Quantitative Aptitude · Seating Arrangements

Linear Seating Arrangement (CA Foundation Logical Reasoning)

Updated 1 October 2026 · Fact-checked

A linear seating arrangement places people or objects in one row, all facing north or all facing south. To solve it, draw numbered boxes, fix the direction of left and right, place the definite clues first, then try the conditional clues one at a time until every position is forced.

Understand Linear Seating Arrangement

In a linear arrangement, people sit in a straight line. Every position is a box in a row. Your job is to fill the boxes using the clues, so that each person gets exactly one box.

The most important idea is direction. Draw the row on paper with north at the top. If everyone faces north, their left is west, which is the left side of your drawing. Their right is east, the right side of your drawing. If everyone faces south, it flips. Their left is east, which is the right side of your drawing. So a clue like "A is to the immediate left of B" points to different boxes in the two cases.

Clues come in a few types. Fixed clues give an exact place, such as "C sits at the extreme right end". Relative clues link two people, such as "D is second to the right of E". Counting clues say how many sit between two people. Negative clues say who is not at a place, such as "F is not at an end". Fixed clues go in first. Relative clues are placed as small blocks that you slide around the row.

The exam asks for a position, a neighbour, a left-right relation, or a count. Once the row is complete, these are just reading questions. The real work is building the row without a wrong assumption.

If a clue fits in two places, do not guess. Note both options and let the next clue remove one.

Key formulas to remember

Mirror rule for positions: Position from left + Position from right = n + 1; n is the total number of persons in the row. Use it to find a position from the other end.
Persons between two people: Between = |p₂ − p₁| − 1; p₁ and p₂ are positions counted from the same end.
Between, using positions from opposite ends: Between = n − (m + k); A is m-th from the left and B is k-th from the right, with A to the left of B. If m + k is more than n, they overlap and A is to the right of B.
Direction rule: facing north: Left = West, Right = East; In a drawing with north at the top, the person's left is the left of your page.
Direction rule: facing south: Left = East, Right = West; The person's left is the right side of your page. Convert every clue before you draw.
Meaning of immediate and second: Immediate = 1 step away; second to the right = 2 steps away; Third to the left of X means 3 boxes to the left of X, with 2 boxes in between.

How to solve Linear Seating Arrangement questions

This method works for any single-row seating question. The first two steps prevent most wrong answers.

1Read the full question and note n, the number of persons, and whether they face north or south. Draw n empty boxes in a row.
2Mark west and east on your drawing. If everyone faces south, remember that each person's left is east, the right side of your page.
3Write the fixed clues first: extreme ends, the middle seat, and exact positions. These cannot move.
4Convert every relative clue into a block, such as B _ C for "C is second to the right of B". Place blocks that touch a fixed person first.
5Use counting clues with the position formula. Check the numbers against n before you commit.
6Apply negative clues to remove options. When a clue fits two places, record both cases and carry them forward.
7Fill the last empty boxes by elimination. Then re-read every clue against your finished row to check that none is broken.
8Read the question again and answer from your row. Watch for left or right from a person's own view, and for "between" counts.

Quickest way: Anchor, Block, Eliminate

When to use it: Use this in the MCQ paper, where each question should take about 90 seconds to 2 minutes. Do it all in one compact line of boxes.

Write the numbers 1 to n above the boxes, with 1 on the west side for north-facing rows. Use the numbers for every count.
Place the most fixed clue first. An end seat or the middle seat gives you an anchor.
Build blocks for the connected clues, such as A B or P _ Q, and drop them around the anchor.
Use the options. If the question asks who sits at an extreme end, test each option against the clues and cross out the ones that break a clue.
If two cases remain after all clues, check whether the question is answerable in both. If the answer is the same in both cases, pick it. If not, you may have misread a clue.
If the row still will not settle after about two minutes, skip the set question. A wrong answer costs 0.25 marks, and a skip costs nothing.

Common mistakes in Linear Seating Arrangement

Treating left as the left of the page when everyone faces south.
Students draw the row quickly and forget that facing south reverses left and right.
Fix: Write "South: Left = East" next to the drawing before you place any clue, and convert each left-right clue.
Reading "second to the right of A" as the next seat.
Students confuse "immediate" (1 step) with "second" (2 steps).
Fix: Count steps from A. Second to the right means 2 boxes away, with exactly one box between.
Counting the two named people when finding persons between them.
Students subtract the positions and forget to subtract 1.
Fix: Use Between = |p₂ − p₁| − 1. Positions 2 and 5 give 2 people between.
Guessing one case when a clue fits two places.
Students want a single drawing and pick one without proof.
Fix: Draw both cases. Carry them to the next clue, where one will usually fail.
Ignoring negative clues such as "not at an end".
Students treat them as less useful than positive clues.
Fix: Use negative clues to remove seats from your list. They often decide the last two persons.
Not re-checking all clues against the final row.
Time pressure and confidence after finding one answer.
Fix: Spend 15 seconds testing each clue on the finished row. This catches direction slips.

