise and their right the next seat anticlockwise. Fix K, put P three seats to K’s right and D two to P’s right. Of the ways of placing W with T three seats to W’s right, only one keeps W away from D’s side, and M three to R’s left then falls into place. Clockwise the circle reads K → M → D → T → P → R → W.

A person’s right is the seat anticlockwise from them. Of the pairs offered, only in KW does the second sit immediately to the first’s right: W occupies the seat on K’s right.