Seating Arrangement

Prerequisites

Direction Sense — you need “clockwise” and “left/right depends on which way a person faces” to be automatic.
Blood Relations — the habit of placing the most certain clue first and marking unknowns as unknown.
Patience with a pencil: seating puzzles are solved on paper, never in your head.

The Hook: The Gram Sabha Seating Plan

Connect

The sarpanch of a gram panchayat near Dhamtari has to seat eight guests around a round table for a Gram Sabha (ग्राम सभा) meeting. The block officer must sit opposite the sarpanch; the patwari wants to sit next to the block officer with his land records; two guests who do not get along must not sit side by side.

Every planner, wedding organiser and exam-hall invigilator solves this kind of puzzle. CSAT gives you the clues and asks you to rebuild the plan — usually followed by three or four questions on the same arrangement.

The question this page answers: how do you turn a list of “second to the left of”, “opposite” and “not next to” clues into one seating chart, quickly and without mixing up left and right?

Why it matters for CGPSC: seating arrangement (बैठक व्यवस्था) puzzles often come as sets, where several questions share one arrangement. Solve the arrangement once and correctly, and every question in the set falls; get one clue wrong and you can lose all of them.

Linear Arrangements: Who Is on Whose Left?

People sit in a row. “Left” and “right” are always the person’s own left and right, so they depend on which way the row faces.

Row faces	Person’s left is	Person’s right is
North (towards the top of the page)	Your left as you look at the page	Your right
South (towards the bottom of the page)	Your right as you look at the page	Your left

Draw it this way every time

Draw the row horizontally with north at the top of the page. For people facing north, left-to-right on paper is their left-to-right. For people facing south, it is reversed: their left is towards the right edge of your page. Write an arrow showing the facing direction above the row before placing anyone.

Worked example 1: a linear row

Six friends — P, Q, R, S, T and U — sit in a row facing north.

R sits third from the left end.
P sits at the extreme right end.
U sits to the immediate left of P.
T sits between R and U.
Q does not sit at either end.

Solve: fix the definite clues first. R is in seat 3 and P in seat 6 (numbering from the left). U is immediately left of P → seat 5. T is between R and U → seat 4. Seats 1 and 2 remain for Q and S; Q is not at an end → Q in seat 2, S in seat 1.

Seat (left → right)	1	2	3	4	5	6
Person	S	Q	R	T	U	P

S is at the extreme left; T is second to the right of Q; three people (Q, R, T) sit between S and U.

Circular Arrangements: The Clockwise Rule

People sit around a table, equally spaced. Everything depends on whether they face the centre or face outward.

Facing	Left means	Right means
The centre	Clockwise	Anticlockwise
Outward	Anticlockwise	Clockwise

Why: picture the person at the bottom of the circle facing the centre (looking up the page). Their left hand points to the left of the page — and moving from the bottom of a clock face towards the 9 o’clock position is clockwise.

Other facts for an even number of equally spaced seats:

“Opposite” means exactly half-way round: in a circle of 8, opposite = 4 seats away; in a circle of 6, 3 seats away.
“Second to the left” of X skips one seat; “between X and Y” can be counted either way round — the question will say which, or use the shorter side.

Worked example 2: an eight-person circle

Eight friends — A, B, C, D, E, F, G and H — sit around a circular table, all facing the centre.

A sits third to the left of D.
B sits opposite A.
E sits to the immediate right of B.
G sits second to the right of E.
C is an immediate neighbour of G.
F is not an immediate neighbour of D.

Solve (facing the centre: left = clockwise, right = anticlockwise):

Place D at the top. Three seats clockwise from D → A at bottom-right.
B opposite A → top-left.
Immediate right of B = one seat anticlockwise → E at the left.
Second to the right of E = two seats anticlockwise → G at the bottom.
G’s neighbours are A (bottom-right) and the bottom-left seat → C at bottom-left.
Two seats remain: top-right (next to D) and right. F cannot be next to D → F at the right, H at top-right.

                 D
          B             H

       E      (table)      F

          C             A
                 G

Reading clockwise from the top: D, H, F, A, G, C, E, B. Check every clue against the chart before answering: D is opposite G, H opposite C, F opposite E, A opposite B.

Ranking in a Row

A different kind of linear question: one person’s position from each end.

$$\boxed{\text{Total in the row} = (\text{position from left}) + (\text{position from right}) - 1}$$$$\boxed{\text{Position from right} = n - (\text{position from left}) + 1}$$$$\boxed{\text{People between positions } a \text{ and } b \text{ (same end)} = |a - b| - 1}$$

Worked example 3

In a row of 30 students, Anil is 10th from the left and Bina is 12th from the right. How many students sit between them?

Convert Bina’s position to the left end: $ 30 - 12 + 1 = 19 $th from the left. Between positions 10 and 19: $ 19 - 10 - 1 = 8 $ students.

The Method

graph TD
    A[Draw the row or circle; mark facing direction] --> B[Place definite clues: ends, fixed seats, opposite]
    B --> C[Chain relative clues from people already placed]
    C --> D{More than one place possible?}
    D -->|Yes| E[Draw each case side by side]
    D -->|No| F[Apply negative clues: not next to, not at end]
    E --> F
    F --> G[Check every clue against the final chart]

Memory Tricks

Anchor these

“Facing centre, left goes with the clock.” Left = clockwise; right = anticlockwise. Facing outward, swap both.
“Facing south, flip the page.” A south-facing row has its left and right reversed relative to your view.
“Definite, then relative, then negative.” Fixed seats first; “next to / second to the left” next; “not next to” last — negative clues only choose between cases.
“Plus, plus, minus one.” Total in a row = left position + right position − 1 (the person is counted twice).
Opposite in a circle of n = n/2 seats away.