Worked examples

Example 1

Five friends P, Q, R, S and T sit in a row facing north. Q sits at the extreme right end. R sits immediate left of Q. P sits second to the left of R. T sits between P and R. Who sits at the extreme left end? (a) P (b) R (c) S (d) T

Show the solution

Draw 5 boxes numbered 1 to 5 from west (left) to east (right). Everyone faces north, so the page left is the persons' left.
Q is at the extreme right, so Q is in box 5.
R is immediate left of Q, so R is in box 4.
P is second to the left of R, so P is 2 steps left of box 4, which is box 2.
T is between P and R, so T is in box 3.
S is the only person left, so S is in box 1. The row is S, P, T, R, Q.

Answer: (c) S

Example 2

Six persons A, B, C, D, E and F sit in a row facing south. A sits at the extreme east end. D sits immediate right of A. B sits third to the right of A. C sits immediate right of B. F sits at the extreme west end. Who sits immediate left of B? (a) A (b) C (c) D (d) E

Show the solution

Draw 6 boxes numbered 1 to 6 from west (left of your page) to east (right of your page).
Everyone faces south, so each person's right is west and left is east. "Right of" means moving toward box 1. "Left of" means moving toward box 6.
A is at the extreme east end, so A is in box 6.
D is immediate right of A, so D is 1 step west of A, in box 5.
B is third to the right of A, so B is 3 steps west of A, in box 3.
C is immediate right of B, so C is 1 step west of B, in box 2.
F is at the extreme west end, so F is in box 1.
E is the only one left, so E is in box 4. The row from west to east is F, C, B, E, D, A.
Immediate left of B is 1 step east of B, which is box 4. E sits there.

Answer: (d) E

Example 3

Seven persons G, H, J, K, L, M and N sit in a row facing north. G sits in the middle. H sits third to the left of G. J sits second to the right of G. K sits immediate right of H. L sits immediate left of G. N sits at the extreme right end. How many persons sit between K and M? (a) 1 (b) 2 (c) 3 (d) 4

Show the solution

Draw 7 boxes numbered 1 to 7 from left to right. Everyone faces north.
G is in the middle, so G is in box 4.
H is third to the left of G, so H is in box 1.
J is second to the right of G, so J is in box 6.
K is immediate right of H, so K is in box 2.
L is immediate left of G, so L is in box 3.
N is at the extreme right end, so N is in box 7.
M is the only one left, so M is in box 5. The row is H, K, L, G, M, J, N.
K is in box 2 and M is in box 5. Persons between = 5 − 2 − 1 = 2 (L and G).

Answer: (b) 2

Exam tips

Check the facing direction in the first line of the question. Many questions in a set share it, and a single misread spoils every answer.
Use the options as a test. For "who sits at the extreme end" questions, check each option against the clues before you build a full row.
Be careful with phrases like "from the left end" and "from the persons' own left". They can point to opposite ends in a south-facing row.
Do the short, fixed-clue sets first and leave the two-case sets for later. With 0.25 negative marking, skip a question that is still unclear after about two minutes.
Practise counting questions with the formulas. They are fast, and you can often answer them without drawing the full row.

Practice questions from Seating Arrangements

Linear Seating Arrangement: frequently asked questions

How do I know which side is left in a linear seating arrangement?

Look at the direction the persons face. If they face north, their left is west, the left of your drawing. If they face south, their left is east, the right of your drawing.

What is the quickest way to solve linear seating questions in the MCQ paper?

Draw numbered boxes, place the fixed clues first, then build blocks for the relative clues. Use the options to test answers when only one position is asked. Skip the question if it takes more than about two minutes.

What should I do when a clue fits two possible seats?

Draw both cases and carry them forward. A later clue, especially a negative one, usually removes one case. If both survive, check that the question has the same answer in both.

How do I find how many persons sit between two people?

Take their positions from the same end and use |p₂ − p₁| − 1. If you know positions from opposite ends, use n − (m + k), valid when the two do not overlap.