Seating Arrangement
🔒 Log in to trackExam strategy for puzzles
🔒 Log in to trackSeating questions come in sets of 3–5 sharing one puzzle. Budget rules:
- Read all clues before drawing anything. Negative clues ('Q does not face the centre') often decide the last seat instantly.
- Solve once, answer many. The first question costs 90–120 seconds; questions 2–4 of the same puzzle cost 15–20 seconds each because the seating is already on paper.
- Skip cleanly. If after one full pass the seating still has two live configurations, park the set and return — CGL reasoning has cheaper marks elsewhere.
- Verify with one closed loop: walk left-neighbour links around your final circle; if the string doesn't close, an arrow was drawn backwards.
Detailed notes
How seating sets appear in exams
Seating questions come in sets of 3 to 5 questions on one puzzle. The first question takes the time; the others should take 10 to 20 seconds each if the puzzle is solved fully. So the real skill is solving the whole arrangement once and cleanly.
Budget and order
- Read every clue once before drawing. Count the people and seats. Note the facing direction. Look for clues that fix a seat outright.
- Build the frame (row, circle or two rows) and write the direction on it.
- Place fixed clues, then chains, then negative clues.
- Write the final arrangement neatly before reading the questions. Most wrong answers in a set come from answering off a half-finished rough drawing.
Two parallel rows
Two rows of m people face each other: row 1 faces south, row 2 faces north. The person at seat i of row 1 faces the person at seat i of row 2.
- A south-facing person's left is the east end. So "A is to the immediate right of B" in the south-facing row means A is one seat west of B.
- "P faces A" links the two rows directly: P and A share the same seat number.
- The two ends of both rows line up. "Sits at an end" in either row means seat 1 or seat m.
Solve once, answer many
Typical follow-up questions:
- Who sits k-th left/right of X — read off the final drawing.
- Which statement is true — check each option against the drawing; exactly one should match.
- If X and Y interchange seats — swap only those two, keep everyone else, then read the new neighbour.
- Odd one out — four pairs of people; three share a relation (say, both at ends or both second to the right), one does not.
Counting arrangements
A few questions ask "in how many ways" instead of "who".
- n people in a row: n! ways. With A and B together: treat AB as one block, (n − 1)! × 2.
- n people in a circle (rotations counted as the same): (n − 1)! ways.
- Fixed clues cut the count: each fixed seat removes a person and a seat from the free pool.
- Always list small cases if the numbers are small; it is quick and it catches double counting.
Attribute grids
When each person also has a drink, city, colour or job, draw a grid: people down the side, seat and attribute across the top. Each clue either fixes a cell or rules one out. Seat clues and attribute clues work together: "the tea drinker sits at the left end" tells you the seat of the tea drinker, not the name. Tie the attribute to a name only when another clue joins them.
Where time is lost
- Mirror images: reading a south-facing left as your own left.
- Assuming "between" means "immediately between".
- Forgetting that "neighbour" allows two sides.
- Treating "k-th to the left" as k people in between (it is k − 1).
- Answering from a case that a later clue had already struck out.
Quick revision
- Read all clues, build the frame with the facing direction, then fill.
- Two rows: seat i of the south row faces seat i of the north row; south-facing left is east.
- Solve fully once; then each follow-up is a 15-second lookup.
- Circle of n: (n − 1)! arrangements; row: n!; a block of 2: (n − 1)! × 2 in a row.
- Attribute grid: people × (seat, attribute); fix names only when a clue joins them.
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: Two parallel rows facing each othervery common3 practice Q
Two rows; one faces north, the other south; 'X faces Y' clues.
Seat i of the south-facing row faces seat i of the north-facing row. South-facing left = east. Use 'faces' clues to jump between rows.
Example: Row 1 (A, B, C) faces south, row 2 (P, Q, R) faces north. B is in the middle of row 1, A immediately right of B, R faces A. Q is not at an end. Who faces P?
B = 2, A = 1 (right of south-facing = west). R = 1, Q = 2, P = 3. Seat 3 of row 1 is C.
Type 2: Solve once, answer manyvery common3 practice Q
A set of questions: true statement, interchange, odd one out.
Finish the whole arrangement neatly first. Then check each option against the final drawing; for 'interchange' swap only the two named people.
Example: Five people face north: P Q R T S. If P and T swap seats, who is immediately left of P?
After the swap: T Q R P S. Left of P = R.
Type 3: Counting arrangementsoccasional3 practice Q
Asks 'in how many ways' instead of 'who'.
Row: n!. Circle: (n − 1)!. A block of two in a row: (n − 1)! × 2. Remove every fixed person and seat before counting.
Example: In how many ways can 4 people sit in a row if A and B must sit together?
Block AB: 3! × 2 = 12.
Type 4: Seats plus attributescommon3 practice Q
Each person also has a drink, colour, city or job.
Grid: people down, seat and attribute across. Fix seats first; join attribute to name only when a clue links them.
Example: Four people in a row: A at the left end drinks something; the milk drinker sits immediately right of A; C drinks juice at the right end; B drinks coffee. What does A drink?
Milk is seat 2 (not A); juice is C, coffee is B. A drinks tea.
Shortcut tricks
⚡ Two-configuration bail-out
When exactly two seatings survive all clues, check what the QUESTION asks: if both configurations give the same answer, mark it and move on — you never needed the extra clue you thought was missing.
Example: Q. After all clues, A and B could swap (seats 2/3). Question: who is opposite E?
Sol. If A/B's two seats are both on the same side, the seat opposite E is unchanged — answer stands either way.
The question only needs the asked seat, not the full unique seating.
Where students lose marks
Restarting the sketch for every question in the set instead of reusing it.
Spending 3+ minutes hoping a fifth re-read reveals a clue that isn't there.
Answering from a partial sketch without checking the remaining clues still hold.
Practice sets — 12 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 12 questions
Suggested time 14 min · wrong answers go to your mistake notebook automatically.