Goa PSC – Reasoning Ability
Topic: Seating Arrangement
A seating‑arrangement question tests your ability to interpret clues, place persons or objects in a linear, circular or grid arrangement, and deduce the final layout.
1. Simple Explanation
- Goal – Determine the exact seat (or relative position) of each person/thing based on the given clues.
- Approach – Treat the problem like a mini‑puzzle:
- List all entities (people, colours, objects, etc.).
- Mark possible positions (often a 1‑D line, 2‑D grid, or circular layout).
- Apply each clue one by one, eliminating impossibilities.
- Iterate until only one arrangement satisfies all clues.
2. Key Points & Common Terms
| Term | Meaning | Example |
|---|---|---|
| Left / Right | Immediate neighbour to the left/right. | “A sits immediately to the left of B.” |
| Between | Exactly one seat between two people. | “C sits between D and E.” |
| Next to | Adjacent seat, not necessarily immediately. | “F sits next to G.” |
| Opposite | Directly across in a circular arrangement. | “H sits opposite I.” |
| Far from | Two seats apart. | “J is two seats away from K.” |
| First / Last | Edge seats in a row. | “L sits at the first seat.” |
| Middle | Exactly in the centre of an odd‑numbered row. | “M sits in the middle seat.” |
| Row / Column | In a 2‑D grid. | “N sits in the first column.” |
Common Pitfalls
- Assuming “first” means leftmost – In many problems “first” refers to the leftmost or the topmost seat; clarify the orientation.
- Ignoring “immediately” – “Next to” vs. “immediately to the left”.
- Over‑counting gaps – “Far from” usually means exactly two seats apart (i.e., one seat between them).
- Circular vs. Linear – In a circle, left/right is relative to the viewer; opposite means 180° apart.
3. Step‑by‑Step Methodology
-
Draw the Layout
- Linear: a single row of numbered seats.
- Circular: a circle with numbered positions.
- Grid: a table with rows & columns.
-
List All Items
- People, colours, objects, etc.
- Keep track of counts (e.g., 5 people → 5 seats).
-
Apply Absolute Clues First
- e.g., “A sits at the first seat.”
- Place them on the diagram.
-
Apply Relative Clues
- Use “left of”, “between”, etc.
- Narrow down possibilities.
-
Use Elimination
- If a seat is occupied, remove it from other candidates.
- If a clue forces a particular arrangement, adopt it.
-
Check Consistency
- After each placement, verify that all clues remain satisfiable.
- If a contradiction appears, backtrack.
-
Complete the Layout
- Fill remaining seats logically.
- Verify all clues once final.
4. Worked Example
Problem
Five friends – A, B, C, D, E – are seated in a row of five seats (1 to 5 from left to right).
- A sits somewhere to the left of B.
- C sits immediately to the right of A.
- D sits at the first seat.
- E sits between B and C.
- B sits at the last seat.
Question: What is the complete seating arrangement?
Step‑by‑Step Solution
| Seat | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Person | D |
-
Seat 1 – D (clue 3).
Seat 1 2 3 4 5 Person D -
Seat 5 – B (clue 5).
Seat 1 2 3 4 5 Person D B -
A is left of B – A must be in seats 1–4.
- Seat 1 already D, so A ∈ {2,3,4}.
-
C immediately to the right of A – So if A=2 → C=3; A=3 → C=4; A=4 → C=5 (but seat 5 is B).
→ A cannot be 4.
→ Two possibilities:- (A=2, C=3)
- (A=3, C=4)
-
E sits between B and C – B is seat 5, so E must be seat 4 (between seat 3 & 5) or seat 2 (between seat 1 & 3) depending on C’s position.
- Case 1: A=2, C=3
- E between B(5) and C(3) → E must be seat 4.
- Seats left: seat 2 (A), seat 3 (C), seat 4 (E).
- Remaining person
- Case 1: A=2, C=3