📚 Seating Arrangement – Reasoning Ability
(For FCI Recruitment – Reasoning Ability Section)
What you’ll learn
• How to translate textual conditions into a visual diagram.
• Common patterns & shortcuts to solve seating‑arrangement questions.
• A step‑by‑step worked example.
• Quick revision checklist for exam day.
1. Simple Explanation
Seating‑arrangement problems ask you to determine the relative positions of a set of people (or objects) given a series of constraints (e.g., “X sits to the right of Y”, “Z must be opposite A”).
The trick:
- Draw a blank diagram (row, circle, or square as described).
- Assign labels (A, B, C, …) to each seat.
- Place the first person using a fixed reference point (e.g., “A sits at the 12 o’clock position”).
- Apply each condition one by one, using elimination or deduction.
- Check consistency after every placement – if a conflict arises, backtrack.
2. Key Points & Common Patterns
| # | Pattern | How to Handle | Quick Tip |
|---|---|---|---|
| 1 | Absolute positions (e.g., “X sits at the 2nd seat from the left”) | Use the given seat number directly. | Keep a table of seat numbers. |
| 2 | Relative positions (e.g., “Y sits to the right of X”) | Count seats clockwise or counter‑clockwise. | Use “next seat” logic; always note the direction. |
| 3 | Opposite/Across (e.g., “Z is opposite A”) | In a circle of 8, opposite means 4 seats apart. | Remember: Opposite = half the total seats (for even numbers). |
| 4 | Between (e.g., “B sits between C and D”) | Place B, then find a spot where C & D are on either side. | “Between” can be immediately or not necessarily immediately – read carefully. |
| 5 | Adjacency (e.g., “E sits next to F”) | Keep them together; treat as a small block. | When multiple adjacency constraints exist, group them into a block. |
| 6 | Direction from a reference (e.g., “G is two seats to the left of H”) | Count seats starting from the reference in the indicated direction. | Left = counter‑clockwise; Right = clockwise. |
| 7 | Circular vs Linear | In a circle, “left” and “right” are relative to the observer; use a fixed starting seat. | For a circle, pick any seat as "12 o’clock" to keep orientation fixed. |
| 8 | Multiple constraints | Start with the most restrictive (e.g., absolute positions). Then satisfy the rest. | If a constraint conflicts, backtrack earlier steps. |
| 9 | Implied positions | Sometimes the only way to satisfy all constraints is to place someone in the last remaining seat. | Use “last seat” strategy. |
3. Worked Example
Problem
8 persons (A, B, C, D, E, F, G, H) are seated around a circular table.
- A sits at the 12 o’clock position.
- B sits to the immediate right of A.
- C sits opposite A.
- D sits between B and C.
- E sits to the left of F.
- G sits immediately to the right of H.
- H sits to the left of A.
Question: Who sits to the left of G?
Step‑by‑Step Solution
| Step | Action | Diagram (simplified) |
|---|---|---|
| 1 | Place A at 12 o’clock (fixed). | A |
| 2 | B is immediately right of A. | A – B |
| 3 | C opposite A (4 seats apart). | A – B – _ – _ – C |
| 4 | D between B and C. Since B is at seat 2 and C at seat 6, D must occupy seat 3 or 5. | |
| 5 | H sits to the left of A (counter‑clockwise). That leaves seat 11 (or seat 8 if we number 1–8). | H – A – B |
| 6 | G immediately right of H → seat 1 (between H and A). | G – H – A – B |
| 7 | E left of F. We have remaining seats: 3,4,5,6,7,8. | |
| 8 | Place D between B (seat 3) and C (seat 6). The only seat that fits is seat 4. | D |
| 9 | Now seats left: 5,7,8. C is at seat 6. | |
| 10 | E left of F: choose E at seat 5 and F at seat 7. | E – F |
| 11 | Remaining seat 8 for the last person (C already seated). Actually C is at seat 6; seat 8 is free for the last person (which is none – but we used all 8). | Completed |
Final seating order clockwise from 12 o’clock:
12 1 2 3 4 5 6 7 8
G H A B D E C F
To the left of G is H.
Answer: H.
4. Quick Revision Summary
| Item | What to Remember |
|---|---|
| Diagram first | Always start with a blank diagram and fixed reference. |
| Absolute → Relative | Use absolute clues (seat numbers) to anchor the diagram; then fill in relative clues. |
| Opposite rule | Opposite = half the total seats (for even numbers). |
| Adjacency | Treat adjacent pairs as “blocks” to simplify placement. |
| Between | “Between” may mean immediately or not necessarily immediately |