Don’t Confuse

This	vs	That
Facing centre: left = clockwise		Facing outward: left = anticlockwise
Row facing north: their left = your left		Row facing south: their left = your right
“Immediate left” — the next seat		“Second to the left” — skip one seat
“To the left of X” — anywhere on that side		“Immediate left of X” — the adjacent seat only
Total = L + R − 1		People between = \|a − b\| − 1

Common Mistakes

Trap 1: Using your own left for the people in the puzzle

For a person facing south, or facing the centre from the top of your circle, their left is your right on the page. Always reason from the person’s facing direction, never from your viewpoint.

Trap 2: Committing to one case too early

When a clue allows two placements, draw both. A negative clue later in the list (“F is not next to D”) usually eliminates one. Students who pick a case at random get the whole set wrong.

Trap 3: Not re-checking the final chart

Once the chart is complete, run through every clue once more. It takes twenty seconds and catches a misplaced “right” before it costs you three or four answers.

Practice

Level 1: Foundation

In a circle where everyone faces the centre, is “left” clockwise or anticlockwise?
In a circle of 10 equally spaced people, how many seats apart are two people sitting opposite each other?
Raju is 8th from the left and 13th from the right in a row. How many people are in the row?
In a row of 25, Gita is 6th from the left. What is her position from the right?
Five people sit in a row facing south. Is the person at the left end of your drawing at their own left end or their own right end?

Answers

Clockwise.
5 seats (half of 10).
20 ($ 8 + 13 - 1 $).
20th ($ 25 - 6 + 1 $).
Their own right end — a south-facing row is reversed on paper.

Level 2: Prelims MCQs

Directions (Q1–Q3): Six friends — P, Q, R, S, T and U — sit around a circular table, equally spaced, all facing the centre.

P sits second to the right of Q.
R sits opposite P.
S sits to the immediate left of R.
T is not an immediate neighbour of Q.

Q1. Who sits opposite S?

(a) Q (b) P (c) U (d) T

Answer: (c) U

Place Q at the top. Facing the centre, right = anticlockwise, so P (second to the right of Q) is two seats anticlockwise — bottom-left. R is opposite P — top-right. S is immediately left of R, one seat clockwise — bottom-right. T and U take the two remaining seats (bottom and top-left); the top-left seat touches Q, so T is at the bottom and U at top-left.

          Q
     U         R
     P         S
          T

Clockwise from the top: Q, R, S, T, P, U. Opposite S (three seats away) is U.

Q2. Who sits to the immediate right of T?

(a) S (b) P (c) U (d) R

Answer: (a) S

Facing the centre, the immediate right is one seat anticlockwise. Anticlockwise from T (bottom) is S (bottom-right). Option (b), P, is T’s immediate left — the left-right swap trap.

Q3. Using the same arrangement, consider the following statements:

U is an immediate neighbour of Q.
T sits opposite Q.
R sits to the immediate left of U.

Which of the statements given above is/are correct?

(a) 1 only (b) 1 and 2 only (c) 2 and 3 only (d) 1, 2 and 3

Answer: (b) 1 and 2 only

U (top-left) sits between P and Q, so statement 1 is correct. Q (top) and T (bottom) are three seats apart in a circle of six — opposite — so statement 2 is correct. The immediate left of U is one seat clockwise from top-left, which is Q, not R — statement 3 is wrong.

Q4. In a row of students, Ritu is 14th from the left end and 19th from the right end. How many students are in the row?

(a) 31 (b) 32 (c) 33 (d) 34

Answer: (b) 32

Total $ = 14 + 19 - 1 = 32 $. Ritu is counted in both positions, so subtract one. Option (c), 33, is the “forgot to subtract” answer.

Q5. Five friends — V, W, X, Y and Z — sit in a row, all facing south. X sits at the extreme left end. Y sits to the immediate right of X. W sits in the middle. V does not sit next to W. Who sits at the extreme right end?

(a) Z (b) X (c) V (d) Y

Answer: (c) V

Facing south, a person’s left is towards the east — the right side of your drawing. So X is at the east end. Y, to X’s immediate right, is one seat towards the west. W is in the middle. The two west-end seats remain for V and Z; V cannot be next to W, so V is at the west end and Z beside W.

On paper (west → east): V, Z, W, Y, X. Their extreme right end is the west end — V. Option (b), X, is the answer you get by reading left and right from your own view.

Level 3: Speed Drill — Solve in 60 Seconds

Each item should take under 60 seconds. In Mains Paper IV (GS-II), draw the row or circle and write the formula used as your working.

In a row of 40 students, Amit is 15th from the left. What is his position from the right?
Ravi is 7th and Sita is 12th from the left of a row. How many people sit between them?
Mohan is 10th from both ends of a row. How many people are in the row?
In a circle facing the centre, P is second to the left of Q. Where is Q relative to P?
A, B, C, D and E sit in a row facing north, in that order from left to right. Who is second to the right of B?
In a row of 30, Anil is 10th from the left and Bina 12th from the right. How many sit between them?