Quantitative Aptitude · Seating Arrangements

Circular Seating Arrangement: Rules, Tricks and Solved MCQs

Updated 1 October 2026 · Fact-checked

A circular seating arrangement places people at equal gaps around a circle, facing the centre or outside. To solve it, draw a circle, number the seats clockwise, and fix the facing direction. Facing the centre, left is clockwise. Facing outside, left is anticlockwise. Opposite seats are n ÷ 2 places apart.

Understand Circular Seating Arrangement

In a circular seating question, a group of people sit around a circle at equal gaps. You are told who sits where relative to others, and you must find a person's neighbour, opposite or position. There is no first or last seat, so you start by fixing one person anywhere.

Every person faces either the centre (inside) or outside. This single fact decides what left and right mean. Mixing it up is the main way students lose marks here.

Clockwise is the direction a clock's hands move, seen from above. Anticlockwise is the reverse. These two directions never change, whatever way people face. Only a person's own left and right change.

Imagine you sit at the bottom of the circle, facing the centre (upwards). Your left hand points to the west, and moving clockwise from the bottom takes you towards the west. So when facing the centre, your left is the clockwise direction and your right is anticlockwise. If you face outside, both flip.

The opposite person sits directly across the centre. With n people equally spaced and n even, the opposite person is n ÷ 2 seats away. If n is odd, nobody sits exactly opposite anybody.

Key formulas to remember

Left and right when facing the centre: Left = clockwise; Right = anticlockwise; Applies to a person who faces the centre. Use it for every 'to the left of' or 'to the right of' clue.
Left and right when facing outside: Left = anticlockwise; Right = clockwise; Exactly the reverse of the facing-centre rule. If the two groups face differently, apply the rule person by person.
Opposite seat: Opposite of seat k = seat k + n ÷ 2 (subtract n if the result is above n); Valid only when n is even and seats are equally spaced. Seats are numbered 1 to n in one direction.
Persons between two opposite people: (n ÷ 2) − 1 on each side; Example: in a circle of 10, 4 persons sit between two opposite people along either arc.
Persons between two seats, shorter way: Persons between = (seat gap) − 1; Seat gap is the number of steps along the arc you are counting. The other arc has n − gap − 1 persons between.
Meaning of 'second to the left of A': Move 2 seats from A in A's left direction; 'Immediate' means 1 seat. Count from A, not from the seat next to A.

How to solve Circular Seating Arrangement questions

This method works for any circular seating question, whether people face inside, outside or a mix.

1Read the whole question first. Note the number of people, equal spacing, and whether everyone faces the centre, faces outside, or a mix.
2Draw a circle and mark n seats. Number them 1 to n clockwise. This fixes one direction for your whole answer.
3Write the left rule at the top of your rough work: facing centre, left = clockwise; facing outside, left = anticlockwise.
4Place the person who has the most definite clues first. A pair of opposites or a direct statement is a good start. Fix this person at seat 1 as there is no true starting seat.
5Convert each clue into a seat number. Move clockwise or anticlockwise according to the person's facing and the words left or right.
6Place the opposite pairs with the n ÷ 2 rule and check that no seat is used twice.
7Fill the remaining people by elimination, and recheck every clue against your diagram.
8Read the question again and answer exactly what is asked, such as the neighbour, the opposite person, or the count between two people.

Quickest way: Seat-number shortcut for MCQs

When to use it: Use this when n is given and the clues are mostly 'nth to the left or right' or 'opposite'. It avoids long diagrams.

Number seats 1 to n clockwise. Put the first named person at seat 1.
Convert each direction to plus or minus. Facing centre: left is +, right is −. Facing outside: left is −, right is +.
Add or subtract the step count from the seat number. Wrap around using n, so seat 0 is seat n and seat n+1 is seat 1.
Add n ÷ 2 for any opposite clue.
Compare final seat numbers. A difference of 1 means neighbours. A difference of n ÷ 2 means opposite.
Use options for elimination. If an option names someone who must sit at a different seat number, strike it out.
If the clues are too tangled, mark the question and move on. Each wrong answer costs 0.25 marks, so do not guess blindly.

