Seating Arrangement – Reasoning Ability
(Arunachal Pradesh Police Constable – Reasoning Ability Section)
Purpose:
Seating‑arrangement problems test your ability to interpret constraints, organise information logically, and deduce the only possible arrangement that satisfies all conditions.
1. Simple Explanation
- Definition: A seating arrangement problem gives you a set of people (or objects) and a list of rules that describe who sits where relative to whom.
- Goal: Determine the exact order or position of each person, or prove that no arrangement is possible.
Typical constraints:
| Type | Description | Example |
|---|---|---|
| Adjacency | Two persons must sit next to each other. | A must sit next to B |
| Opposite / Across | Two persons must be on opposite sides of a table or opposite each other. | C must be opposite D |
| Left / Right | One person must sit to the left/right of another. | E must be immediately to the left of F |
| Distance | Exactly k seats between two persons. | G and H must have exactly 2 persons between them |
| Fixed Position | One person is fixed at a particular seat (often “Seat‑1” or “Seat‑5”). | I must sit at seat‑1 |
| Group | A set of persons must sit together. | J, K, L must sit together |
| Exclusion | Certain persons cannot sit together or in a particular order. | M cannot sit next to N |
2. Key Points (Quick Reference)
| Step | What to Do | Tip |
|---|---|---|
| 1. List all persons | Write names/initials. | Use a grid/table if many. |
| 2. Identify fixed positions | Any seat numbers or “Seat‑1” constraints. | Place them first. |
| 3. Apply adjacency rules | Group people that must sit together. | Use “blocks”. |
| 4. Apply left/right rules | Order blocks/individuals accordingly. | Respect direction (clockwise). |
| 5. Apply distance rules | Count seats between two persons. | Use placeholders for unknowns. |
| 6. Check for contradictions | Ensure no rule is violated. | If conflict → no solution. |
| 7. Verify all conditions | Re‑read each rule against your arrangement. | One‑by‑one. |
Quick mnemonic: Fixed → Adjacency → Left/Right → Distance → Exclusion.
3. Worked Example
Problem Statement
8 persons – A, B, C, D, E, F, G, H – are to sit in a straight row of 8 seats numbered 1 to 8 from left to right.
The following conditions apply:
- A sits at seat 1.
- B sits immediately to the right of C.
- D sits somewhere between E and F, with E to the left of D.
- G sits exactly one seat to the left of H.
- C sits at least two seats away from E.
- H sits in seat 8.
Find the seating arrangement.
Solution Steps
| Step | Action | Reasoning |
|---|---|---|
| 1. Fix seats 1 and 8 | Seat 1 → A. Seat 8 → H. | From rules 1 & 6. |
| 2. Place G | G must be exactly one seat left of H → G at seat 7. | Rule 4. |
| 3. Place B & C | B is immediately right of C → possible pairs (C,B) = (2,3), (3,4), (4,5), (5,6), (6,7). | Seats 1 & 7 already occupied. |
| 4. Apply distance rule (C & E) | C must be at least two seats away from E. | So C cannot be adjacent to E. |
| 5. Place D, E, F | D must be between E and F, with E left of D. | This creates a block E – D – F (E left, F right). |
| 6. Consider remaining seats | Seats left: 2,3,4,5,6. (Seat 7 already G, seat 8 H). | We need to fit C,B and the block E-D-F. |
| 7. Test possible C‑B pairs | ||
| – If C=2, B=3 → E cannot be 1 or 3 (adjacent), so E could be 4,5,6. But E left of D, F to right, so E=4, D=5, F=6 works. Check C‑E distance: C=2, E=4 → 1 seat between → violates “at least two seats”. Reject. | ||
| – If C=3, B=4 → E cannot be 2 or 4. E could be 5 or 6. Try E=5, D=6, F=?? but seat 6 already B. Reject. | ||
| – If C=4, B=5 → E cannot be 3 or 5. E could be 6. Then D=?? but D must be between E and F, impossible because only seat 7 is free but G already there. Reject. | ||
| – If C=5, B=6 → E cannot be 4 or 6. E could be 2 |