Last reviewed 22 Sept 2026 · 6 min read
Work the clues in the right order
The arrangement is found by the order in which clues are used, not by cleverness:
- Fixed positions — "P sits at the extreme left", "Q is third from the right".
- Blocks — "R sits immediately to the left of S": treat RS as one piece and slide it along.
- Relative clues — "T sits between U and V" (which may be either way round).
- Negative clues last — "W does not sit at either end" eliminates, and elimination is only useful once there is something to eliminate.
When a clue allows two placements, draw both and carry them forward. Most puzzles kill one of them within two clues, and the person who rubbed out has to start again.
Linear arrangements
A single row of 6 to 8 people, all facing the same way (usually north). Then:
- If all face north, your left is their left as drawn — the leftmost seat is position 1.
- If all face south, left and right are reversed with respect to the paper.
Two rows facing each other: row 1 faces south, row 2 faces north; the person opposite is directly across. Then P's "right" in row 1 sits across from someone on Q's "left" in row 2 — mark the facing arrow on each row before placing anybody.
Circular arrangements
Facing the centre: clockwise is to a person's left, anticlockwise is to their right. Facing outward: the opposite — clockwise is to their right.
For people evenly spaced, the person opposite someone is places away (only when is even). In a circle, "third to the left of X" is counted going round in X's left direction, skipping two seats.
Square and rectangular tables
Common form: eight people, four at the corners and four at the middles of the sides; corner-sitters face the centre and middle-sitters face outward, or the reverse. The facing rule above then applies person by person, not to the whole table — which is exactly what the question is testing.
Reading the clue words
| Clue | Means |
|---|---|
| "Immediately to the left of" | adjacent, no one between |
| "To the left of" | anywhere on that side |
| "Third to the left of" | exactly two people in between |
| "Between A and B" | either order unless stated |
| "Exactly between" | equidistant from both |
| "Not adjacent to" | at least one seat apart |
Worked examples
Six friends A to F sit in a row facing north. C is at the extreme right. A is second from the left. B is immediately to the right of A. D is not at either end. Where does B sit?
Solution. Positions 1–6 from the left: A is 2, so B is 3, and C is 6. B sits third from the left.
In a row of five seats, P and Q sit together, and R sits at one end. How many arrangements place PQ in that order with R at the left end?
Solution. With R fixed at seat 1, the block PQ may occupy seats 2-3, 3-4 or 4-5 → 3 placements (the remaining two people fill the rest in ways each, giving 6 full arrangements).
Five people sit round a circle facing the centre. B is to the immediate left of A. Who is clockwise from A?
Solution. Facing the centre, clockwise is towards a person's left → B.
Six people sit round a circle facing outward. If X is third to the left of Y, how many people sit between them going clockwise from Y?
Solution. Facing outward, left is anticlockwise, so X is three places anticlockwise from Y — that is three places clockwise the other way round the six-seat circle, leaving two people between them clockwise from Y.
Eight people sit evenly round a circular table. Who sits opposite the person who is third to the right of P?
Solution. Third to the right of P is a definite seat; opposite is four seats further on, which is the person third to the left of P.
Six people sit in two rows of three facing each other. A, B, C face south; D, E, F face north. A is opposite E, and B sits to the immediate right of A. Who is opposite B?
Solution. A faces south, so A's right is towards the paper's left. B is there, and the person opposite B is the one to E's left as E faces north — that is D or F, decided by the next clue. Without it, it cannot be determined.
In a circle of ten facing the centre, if M is fourth to the left of N, how many sit between them on the other side?
Solution. Four places one way leaves places the other way, so five people sit between them going the long way round.
Five students sit in a row. P is not at either end, Q is at the extreme left, and R sits immediately to the right of P. If S is at the extreme right, where does T sit?
Solution. Q is 1 and S is 5. P cannot be 5, and R follows P, so P is 2, 3 or 4 with R next. If P=2, R=3, T=4. If P=3, R=4, T=2. Both survive, so T sits at position 2 or 4 — a second clue is needed to fix it.