📚 Seating Arrangement – Reasoning Ability
(For Nagaland Patwari / Lekhpal Competitive Exam)
1. Simple Explanation
A seating arrangement problem asks you to determine who sits where based on a set of clues.
- Positions are usually numbered or described by relative directions (e.g., “next to”, “opposite”, “to the left of”).
- Clues give relationships (e.g., “A is sitting to the left of B” or “C is not next to D”).
- Your goal is to place every person in a unique seat that satisfies all clues simultaneously.
2. Key Points to Remember
| # | Concept | How to Apply |
|---|---|---|
| 1 | Type of Arrangement | - Linear (1‑5, 1‑7, etc.) - Circular (around a table) – “next to” means two neighbors. - Row/Column (two rows × N columns). |
| 2 | Direction Tags | - Left/Right: directly adjacent. - Opposite / Across: one seat away in a circular or a row‑column grid. - Between / Next to / Far from: may need counting. |
| 3 | Counting Rules | - “Two people are between X and Y” means there are exactly two seats separating them. - “X sits immediately next to Y” means adjacency with no seats in between. |
| 4 | Logical Deductions | 1. List all constraints. 2. Start with fixed positions (e.g., someone at seat 1 or at the far left). 3. Use elimination: if a person cannot be in a seat, remove that possibility. 4. Cross‑check every clue after each placement. |
| 5 | Common Pitfalls | - Confusing “left of” with “to the left of” (they mean the same). - Forgetting that “opposite” in a 6‑seat circular table is 3 seats away. - Assuming a person can occupy more than one seat. |
| 6 | Answer Format | Usually “Seat 1 – X, Seat 2 – Y, …” or “X is sitting to the left of Y”. Keep the answer concise. |
3. Worked Example
Problem
7 people – A, B, C, D, E, F, G – are to be seated in a straight row of 7 seats (Seat 1 on the leftmost side).
Clues:
- A sits immediately to the right of B.
- C sits two seats to the right of D.
- E sits between B and F (exactly one person between them).
- G sits at the far right (Seat 7).
- A is not in Seat 6.
Find the seat number of each person.
Step‑by‑Step Solution
| # | Observation | Reasoning |
|---|---|---|
| 1 | Seat 7 = G (given). | |
| 2 | Seat 1 cannot be A (since A is right of B). | So B cannot be in Seat 7. |
| 3 | A is immediately right of B → if B in Seat 1 → A in Seat 2. | Test this possibility. |
| 4 | C is two seats right of D → possibilities: (D=1,C=4), (D=2,C=5), (D=3,C=6), (D=4,C=7). | D cannot be 4 because Seat 7 is G. |
| 5 | E sits between B and F (one person between). | If B=1, E must be in Seat 3 and F in Seat 4 (or F=3, E=5). |
| 6 | Check consistency with clue 2. | If D=2, C=5; but Seat 2 already A. Contradiction. |
| 7 | Try D=3, C=6. | Seat 3 would be D, Seat 6 would be C. |
| 8 | Place B=1, A=2, D=3, C=6, G=7. | Remaining seats: 4,5 for E and F. |
| 9 | E sits between B(1) and F → If F in 4, E in 3? Already D. So F must be in 5, E in 4. | Check: B(1) – E(4) – F(5); there is one seat (4) between B and F? Actually seats 1 and 5 have seats 2,3,4 between → 3 seats → Not allowed. |
| 10 | Re‑evaluate: maybe B not in 1. | Let’s try B in Seat 3? Then A in Seat 4. |
| 11 | B=3, A=4, D=1, C=4? No conflict because Seat 4 already A. | Not valid. |
| 12 | B=2, A=3? But A cannot be Seat 6. | Seat 3 is fine. |
| 13 | B=2, A=3, D=1, C=4, G=7. | Seats left: 5,6 for E & F. |
| 14 | E between B(2) and F → if F in 5, E in 4? Seat 4 already C. | So F cannot be 5. |
| 15 | F in 6, E in 5. | Check: B(2) – E(5) – F(6): seats 3 & 4 between B & F → two seats → not “exactly one person between” → invalid. |
| 16 | B=4, A=5? A cannot be 6 but 5 ok. | D=1, C=4? Conflict. |
| 17 | Correct arrangement (found by systematic elimination):** |
- Seat 1 – D
- Seat 2 – B
- Seat 3 – A
- Seat 4 – E
- Seat