Seating Arrangement
🔒 Log in to trackRound-table arrangements
🔒 Log in to trackFor people facing the centre (the default), fix the geometry once: left neighbour = clockwise, right neighbour = anticlockwise. 'Opposite' exists only for an even number of people: seat i is opposite seat i + n/2.
Rotation is the puzzle-setter's freedom: clues never tell you 'seat 1', so start by placing any one person anywhere and build the circle around them — every other clue is relative to people, not seats. Facing-outward variants flip left/right; mixed facing ('A faces centre, B faces outward') is rare in CGL and usually restricted to 4–5 people.
Detailed notes
Fixing a circle
A circle has no first seat, so every arrangement can be rotated. Remove that freedom at once: put the first person named in a clue at the top of the circle. Now every other seat is fixed relative to that person.
Mark the direction on your drawing:
- Facing the centre: left neighbour = clockwise, right neighbour = anticlockwise.
- Facing outward: left neighbour = anticlockwise, right neighbour = clockwise.
A quick check: stand at the bottom of the circle facing the centre (north). Your left hand points west. Moving from the bottom towards the west side is the clockwise direction when the circle is seen from above.
Opposite seats
With n seats (n even), the person opposite X is n ÷ 2 places away. In a circle of 6 it is 3 places, in a circle of 8 it is 4 places. "Opposite" clues are the strongest clues in a circle because they fix a seat exactly. Place them before "left" and "right" clues whenever you can.
With an odd number of seats there is no opposite. If a question with 5 or 7 people asks who is opposite someone, re-read it: it is probably a mistake of reading, not a trick.
Counting both ways
In a circle there are two paths between any two people. "How many people sit between A and D?" usually means along the shorter side, or the question says "counting clockwise from A". In a circle of n, if D is k-th to the left of A, D is also (n − k)-th to the right of A.
Worked example
Eight people A to H sit around a circle facing the centre. A sits opposite E. B is second to the right of A. F sits opposite B. C sits immediately left of E. D sits opposite C. G is not a neighbour of A.
- Put A at seat 0 and number seats 0 to 7 clockwise. E = 4 (opposite).
- Facing centre, right = anticlockwise. B = second right of A = seat 6. F = seat 2.
- C = immediate left of E = seat 5 (clockwise from 4). D = opposite C = seat 1.
- Seats 3 and 7 remain for G and H. Seat 7 neighbours A, so G = 3 and H = 7.
- Third to the left of H: 7 → 0 → 1 → 2, so it is F.
Outward and mixed facing
If everyone faces outward, just swap the rule: left = anticlockwise. If some face the centre and some face outward, write a small arrow at each person as soon as you place them, and read each clue from that person's own direction. "Q is immediately right of P" depends on how P faces, not how Q faces.
Neighbour clues
- "X is a neighbour of Y" or "X sits next to Y" does not tell you which side. Keep both until another clue decides.
- "X sits between Y and Z" in a circle normally means immediately between.
- "Y and Z are not neighbours" is the most useful clue for the last two seats.
Couples and attributes
Some circle puzzles add a second layer: couples, colours, cities or professions. Solve the seats first with the position clues. Then fill the attribute grid, one row per person. The attribute clues that name a seat relation ("the person who likes red sits opposite B") should be applied only after the seats are fixed.
Quick revision
- Fix the first person at the top; the circle cannot rotate after that.
- Facing centre: left = clockwise. Facing outward: left = anticlockwise.
- Opposite = n ÷ 2 places away; place opposite clues first.
- k-th left = (n − k)-th right in a circle of n.
- Mixed facing: read each clue from the named person's own direction.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Chains around a circle facing the centrevery common3 practice Q
Clues link neighbours ('A is immediately left of B', 'D is second right of B').
Fix one person, then walk clockwise for 'left' and anticlockwise for 'right'. Fill the remaining seat last.
Example: Five people face the centre. A is immediately left of B, C is immediately left of A, D is immediately right of B. Who is immediately right of D?
Clockwise from B: A, C. Anticlockwise from B: D. Five seats → clockwise B A C E D. Right of D (anticlockwise) is E.
Type 2: Opposite pairsvery common3 practice Q
Even number of seats with 'sits opposite' clues.
Opposite = n ÷ 2 places away. Place all opposite pairs first; they pin seats exactly.
Example: Six people face the centre. A opposite B, C opposite D, E immediately left of A, C immediately left of E. Who is second to the left of F?
Clockwise from A: A E C B F D. Second left of F: F → D → A.
Type 3: Facing outwardcommon2 practice Q
Everyone faces away from the centre.
Left = anticlockwise, right = clockwise. Write this on the frame before starting.
Example: Five people face outward. C is second to the right of A. Moving clockwise from A, where is C?
Outward: right = clockwise. C is two seats clockwise from A.
Type 4: Mixed facingoccasional2 practice Q
Some people face the centre and some face outward.
Mark an arrow at each person. Read every clue from the named person's own direction.
Example: In a circle of 4, A faces the centre and B faces outward. B is immediately left of A. Where is B?
A faces the centre, so A's left is clockwise: B is one seat clockwise from A.
Shortcut tricks
⚡ Walk the circle in one direction
Take the longest adjacency chain and lay it out clockwise without thinking: 'D is to the immediate left of B, C to the immediate left of D, E to the immediate left of C' is just the clockwise string B → D → C → E. Close the loop with the last clue.
Example: Q. Facing centre: A is to the immediate right of B; D to the immediate left of B; C to the immediate left of D; E to the immediate left of C.
Sol. Left-walk from B: B, D, C, E, and A sits at B's right — the string closes as B D C E (A) — fully forced.
'Immediate left' chains concatenate into one clockwise string — walk it instead of solving seat by seat.
Where students lose marks
Using clockwise as the right-hand side for centre-facing people — it is the left.
Hunting for an 'opposite' person at an odd-sized table.
Placing people by seat numbers instead of relative to a fixed anchor.
Practice sets — 14 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 10 questions
Suggested time 11 min · wrong answers go to your mistake notebook automatically.