Seating arrangement: Reasoning Ability Notes for Assam PSC

Seating Arrangement – Reasoning Ability

(Assam PSC – Practice & Revision Notes)

Why it matters
Seating‑arrangement questions test your ability to interpret constraints, deduce relative positions and check consistency.
Mastering a systematic approach saves time and reduces errors.

1. Simple Explanation

Goal: Place a set of people (or objects) in a line or circle satisfying all the given conditions.
Common constraints
- “A sits to the left/right of B”
- “C sits between D and E”
- “X sits opposite Y” (circular seating)
- “No two of A, B, C sit together”
- “Exactly two persons sit between X and Y”
Approach
1. List all constraints clearly.
2. Draw a simple scaffold (empty seats).
3. Place the most restrictive elements first (e.g., a “between” constraint or a fixed seat).
4. Use deduction to fill remaining seats.
5. Check for contradictions; if found, backtrack.

2. Key Points & Tips

#	Point	Why it matters	Quick Tip
1	Identify absolute positions (e.g., “A sits at the 1st seat” or “C sits opposite D”)	Sets a reference frame	Mark them first
2	Prioritize “between” constraints	These lock relative order	Place the middle person first
3	Handle “opposite” in circles	Opposite pairs reduce options	Place one, then immediately place its opposite
4	Count seats between	Must match the exact number	Use the formula `distance = seats between + 1`
5	Check “no adjacency”	Eliminates immediate neighbors	Shade forbidden adjacent slots
6	Use a “grid” or “table” for clarity	Keeps track of positions	1‑row table for linear, 1‑circle row for circular
7	Backtrack if stuck	Constraints may conflict	Undo last placement, try alternative
8	Verify after full placement	Avoid oversight	Re‑read all constraints

3. Worked Example

Problem Statement

Five people – A, B, C, D, E – are to sit in a row of five seats.

Constraints:

A sits to the left of B.

C sits between D and E.

B sits exactly one seat to the right of D.

No two of A, C, E sit together.

Question: Find a possible seating arrangement.

Step‑by‑Step Solution

Step	Action	Reasoning
1	List constraints	A left of B; C between D & E; B one seat right of D; A, C, E not adjacent.
2	Draw empty row	`1 2 3 4 5`
3	Place “B one seat right of D”	Means D and B are consecutive with B to the right. Possible pairs: (1‑2), (2‑3), (3‑4), (4‑5).
4	Try pair (2‑3)	Place D at seat 2, B at seat 3.
5	Apply “C between D and E”	With D at 2, C must be somewhere between D and E. Since seats 1 & 4 & 5 are available, the only way C can be between D and E is if E is to the right of C and D. So potential order: D – C – E.
6	Place C at seat 4, E at seat 5	Fits “between” (D at 2, C at 4, E at 5). But check adjacency: C (seat 4) adjacent to B (seat 3) → violates “no two of A, C, E sit together”. So this placement fails.
7	Backtrack – try pair (3‑4)**	Place D at seat 3, B at seat 4.
8	Place C & E	To satisfy “C between D and E”, we need D – C – E or E – C – D. Since D at 3, only seats 1,2,5 remain. The only arrangement that keeps C between D and E is: E at seat 1, C at seat 2, D at 3. (E – C – D).
9	Check adjacency rule	A, C, E cannot sit together. With E at 1, C at 2 → E & C are adjacent → invalid.
10	Backtrack further – try pair (4‑5)**	Place D at seat 4, B at seat 5.
11	Place C & E	Remaining seats: 1,2,3. To have C between D (4) and E, E must be left of C. Only feasible order: E at 1, C at 2, D at 4 → but C at 2 is adjacent to A? We haven't placed A yet.
12	Place A	Remaining seat 3. A at seat 3. Check constraints:

A left of B? yes (3 < 5).
No two of A, C, E together? A(3) adjacent to C(2) → violates rule. | |13| Backtrack again – try pair (