Common mistakes in Circular Seating Arrangement

Treating left as clockwise for people facing outside
Students learn the facing-centre rule first and apply it to every question without checking the facing.
Fix: Write the rule at the top of your rough work before starting. Underline whether the question says inside or outside.
Counting the starting person as step one
In everyday counting we begin at 1 on the first thing we see, so 'third to the left of A' gets counted from A itself.
Fix: A is step zero. The seat next to A is step one. Use the number-plus-steps method to avoid miscounting.
Looking for an opposite person when n is odd
Students remember 'opposite' as a feature of every circle and force a placement.
Fix: Check that n is even before using the n ÷ 2 rule. With odd n and equal spacing, no exact opposite exists.
Mixing up persons between and seat gap
Both are small numbers close to each other and are easy to confuse under time pressure.
Fix: Persons between = gap − 1. Always say 'between' or 'gap' in your head before subtracting.
Forgetting that clockwise and anticlockwise are fixed, while left and right depend on facing
Students think left and right are properties of the circle, not of the person.
Fix: Anchor everything in clockwise numbering. Convert each person's left or right into plus or minus using their own facing.
Not rechecking the diagram against all clues
Once a seating looks right for the main clue, students stop and choose an option.
Fix: Spend ten seconds testing each clue against your final seats. One failed clue means you must try the other direction.

Worked examples

Example 1

Eight persons P, Q, R, S, T, U, V and W sit around a circle at equal gaps, all facing the centre. P sits opposite R. Q sits immediate left of P. S sits third to the right of P. Who sits opposite S? Options: (A) P (B) Q (C) R (D) T

Show the solution

Number seats 1 to 8 clockwise and place P at seat 1.
P is opposite R, so R is at seat 1 + 4 = 5.
All face the centre, so left is clockwise. Q is immediate left of P, so Q is at seat 2.
Right is anticlockwise. S is third to the right of P, so move 3 seats anticlockwise from seat 1: seat 8, seat 7, seat 6. S is at seat 6.
The opposite of seat 6 is 6 + 4 = 10, which is seat 2.
Seat 2 is Q.

Answer: (B) Q

Example 2

Twelve persons sit around a circle at equal gaps, all facing outside. X sits fourth to the left of Y. Z sits opposite Y. How many persons sit between X and Z along the shorter arc? Options: (A) 0 (B) 1 (C) 2 (D) 3

Show the solution

Number seats 1 to 12 clockwise and place Y at seat 12.
Facing outside, left is anticlockwise. X is fourth to the left of Y, so X is at seat 12 − 4 = 8.
Z is opposite Y, so Z is at seat 12 + 6 = 18, which is seat 6.
The gap between seats 6 and 8 is 2 steps along the shorter arc.
Persons between = gap − 1 = 1 (the person at seat 7).

Answer: (B) 1

Example 3

Eight persons sit around a circle at equal gaps, all facing the centre. A sits third to the left of B. C sits second to the right of A. What is C's position with respect to B? Options: (A) Immediate left of B (B) Immediate right of B (C) Second to the left of B (D) Opposite B

Show the solution

Number seats 1 to 8 clockwise and place B at seat 1.
Facing the centre, left is clockwise. A is third to the left of B, so A is at seat 1 + 3 = 4.
Right is anticlockwise. C is second to the right of A, so C is at seat 4 − 2 = 2.
Seat 2 is one step clockwise from B at seat 1. Clockwise is the left direction for a person facing the centre.
So C is the immediate left of B.

Answer: (A) Immediate left of B

Exam tips

Write the left rule for the facing direction at the top of your rough work before reading the clues.
Number seats clockwise and use plus and minus arithmetic. It is faster and safer than redrawing the circle repeatedly.
Check whether n is even before using any opposite clue. A question with odd n tests whether you notice this.
Use the options to eliminate. Once you know one person's seat, any option placing them elsewhere is wrong.
Skip questions with a mix of facing directions and many unknowns if time is short. Each wrong answer costs 0.25 marks.

Practice questions from Seating Arrangements

Circular Seating Arrangement: frequently asked questions

What is the difference between clockwise and anticlockwise in a circular arrangement?

Clockwise is the direction a clock's hands move when seen from above, and anticlockwise is the opposite. These directions are fixed and do not depend on who is facing where. Only a person's left and right change with their facing.

For persons facing the centre, is left clockwise or anticlockwise?

Left is clockwise. Imagine standing at the bottom of the circle facing the centre: your left hand points the way a clock's hands would take you from that point. Your right is anticlockwise.

How do I find the person opposite someone in a circle?

If there are n people, with n even and equal spacing, add n ÷ 2 to the seat number. If the result is more than n, subtract n. If n is odd, no one sits exactly opposite.

What changes when people face outside instead of inside?

Left and right swap their directions. Facing outside, left is anticlockwise and right is clockwise. Everything else, including the opposite rule and the counting of seats, stays the same.