Arrangement puzzles are the analytical section's centre of gravity, and the single biggest source of lost time on the paper. A five-person row with four conditions can be solved in four minutes with a written diagram, or in twelve minutes — usually unsuccessfully — by holding the conditions in your head.
They are also the most reliable marks available once you have the procedure, because each puzzle comes as a set of three to five questions sharing one setup. Get the diagram right once and the whole set is nearly free.
Never solve an arrangement in your head. Draw a strip of boxes and write conditions into it.
The model's payoff is that the diagram becomes a machine: the questions at the end are answered by reading the strip, not by re-deriving.
| Condition | What you write |
|---|---|
| A is immediately before B | [A B] as one sliding block |
| A is not adjacent to C | crosses on the two seats beside A |
| Exactly two people sit between A and B | A _ _ B or B _ _ A, three seats apart |
| A is somewhere to the left of B | A < B (an inequality, not a distance) |
| A is opposite B | write A and B in opposite seats at once |
Five students — A, B, C, D and E — sit in a row of five seats, numbered 1 to 5 from left to right.
Draw the strip and apply the steps:
The unique arrangement is C, D, E, B, A. Read off the answers: E is in the middle seat, D is immediately right of C, and the seat beside A - A is at the right end - is occupied by B.
Six people — A, B, C, D, E and F — sit around a circular table facing the centre.
Draw six seats clockwise. Put A at the top. Facing the centre, left is clockwise, so B takes the next seat clockwise; right is anticlockwise, so C takes the next seat anticlockwise. D goes opposite A, three seats away. The two remaining seats, opposite each other, belong to E and F — and E is not adjacent to C, which places E next to B and F next to C.
Clockwise from A: A, B, E, D, F, C. The deductions worth noticing: A is opposite D, B is opposite F, and C is opposite E. Any question about who sits opposite whom is answered by reading the ring.
In the row puzzle (C, D, E, B, A), who sits in the middle seat?
In the circular arrangement (A, B, E, D, F, C clockwise), who sits opposite B?
For people seated around a table facing the centre, a person's left is:
A question asks which option "could be true". What is the correct method?
Without looking back: what is the difference between "between" and "immediately", and where is a person's left when they face the centre?
The answer: "immediately" means no seat in between while "between" only requires separation; and facing the centre, left is clockwise.
When people face the centre, a person's left is . The phrase "immediately before" means the two occupy adjacent seats as a . In a circle of six, a person's opposite is seats away, and a "could be true" question is answered by .
Five colleagues P, Q, R, S and T sit in a row. P sits at the left end; T sits immediately to the right of P; R does not sit next to T; Q is to the right of S. Solve it and then say what an extra condition would have to be in order to fix S and Q completely.
P is at the left end, so seat 1 is P, and T immediately right of P puts T in seat 2. R does not sit next to T, so R is not in seat 3. The remaining seats 3, 4 and 5 hold R, S and Q, with Q to the right of S. Cases: R = 4 leaves S and Q in 3 and 5, and Q right of S gives S = 3, Q = 5, so P T S R Q. R = 5 leaves S and Q in 3 and 4, and Q right of S gives S = 3, Q = 4, so P T S Q R.
So the puzzle as given is not unique: two arrangements survive, P T S R Q and P T S Q R. A "must be true" question would ask about what is common to both - P is at the left end, T is immediately right of P, and S is in seat 3. To pin Q as well you need one more relational fact: "Q is at the right end" forces P T S R Q. Note that a fact already true of both arrangements, such as "S sits exactly in the middle", removes nothing.
The practical lesson is the one that saves marks: when your diagram still has multiple cases, do not force a single answer. Answer only what is forced, and use elimination for the questions that ask about possibilities.
Seating is the visual half of the puzzle family. The next lesson takes the same grid method into the puzzles about order and schedule — who meets when, who is assigned to which day — where the diagram is a calendar rather than a row.