Advanced Study Notes – Reasoning Ability (Puzzles)
Prepared for the Nagaland Patwari / Lekhpal Examination
MIT‑Level Treatment – From First Principles to Edge‑Case Analysis
1. Introduction
Puzzles are a cornerstone of the Reasoning Ability section. They test:
| Skill | Example |
|---|---|
| Deductive reasoning | “If A is true, then B is false.” |
| Pattern recognition | “What comes next in the sequence 2, 4, 8, 16, …?” |
| Combinatorics & counting | “How many seating arrangements satisfy the constraints?” |
| Graph theory & CSP (Constraint Satisfaction Problems) | “Can the given graph be colored with 3 colors?” |
These notes give a rigorous, university‑level view of puzzles, starting from the fundamentals of logic and combinatorics, then exploring advanced theory (NP‑completeness, graph coloring, CSPs), and finally presenting edge‑case handling and a challenging sample problem with full solution.
Tip: In the exam you rarely have time for exhaustive proofs. Use the theory to guide your intuition, then check your answer carefully.
2. Types of Puzzles and Their Formal Models
| Puzzle type | Formal model |