Puzzles: Reasoning Ability Notes for Bihar PSC

📚 Bihar PSC – Reasoning Ability

Topic: Puzzles

Puzzles are a staple of the Reasoning Ability section.
They test pattern recognition, logical deduction, and quick mental math.
These notes give you a quick, clear framework to tackle every puzzle type.

📌 1. Simple Explanation

A puzzle is a problem presented in a narrative or visual form that requires you to find the correct arrangement, order, or answer by applying logic, deduction, or simple calculation.
Typical formats:

Format	Example	Key Skill
Number pattern	2, 4, 8, 16, …	Recognise arithmetic/geometric progression
Word/letter pattern	CAT – DOG – ?	Identify word/letter relationships
Spatial/arrangement	5 people seated around a table with constraints	Use elimination & positional logic
Riddle/logic	“I speak without a mouth …”	Deductive reasoning

🗝️ 2. Key Points & Techniques

#	Technique	What to Look For	Why It Helps
1	Identify the question type	Is it a sequencing, placement, or “who/what” question?	Guides the strategy (e.g., “place” puzzles need positional logic).
2	Write down all constraints	List every given fact (e.g., “A is not next to B”).	Keeps track of what’s fixed and what’s variable.
3	Create a grid or table	For placement puzzles: rows = positions, columns = attributes.	Visualizes possibilities & eliminated options.
4	Look for “unique” clues	Any statement that singles something out (e.g., “Only one person is older than X”).	Gives a starting point.
5	Use process of elimination	Cross out impossible options.	Reduces the search space.
6	Check for “order” clues	“X is before Y”, “Z is the third.”	Helps place items in a linear sequence.
7	Spot patterns in numbers	Arithmetic progression, powers, sums, differences.	Speeds up numeric puzzles.
8	Test your hypothesis	After placing something, check if all constraints remain satisfied.	Avoids contradictions early.
9	Work backwards	Start from the answer and trace back.	Useful when forward deduction stalls.
10	Keep the time	Aim for 1–2 min per puzzle.	Time‑management is key in PSC.

🧩 3. Worked Example

Puzzle (Placement type)

There are 5 people – A, B, C, D, E – seated in a row facing north. They are standing in order of their ages from youngest to oldest. The following constraints are given:

B is older than C.

A is not adjacent to B.

C is next to E.

D is older than A.

The oldest person is sitting at the far right.
Determine the seating order from left to right.

Step‑by‑Step Solution

Step	Action	Reason
1	List all ages (1 = youngest, 5 = oldest).	Ages are distinct and sequential.
2	Place the oldest (5) at the far right.	Constraint 5.
3	Position C next to E	C & E must be adjacent.
4	Place B older than C → B cannot be 1.	From constraint 1.
5	Place D older than A → D cannot be 1 or 2 if A is 1.	From constraint 4.
6	Check adjacency of A & B – A cannot be next to B.	Constraint 2.
7	Trial placement: Assume C is at seat 2, E at seat 3.	C & E adjacent.
8	Assign ages:

Seat 5 (far right): age 5 (oldest).

Seat 2 (C): age 2 (must be younger than B).

Seat 3 (E): age 3 (older than C). | Fits all constraints. | | 9 | Place B: B must be older than C (age >2) and not next to A.
Try B at seat 4 (age 4). | Seat 4 is not adjacent to seat 1 (where A will be). | |10 | Place A: remaining seat 1, age 1. | Age 1 is youngest. | |11 | Place D: remaining seat 5, age 5. | D older than A satisfied. | |12 | Verify all constraints:
• B (age 4) > C (age 2). ✔️
• A (seat1) not adjacent to B (seat4). ✔️
• C (seat2) next to E (seat3). ✔️
• D (age5) > A (age1). ✔️
• Oldest at far right. ✔️ | All satisfied. |

Final seating order (left to right)
A (age 1) – C (age 2) – E (age 3) – B (age 4) – D (age 5)

Quick Recap of Why It Worked

Fixed anchors (oldest at far right, adjacency of C & E) reduce possibilities.
Process of elimination (age restrictions for B & D) further prunes options.
Trial & check ensures no contradiction.

📌 4. Quick Revision Summary

Item	What to Remember