Seating Arrangement
🔒 Log in to trackExam strategy for puzzles
🔒 Log in to trackSeating questions come in sets that share one puzzle. Solve the whole seating once, write it neatly, and then each question is a quick lookup. Two rows, counting arrangements and attribute grids are the other forms you will meet.
How seating sets appear
A set has three to five questions on one puzzle. The first question takes the time. The others should take 10 to 20 seconds if the seating is fully solved.
So the real skill is to solve the whole arrangement once, cleanly.
Budget and order
- Read every clue once before you draw. Count the people and the seats. Note the facing direction. Look for clues that fix a seat outright.
- Build the frame and write the direction on it.
- Place fixed clues, then chains, then negative clues.
- Write the final seating neatly before you read the questions.
Tip: Most wrong answers in a set come from reading a half-finished rough drawing.
Two parallel rows
Two rows face each other. Row 1 faces south. Row 2 faces north. Seat of row 1 faces seat of row 2.
- A south-facing person's left is the east end. "A is immediate right of B" in the south row means A is one seat west of B.
- "P faces A" joins the two rows. P and A have the same seat number.
- Both rows share the same ends.
Solve once, answer many
The follow-up questions are of a few kinds.
- Who sits -th left or right of X: read the drawing.
- Which statement is true: test each option on the drawing.
- X and Y interchange seats: swap only those two, then read again.
- Odd one out: three pairs share a relation and one does not.
Counting arrangements
Some questions ask "in how many ways".
- people in a row: ways.
- Two people who must sit together: treat them as one block, .
- people around a circle, with rotations counted as the same: .
- Each fixed seat removes one person and one seat from the free pool.
Rule: For small numbers, list the cases. It is fast and it catches double counting.
Attribute grids
Each person may also have a drink, city or job. Draw a grid with people down the side and seat plus attribute across the top. Each clue either fixes a cell or rules one out.
"The tea drinker sits at the left end" fixes the seat of the tea drinker, not the name. Tie a name to an attribute only when another clue joins them.
When to skip
Give one full pass to each set. If two seatings are still alive after every clue, look at the questions. If they need the exact seating, park the set. Come back if time is left, because other questions give marks more cheaply.
Where time is lost
- Reading a south-facing left as your own left.
- Taking 'between' to mean 'immediately between'.
- Forgetting that 'neighbour' allows two sides.
- Answering from a case that a later clue already struck out.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Two parallel rows facing each other
Two rows sit facing each other. One faces north, the other south, and clues say 'X faces Y'.
Draw two rows and write the facing on each.
Solve each row with its own left and right rule.
Join the rows with 'faces' clues at equal seat numbers.
Seat faces seat , so one solved row fixes the other.
Row 1 has A, B, C, D facing south. Row 2 has P, Q, R, S facing north. In row 1, C is immediate right of B, D is at the east end, and A is not at an end. In row 2, P faces C, R is immediate right of P, and S faces A. Who faces D?
Show solutionHide solution
Row 1: D = seat 4. C is immediate right of B, so C is one seat west of B.
A is not at an end, so A = 3, B = 2, C = 1. Row 1 is C B A D.
Row 2: P = seat 1. R = seat 2. S faces A, so S = seat 3. Q = seat 4.
D is seat 4, so the person facing D is Q.
Q
Solve once, answer many
A set of questions asks for a true statement, an interchange or an odd one out.
Write the final seating neatly.
For an interchange, swap only the two named people.
Read each question off the new drawing.
One clean seating answers every question in the set.
The final row is D E A C B from the west. If C and E interchange seats, who sits immediate right of A?
Show solutionHide solution
Swap C and E: the row becomes D C A E B.
The immediate right of A (facing north) is the next seat east.
E
Counting arrangements
The question asks 'in how many ways' instead of 'who'.
Decide if it is a row or a circle.
Glue any pair who must sit together into one block.
Count blocks, multiply, and then multiply by the order inside the block.
Choices are counted seat by seat, so each fixed group behaves as one unit.
In how many ways can 5 people sit in a row if A and B must always sit together?
Show solutionHide solution
Treat AB as one block. With 3 other people there are 4 units.
Units can be arranged in ways.
A and B can swap inside the block: .
48
Seats plus attributes
Each person also has a drink, colour, city or job.
Draw a grid with people, seat and attribute.
Fix the seats first from the seat clues.
Tie each attribute to a name only when a clue joins them.
Seat clues and attribute clues work on different rows of the grid, and one name joins them.
Four people A, B, C, D sit in a row facing north. A is at the east end and B is immediate left of A. The tea drinker is at the west end. The milk drinker is immediate right of the tea drinker. C drinks milk. A drinks water. Who drinks juice?
Show solutionHide solution
A = seat 4, B = seat 3. C and D take seats 1 and 2.
Tea is at seat 1 and milk is at seat 2. C drinks milk, so C = seat 2 and D = seat 1 (tea).
A drinks water, so B drinks juice.
B
Two seatings survive
After all the clues, two seatings remain. Check what the question asks.
List the two seatings that survive.
Read the asked seat in both.
If both give the same person, mark it and move on.
The question needs one seat, not the full unique seating.
Five people A to E sit in a row facing north. A is in the middle. E is at the east end. D is immediate left of E. B and C fill the other seats in any order. Who sits immediate right of A?
Show solutionHide solution
A = seat 3, E = seat 5, D = seat 4.
B and C take seats 1 and 2 in either order.
Immediate right of A is seat 4 in both cases.
D
Shortcuts that save time
When exactly two seatings survive, check what the question asks. If both give the same answer, mark it and move on.
After all clues, A and B could swap seats 1 and 2. Who sits at the east end?
Show solutionHide solution
The swap touches only seats 1 and 2.
The east end is not in the swap.
The east-end person is the same either way
In a circle, walk the left-neighbour links around your final drawing. If the string does not close, one arrow was drawn backwards.
Facing the centre, the left chain is B, D, C, E and A is the immediate right of B. Does the loop close?
Show solutionHide solution
A is right of B, so A is just before B clockwise.
The chain goes B, D, C, E, A and back to B.
Yes, it closes
Mistakes to avoid
Where most students lose marks on this subtopic.
Answering from a rough half-drawn seating.
Write the final seating neatly before you read the questions.
Swapping more people than the question names.
Swap only the two named people.
Using for a circle.
A circle with rotations equal gives .
Tying an attribute to a name before a clue joins them.
Fix seats first. Join an attribute to a name only with a clue.
Spending long on a set with two live seatings.
Check if the question needs the full seating. If not, move on.
Quick revision
Read this the night before the exam.
Read all clues, build the frame with its facing, then fill.
Two rows: seat of the south row faces seat of the north row.
Solve fully once. Each follow-up is a 15-second lookup.
Row: . Circle: . Row with a pair together: .
Attribute grid: fix seats, then tie names to attributes.
Practice: 12 questions
Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.
Topic test · 12 questions
Suggested time 14 min · wrong answers go to your mistake notebook automatically.