Seating‑Arrangement Study Notes
(Civil Judge Exam – Reasoning Ability)
1. What is a Seating‑Arrangement Problem?
- You are given a list of people and a list of seats (rows, columns, or a circle).
- Rules tell where each person can or cannot sit.
- Your job: find the only possible arrangement (or all possible ones).
Think of it like solving a tiny puzzle: place the pieces so every rule fits.
2. Everyday Analogy
Imagine you’re arranging a family photo:
- Grandma must be in the middle.
- Dad can’t sit next to Mom.
- Kid A wants to sit on the right side.
- Everyone else can sit anywhere else.
You draw a quick sketch, place Grandma first, then fill the rest while checking the rules.
That sketch‑and‑check method works for exam questions too.
3. Common Rules You’ll See
| Rule | What it really means | Quick Hint |
|---|---|---|
| X sits next to Y | X must be in an immediately adjacent seat (left or right). | Draw a line between X and Y. |
| X sits on the left of Y | X is somewhere to the left side of Y, not necessarily directly next. | Put X first, then Y to its right. |
| X sits opposite Y | In a circular table, X is directly across from Y. | Draw a circle and mark opposite seats. |
| X and Y sit together | Same as “next to”, but you don’t know who is on the left. | Treat them as a group. |
| X sits at the end | X occupies the far left or far right seat. | Mark an end seat for X. |
| Exactly two seats between X and Y | Count two empty seats between them. | Count 1‑2‑3 between X and Y. |
| X sits at seat number 3 | Zero‑based? Usually 3rd seat from the left. | Label seats 1,2,3… and put X at 3. |
Tip: Write each rule in your own words. This avoids mis‑reading.
4. Step‑by‑Step Solving Strategy
- List the people and the seats (or rows/columns).
- Write every rule in a simple sentence.
- Identify fixed points
- People who must sit at a specific seat or end.
- Pairs that must sit together.
- Create a sketch (grid or circle).
- Place fixed points first.
- Use elimination
- If X cannot sit next to Y, cross off that spot.
- If X must be left of Y, place X before Y.
- Iterate
- Repeat steps 5–6, updating the sketch until all people are placed.
- Check every rule to ensure no contradictions.
- Mark the final arrangement and double‑check.
5. Tiny Example
People: Alice, Bob, Carol, Dave
Seats: 1, 2, 3, 4 (left to right)
Rules
- Alice sits next to Bob.
- Carol sits to the left of Alice.
- Dave sits at the far right seat.
Solution
| Seat | Person |
|---|---|
| 1 | Carol |
| 2 | Alice |
| 3 | Bob |
| 4 | Dave |
Check
- Alice (seat 2) is next to Bob (seat 3). ✔️
- Carol (seat 1) is to the left of Alice (seat 2). ✔️
- Dave is at seat 4 (far right). ✔️
6. Quick Tips for Exam Day
- Draw a clean sketch – a neat diagram saves time.
- Use abbreviations (e.g., A=Alice, B=Bob).
- Red‑cross seats that can’t be used for a person.
- Work from the hardest rule (e.g., fixed position) to the easiest.
- If stuck, try a different arrangement – usually only one will satisfy all rules.
- Always double‑check after placing the last person.
7. Practice Problem (Try It)
People: Emma, Frank, Gina, Harry
Seats: 1, 2, 3, 4 (left to right)
Rules
- Frank sits next to Emma.
- Gina does not sit at seat 1.
- Harry sits to the right of Gina.
- Emma sits at seat 3.
Your task: Fill the table.
Answer
| Seat | Person |
|---|---|
| 1 | Frank |
| 2 | Gina |
| 3 | Emma |
| 4 | Harry |
Why?
-
Emma is fixed at seat 3.
-
Frank must be next to Emma → seat 2 or 4.
-
Gina cannot be seat 1 → choose seat 2.
-
Frank then goes to seat 4.
-
Harry must be to the right of Gina → seat 4, but Frank already there → swap:
- Put Frank at seat 2, Gina at seat 4, leaving seat 1 for Harry.
- Check all rules:
- Frank (seat 2) next to Emma (seat 3). ✔️
- Gina (seat 4) ≠ seat 1. ✔️
- Harry (seat 1) is not right of Gina (seat 4) → Oops!
- Sorry, correct arrangement is:
Seat Person 1 Harry 2 Frank 3 Emma