Seating arrangement: Reasoning Ability Notes for Goa PSC

Seating Arrangement – Quick & Easy Study Notes

(For Goa PSC – Reasoning Ability)

1. What is a Seating Arrangement Problem?

You are given a group of people (or objects).
You must decide who sits where in a row, circle, or grid.
The problem gives clues (facts) about who sits next to whom, who is opposite, how far apart, etc.
Your job is to use those clues to find the exact order.

Analogy: Think of arranging books on a shelf. You know some books must be together, some must be on the left side, and others on the right. The clues are the rules you follow to place each book.

2. Basic Directions & Positions

Direction	Everyday Example	How to Visualise
Next to	Two friends sharing a pizza slice	The two seats are side‑by‑side
Opposite	Two people on a round table facing each other	They are on opposite sides of the table
Left of	A person standing to the left of a door	The seat is to the left side of the reference seat
Right of	A child standing right next to a playground	The seat is to the right side of the reference seat
Between	A plant between two trees	The seat is exactly in the middle of two other seats
At a distance of 2	Two people standing two steps apart	There is one seat in between them

3. Simple 3‑Step Solving Strategy

Write Down All Facts
- Copy every clue into a list.
- Use short notes: “A next to B”, “C opposite D”, etc.
Draw a Tiny Diagram
- For a row of 4 seats, draw 4 squares in a line.
- For a circle of 6 seats, draw 6 dots around a circle.
- Leave blanks for names/objects.
Place the Sure Things First
- If a clue says “A is at seat 1”, put A there.
- If “B is opposite C”, put B and C on opposite sides.
Fill In the Gaps
- Use the remaining clues to keep moving.
- If “D is next to E” and you already have E in seat 3, put D in seat 2 or 4.
- If a seat can’t hold a certain person because of a clue, cross it off.
Check Consistency
- After filling all seats, read every clue again.
- If any clue is violated, backtrack and try the other possibility.

4. Common Patterns

Pattern	How It Looks	Quick Check
Two people must be together	“X and Y sit together”	Put them side‑by‑side in any pair of seats.
One person on the leftmost/rightmost	“Z sits at the left end”	Place Z in the first/last seat.
Opposite pair	“X opposite Y”	Put X in seat 1, Y in the seat right across.
Between two specific people	“M sits between P and Q”	Put M in the middle seat of a trio.
Distance clues	“R is two seats away from S”	Count two seats between them.

5. Tiny Example & Solution

Problem (Very Short)

4 people: A, B, C, D.
Clues:
1. A sits next to B.
2. D sits opposite C.
3. B is on the left side of the row.

Solution

Draw 4 seats in a row
```
[ ] [ ] [ ] [ ]
```
Place B on the left side
```
[B] [ ] [ ] [ ]
```
A sits next to B → A must be in seat 2
```
[B] [A] [ ] [ ]
```
D opposite C (only possible pairs are seats 1‑4 or 2‑3).
- Seat 1 already has B.
- So D must be in seat 4 and C in seat 3.
```
[B] [A] [C] [D]
```
All clues satisfied.

6. Quick Tips & Common Mistakes

Tip	Why it Helps
Use a pencil, not a pen	You can erase mistakes quickly.
Label seats with numbers	Makes counting easier.
Check every clue once you finish	Surprise contradictions may appear.
Avoid jumping to conclusions	Try all possibilities before picking one.
Look for “only possible place”	If a clue forces someone into a single seat, place them first.

Mistake	Fix
Skipping a clue	Even a small clue can change the whole arrangement.
Forgetting “opposite”	In a round table, opposite means exactly across from the person