Seating arrangement: Reasoning Ability Notes for Andhra Pradesh Police Constable

Seating Arrangement – Reasoning Ability

For the Andhra Pradesh Police Constable Examination

Purpose of this section
Seating‑arrangement problems test your ability to interpret constraints, visualize relative positions, and deduce a unique arrangement. They often involve a small set of people (or objects) and a handful of conditions such as “next to”, “between”, “to the left of”, etc.

1. Simple Explanation

Identify the entities – People, seats, objects.
List all constraints – Write them as short statements.
Choose a reference point – Usually the leftmost seat or the person who appears most often in the constraints.
Place entities one by one – Start with the most restrictive constraints.
Check consistency – After each placement, verify that all constraints still hold.
Iterate – If a conflict arises, backtrack and try a different arrangement.

Tip: Always work left‑to‑right or top‑to‑bottom unless a constraint forces a reverse order.

2. Key Points & Strategies

Category	What to Look For	How to Use
Relative Position	“next to”, “next to on the left/right”, “between”, “at least 2 seats apart”	Convert to a distance or adjacency rule.
Absolute Position	“seated in the 3rd seat”, “first seat from the left”, “at the end”	These fix a person’s location immediately.
Order Constraints	“A is to the left of B”, “C is somewhere after D”	Use directional arrows (→ or ←) to track order.
Group Constraints	“E and F are together”, “G is not next to H”	Treat the group as a single block or note the forbidden adjacency.
Multiple Constraints	When a person appears in several rules	Combine them: e.g., if A is left of B and also next to C, then C must be between A and B or before A.
Logical Deduction	“Only one seat between X and Y”	Count seats: if total seats = 7, then X‑Y distance = 3.
Elimination	If a placement violates any rule, discard it.	Keep a “candidate list” for each seat.

Common Mistakes

Assuming “between” means directly adjacent – It means somewhere between, not necessarily next to.
Ignoring the direction of “left/right” – In a circular arrangement, “left” can be ambiguous; always clarify.
Mixing up “next to” and “separated by” – Next to means 0 seats in between; separated by 1 seat means 1 seat in between.
Forgetting that constraints can be transitive – If A next to B and B next to C, then A may be next to C (if seats are only 3).

3. Worked Example

Problem
There are 7 officers seated in a row: A, B, C, D, E, F, G.
Constraints:

A sits somewhere to the left of B.
C sits next to D.
E sits between A and B.
F sits at the third seat from the left.
G does not sit next to C.

Goal: Determine the exact order from left to right.

Step‑by‑Step Solution

Step	Action	Reasoning
1	Place F	Constraint 4 gives a fixed position.
2	Use “C next to D”	Treat (C,D) as a block (order unknown).
3	Place A left of B, E between them	So the order must be A – E – B (E is exactly between them).
4	Combine blocks	We have three blocks: A‑E‑B (size 3), C‑D (size 2), and F (size 1). Total seats = 3+2+1 = 6 > 7? Wait, we forgot G. G occupies 1 seat. So we need to fit all 7 seats.
5	Decide placement of blocks around F	Since F is fixed at seat 3, we place the blocks left and right of F.
6	Try placing A‑E‑B at seats 1‑3	That would put B at seat 3, conflicting with F. Reject.
7	Place A‑E‑B at seats 1‑3? No.	Next try seats 2‑4: A=2, E=3, B=4 → F would be at seat 3 but occupied by E. Reject.
8	Place A‑E‑B at seats 3‑5: but seat 3 is F → reject.
9	Place A‑E‑B at seats 4‑6: A=4, E=5, B=6 → works.	F is 3, fine.
10	Place C‑D block at remaining seats 1‑2 or 7‑8?	Only seats left: 1,2,7. Need 2 consecutive seats. Options: 1‑2 or 7‑? Can't use 7‑? because 8 doesn't exist. So place C‑D at seats 1‑2.
11	Place G at the remaining seat 7	Check constraint