Reasoning Ability – Puzzles
For the Jharkhand Police Sub‑Inspector (SI) Examination
Objective – To provide a concise, exam‑oriented guide to solving puzzles that appear in reasoning tests.
Target – Competitive exam takers (IIT‑JEE level rigor, but adapted to Police‑SI syllabus).
Structure –
- Types of puzzles & key strategies
- Formal logic notation & useful formulae
- Problem‑solving framework
- Common pitfalls & tricks
- Sample puzzles with full solutions
- A hard practice question (with answer)
Tip – For every puzzle, aim to translate the text into a set of logical statements.
Then use a table/grid or pattern‑mapping to deduce the only possible arrangement that satisfies all constraints.
1. Types of Puzzles in Reasoning Ability
| Category | Typical Features | Common Constraints |
|---|---|---|
| Number Puzzles | Sequences, sums, differences, ratios | Arithmetic/Geometric patterns, hidden “magic” numbers |
| Word/Letter Puzzles | Anagrams, word ladders, letter‑substitution | Letter positions, semantic clues |
| Spatial/Seat‑Arrangement | People/objects placed in rows/columns | Relative positions (“to the left of”, “next to”) |
| Logical‑Deduction (Grid) Puzzles | Multiple entities with attributes | Exclusive & inclusive relationships |
| Pattern‑Recognition | Shapes, colors, numbers | Symmetry, repetition, transformation |
| Cryptograms / Binary Puzzles | Binary sequences, true/false statements | Logical connectives, parity |
Every puzzle falls into one of these categories. Mastering each type gives you a toolbox for any question.
2. Logical Connectives & Formal Notation
| English | Symbol | Example |
|---|---|---|
| NOT | ¬ | “Not A” → ¬A |
| AND | ∧ | “A and B” → A ∧ B |
| OR | ∨ | “A or B” → A ∨ B |
| IF … THEN | → | “If A then B” → A → B |
| IF AND ONLY IF | ↔ | “A iff B” → A ↔ B |
| XOR (exclusive‑or) | ⊕ | “Either A or B, but not both” → A ⊕ B |
Useful Logical Equivalences
| Rule | Symbolic Form | Practical Usage |
|---|---|---|
| Contrapositive | (A → B) ≡ (¬B → ¬A) | Flip direction when “not B” is given |
| De Morgan | ¬(A ∧ B) ≡ ¬A ∨ ¬B | Convert “not both” to “either not” |
| Distributive | A ∧ (B ∨ C) ≡ (A∧B) ∨ (A∧C) | Break down compound statements |
| Double Negation | ¬¬A ≡ A | Remove redundant “not” |
Converting a textual clue into these symbols eliminates ambiguity and makes deduction systematic.
3. Problem‑Solving Framework
- Read Carefully & Highlight Facts