Seating arrangement: Reasoning Ability Notes for Tripura Police Constable

Reasoning Ability – Seating Arrangement

Study Notes for Tripura Police Constable (TPC) Exam

1. What is a Seating‑Arrangement Question?

A seating‑arrangement puzzle asks you to determine the relative positions of a group of people (or objects) based on a list of clues.

Positions are usually on a straight line (row), a circle, or a grid.
Clues are statements of relationships such as A sits to the left of B, C is between D and E, F sits opposite G, etc.
The goal is to deduce the exact order or the position of a particular person/object.

2. Key Points & Strategies

#	Strategy	How to Apply
1. Draw a Skeleton	Sketch a simple line or grid with empty slots.	Label slots 1–n (left to right).
2. List All Participants	Write down every person/object.	Mark unknowns in the slots.
3. Translate Clues into Constraints	Convert verbal clues into algebraic or positional terms.	“A is to the left of B” → `pos(A) < pos(B)`
4. Apply “Direct Placement”	If a clue pins a person to a specific slot (e.g., “C sits in the 3rd position”), place them immediately.
5. Use “Relative Placement”	For clues involving distances (e.g., “D is two seats to the right of E”), calculate possible positions.
6. Eliminate Impossible Positions	Remove slots that violate any clue.
7. Employ “Chain Reasoning”	Combine several clues to find indirect relationships.
8. Back‑track if Needed	If a contradiction appears, reconsider earlier placements.
9. Double‑Check All Clues	Ensure every clue is satisfied in your final arrangement.
10. Keep a “Clue‑Checklist”	Tick off clues as you satisfy them to avoid missing any.

Common Terminology

Term	Meaning
Left of / Right of	Immediate neighbor or any seat to the left/right.
Between	Person X sits somewhere between Y and Z (not necessarily adjacent).
Opposite	In circular seating, directly across from another seat.
Seat Count	Number of seats between two persons.
Order	Sequence from left to right (or clockwise).

3. Worked Example

Problem Statement

There are 6 people – A, B, C, D, E, and F – seated in a single row.

A sits immediately to the left of B.

C sits somewhere to the right of D.

E sits between A and C.

F is not at either end.

D sits two seats to the right of F.

B sits third from the left.

Find the seating order from left to right.

Step‑by‑Step Solution

Step	Action	Reasoning
1. Draw 6 slots	`1 2 3 4 5 6`	Straight line, positions 1–6.
2. Apply clue 6	B is the 3rd from the left → `pos(B)=3`.	Direct placement.
3. Apply clue 1	A immediately left of B → `pos(A)=2`.	A sits at slot 2.
4. Apply clue 5	D is two seats right of F.	Let `pos(F)=x`. Then `pos(D)=x+2`.
5. Apply clue 4	F not at ends → `pos(F)` cannot be 1 or 6.	So `x ∈ {2,3,4,5}`.
6. Combine with clue 5	Since `pos(D)=x+2`, D must be ≤6.	`x+2 ≤ 6` → `x ≤ 4`.
7. Combine with clue 5 & 4	Possible (F,D) pairs: (2,4), (3,5).	(4,6) would place F at 4, D at 6 (allowed), but D cannot be 6? Actually D can be 6. Wait check: F cannot be 6 so (4,6) is possible. Let's list all: x=2→D=4, x=3→D=5, x=4→D=6. All satisfy constraints.
8. Use clue 3	E sits between A (slot 2) and C.	So C must be to the right of E, and E must be somewhere between 2 and C.
9. Place C	C must be to the right of D (clue 2).	D’s position depends on choice.
10. Test each (F,D) pair
- Case 1: `pos(F)=2`, `pos(D)=4`	But slot 2 already has A → impossible.
- Case 2: `pos(F)=3`, `pos(D)=5`	Slot 3 already has B → impossible.
- Case 3: `pos(F)=4`, `pos(D)=6`	Slot 4 empty, slot 6 empty → feasible.
11. Place F and D	`pos(F)=4`, `pos(D)=6`.
12. Place C	C must be to the right of D → impossible because D is at the end. Wrong reading