Seating arrangement for AFCAT: linear rows and circular tables, solved clue by clue

A seating arrangement question gives you five to eight people, a row or a table, and a handful of clues. Then it asks two or three questions about the final order. It is the slowest verbal-reasoning type in AFCAT, and the one where candidates most often lose time without getting a mark, because they start drawing before they know which clue to use first.

The good news: every puzzle yields to the same order of work. Once you have that routine, a five-person row takes about a minute and a six-person circle not much more.

The clue vocabulary

Most mistakes come from misreading one of these phrases.

"Left" and "right" are always from the seated person's own point of view.

Left and right in each layout

To check the circle rule, imagine sitting at the bottom of a round table facing the centre, which means facing up the page. Your left hand points to the left of the page, towards the 9 o'clock position, which is the clockwise direction from 6 o'clock.

The solving order

1. Draw the frame. Number the seats 1 to n from left to right for a row, facing north unless told otherwise. For a circle, draw n seats and mark the clockwise direction with an arrow.
2. Place fixed clues. Ends, the middle, "third from the left end". These pin a person to one seat.
3. Place relative clues joined to someone already placed. "Immediate left of R" is useless until R is placed, so hold it back.
4. Branch only when forced. If a clue gives two options, draw both cases side by side and let later clues kill one.
5. Use negative clues last. "Q does not sit next to T" rarely places anyone but often decides between two cases.
6. Check every clue once more against the final order before answering.

In a circle, nobody has a fixed seat, so place the first person anywhere. Every other seat is then fixed relative to that person.

Worked puzzle 1: a row of seven

Seven people, P, Q, R, S, T, U and V, sit in a row facing north.

• T sits exactly in the middle.
• R sits at one of the ends.
• Q sits second to the left of R.
• P sits to the immediate left of T.
• U does not sit at either end.
• S sits at one of the ends.
• V sits next to P.

Solution.

• Seats 1 to 7, left to right. T is in the middle: T = 4.
• P is to T's immediate left: P = 3.
• R is at an end, so R = 1 or 7. Q is second to R's left, which needs two seats on R's left. If R = 1 there are none. So R = 7 and Q = 5.
• S is at an end and seat 7 is taken, so S = 1.
• Seats 2 and 6 remain for U and V. V sits next to P (seat 3), so V = 2 and U = 6. U is not at an end, which checks out.

Final order, left to right: S, V, P, T, Q, U, R.

• Who sits between T and U? Q.
• How many people sit between S and Q? Three (V, P and T).
• Who is third to the right of V? Q (seats 3, 4, 5).

No other seating of the seven people satisfies all seven clues, so the answers are safe.

Worked puzzle 2: a round table of six

Six people, A, B, C, D, E and F, sit around a circular table facing the centre.

• A sits opposite D.
• B sits to the immediate left of A.
• C sits to the immediate right of A.
• F does not sit next to C.

Solution. Number the seats 0 to 5 going clockwise and put A in seat 0.

• D is opposite A: D = 3.
• Facing the centre, left is clockwise. B is to A's immediate left: B = 1.
• Right is anticlockwise. C is to A's immediate right: C = 5.
• Seats 2 and 4 remain for E and F. C's neighbours are seats 4 and 0, so F cannot be in seat 4. F = 2 and E = 4.

Clockwise from A: A, B, F, D, E, C.

• Who sits opposite B? Seat 1 is opposite seat 4: E.
• Who sits opposite C? Seat 5 is opposite seat 2: F.
• Who is to the immediate right of F? One seat anticlockwise from seat 2 is seat 1: B.

Worked puzzle 3: when a clue branches

Six people, U, V, W, X, Y and Z, sit in a row facing north.

• W is at the left end.
• Z is third from the right end.
• U sits to the immediate right of W.
• X sits at the right end.
• V does not sit next to X.

Solution.

• W = 1 and X = 6.
• Third from the right end of six seats is seat 4: Z = 4.
• U is to W's immediate right: U = 2.
• V and Y share seats 3 and 5. Two cases: V = 3, Y = 5, or V = 5, Y = 3.
• V is not next to X (seat 6), so V cannot be 5. V = 3, Y = 5.

Order: W, U, V, Z, Y, X. Who sits between Z and X? Y.

Linear or circular: a comparison

Practice set

Six people, G, H, J, K, L and M, sit around a circular table facing the centre.

• H sits opposite G.
• J sits to the immediate right of G.
• M sits second to the left of G.
• L sits next to J.

1. Who sits opposite M?
2. Who sits to the immediate left of K?
3. Who sits between H and J?
4. Who sits to the immediate right of H?
5. A new puzzle: five people sit in a row facing south. Looking at their faces, you see them in the order A, B, C, D, E from your left. Who is at the right end of the row, from the people's own point of view?
6. In the same row facing south, who sits to the immediate left of C, from C's own point of view?

Answers. Put G in seat 0. H = 3 (opposite). Right is anticlockwise, so J = 5. Left is clockwise, so M = 2. L sits next to J; J's neighbours are seats 4 and 0 (G), so L = 4 and K = 1. Clockwise from G: G, K, M, H, L, J. No other seating fits all four clues.

1. J. Seat 2 is opposite seat 5.
2. M. One seat clockwise from K (seat 1) is seat 2.
3. L. H is seat 3, J is seat 5, and L sits in seat 4 between them.
4. M. One seat anticlockwise from seat 3 is seat 2.
5. A. They face you, so their right is your left.
6. D. C's left is your right, and D is on C's right as you look at the row.

What to do next

• Redo puzzle 1 without looking, saying aloud which clue you use and why at each step.
• Solve two linear and two circular puzzles a day for a week. Time each full set, aiming for 90 seconds per arrangement.
• Practise at least three puzzles with people facing south or outwards, since that is where marks leak.
• Then move to syllogisms, and keep direction sense fresh, since both reward a quick sketch.