Seating Arrangements for CA Foundation
Seating arrangement puzzles: people in a row facing north or south, around a table facing in or out, and position counting from either end.
Quantitative AptitudePaper 3, Logical Reasoning12 MCQs2 lessons2 flashcards3 memory tricks
Practise Seating Arrangements free
What you'll learn
- Linear arrangements
Solve row puzzles and position questions. - Circular arrangements
Use left and right correctly around a table.
Key formulas
| Position from right | Total − position from left + 1 |
|---|---|
| Total in a row | Position from left + position from right − 1 |
Concepts explained
Linear seating arrangements
In a row, place people with fixed positions first, then use 'immediate left/right' clues and finally 'not' clues; mind which way they face.
What it means
- Facing north: right is your right on paper; facing south: reversed.
- Ends and middle are the best starting clues.
- Draw blanks for every seat.
- Re-read every clue against the final order.
- A middle, B right of A, C left end, D left of A
Answer: C D A B E
- B 2nd, E right of B, A right end, D not left end
Answer: C B E D A
Related terms
- Two rows facing each other: one row faces north, the other south
- Ranking: same counting rules as rows
Exam tip: When two arrangements seem possible, find the clue that removes one.
Circular seating arrangements
Around a table facing the centre, left is clockwise and right is anticlockwise; facing outward, it's the reverse.
What it means
- Opposite seat (n even): n/2 seats away.
- People between opposite seats: n/2 − 1 each side.
- Fix one person to remove rotation.
- Square table: corners and middles of sides may both be used.
- P, Q, … clockwise, facing centre
Answer: Q is P's immediate left
- Six seats
Answer: Three seats away
Related terms
- Rotation: same arrangement turned round the table
- Mixed facing: some face in, some out
Exam tip: Draw the circle and write 'L = clockwise' at the top before placing anyone.
Position from either end
Position from left + position from right = total + 1.
What it means
- Position from right = total − position from left + 1.
- Total = left position + right position − 1.
- If two people swap, use each person's new position.
- People between A and B = |position difference| − 1.
- 7 people, 3rd from left
Answer: 5th from right
- 8th from left, 12th from right
Answer: 19
Related terms
- Ranking in class: same formula with ranks
- Overlap: if ranges overlap, subtract the shared people
Exam tip: The person themselves is counted from both ends, so subtract 1.
Memory tricks
Facing centre: left = clockwise, right = anticlockwise.
Total = left position + right position − 1.
Solve seating puzzles from definite clues to negative clues.
Try 3 CA Foundation-style questions
Q1. Five friends sit in a row facing north. A is in the middle. B is to the immediate right of A. C is at the extreme left. D is to the immediate left of A. Where does E sit?
- At the extreme left
- At the extreme right
- In the middle
- Second from the left
Show answer
Answer: (2) At the extreme right
Left to right: C, D, A, B, E. Facing north, right is east, so E is at the extreme right.
Q2. A, B, C, D and E sit in a row facing north. B is second from the left. E is to the immediate right of B. A is at the extreme right. D isn't at the extreme left. Who is at the extreme left?
- C
- D
- A
- E
Show answer
Answer: (1) C
Positions: 2 = B, 3 = E, 5 = A. C and D take 1 and 4; D isn't at 1, so C is at the extreme left and D is fourth.
Q3. In the row C, B, E, D, A (left to right, facing north), who sits between E and A?
- B
- D
- C
- No one
Show answer
Answer: (2) D
E is third and A fifth, so D (fourth) is between them.
Practise all 12 questions Free · explanations for every option · see where you go wrong