Seating arrangement

Seating Arrangement – Easy Study Notes

(Reasoning Ability – Manipur Patwari / Lekhpal Program)

1. What is a Seating Arrangement Question?

A seating‑arrangement problem asks you to decide who sits where at a table or in a line.
You are given a set of clues (rules) and you must line up the people (or objects) so that all clues are true.

Think of it like arranging your friends for a family photo:

• Some friends must be next to each other.
• Some friends cannot sit together.
• Some have to be on a particular side of the table.

Your job is to place everyone correctly.

2. Everyday Analogy

• People = LEGO blocks
• Table = a row of LEGO studs
• Clues = the instructions on the LEGO manual

Just follow the instructions, place each block in the right spot, and you’ll finish the picture.

3. Simple Rules to Remember

4. Step‑by‑Step Strategy

1. List the People
   Write down all names (or objects) in a row.
2. Write the Clues
   Copy each clue exactly as it appears.
3. Create a Blank Table

   | Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5 |
   |--------|--------|--------|--------|--------|
   |        |        |        |        |        |
   

4. Apply the Most Restrictive Clue First
   • If someone must be 3rd from left, put them in seat 3.
   • If someone must sit next to someone else, keep them adjacent.
5. Fill in the Gaps
   • Use “not adjacent” clues to rule out positions.
   • Use “left of” clues to set relative order.
6. Check All Clues
   Go through each clue one by one.
   If a clue is violated, backtrack and swap.
7. Confirm
   Once all clues are satisfied, you have your answer.

5. Tiny Example (5 People, 5 Seats)

People:

• A, B, C, D, E

Clues:

1. A sits somewhere to the left of B.
2. C sits immediately next to A.
3. D does not sit next to B.
4. E sits 2nd from the right.

Step 1 – Blank Table

| Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5 |
|--------|--------|--------|--------|--------|
|        |        |        |        |        |

Step 2 – Apply Clue 4

E is 2nd from the right → Seat 4.

| Seat 1 | Seat 2 | Seat 3 | Seat 4 | Seat 5 |
|--------|--------|--------|--------|--------|
|        |        |        |   E    |        |

Step 3 – Apply Clue 2

C is next to A.
We don’t know which side yet, but they must be consecutive.

Step 4 – Apply Clue 1

A must be left of B.
So B cannot be in seat 1 if A is in seat 1? Wait, A must be left of B, so A could be 1, B could be 2,3,4,5.

Step 5 – Apply Clue 3

D cannot sit next to B.

Let’s try a quick arrangement:

Check clues:

1. A left of B ✔
2. C next to A ✔ (C is seat 2, A seat 1) ✔
3. D not next to B – B is seat 3, D seat 5 → there is seat 4 between them ✔
4. E seat 4 ✔

All clues satisfied! So the seating is A – C – B – E – D.

6. Quick Tips