Reasoning Ability – Puzzles
Program: Mizoram Police Constable
Topic: Puzzles (Logic, Pattern & Arrangement)
Purpose:
Puzzles test the ability to understand a set of constraints, use logical deduction, and arrive at a unique solution. Mastering puzzles improves critical thinking, attention to detail, and speed – all essential for police work.
1. Simple Explanation
| Puzzle Type | What It Looks Like | Typical Goal |
|---|---|---|
| Seating/Arrangement | A row of seats/rooms/boats, each with attributes (color, nationality, etc.) | Find the order or who sits where. |
| Pattern/Sequence | Numbers/letters that follow a rule (e.g., +2, –3, +4…) | Identify the next element or the rule. |
| Sudoku‑style | 9×9 grid with numbers 1–9 | Fill the grid respecting row/column/box constraints. |
| Word/Letter | Sentences with missing letters/words | Determine the missing part from clues. |
| Logical Deduction | A set of statements (e.g., “If A then B”) | Determine the truth value or a specific outcome. |
All puzzles share a common structure:
- Read the problem carefully – ignore irrelevant words.
- List all given facts (constraints).
- Identify unknowns you need to figure out.
- Apply constraints one by one (eliminate, infer, cross‑check).
- Verify consistency – the final arrangement must satisfy all clues.
2. Key Points for Solving Puzzles
| Step | Tip | Example |
|---|---|---|
| 1. Read Twice | First read for a rough idea, second for hidden constraints. | “The third person drinks tea” – note the position. |
| 2. Create a Table or Grid | Organize data visually. | Rows = positions, columns = attributes. |
| 3. Use Elimination | Remove impossible options. | If “A does not own a dog” → cross‑out dog for A. |
| 4. Apply “If … then …” Rules | Chain deductions. | If B is third, then C cannot be third. |
| 5. Look for “Only One” Constraints | Helps lock in a single choice. | Only one person drinks coffee. |
| 6. Cross‑Check | After filling a value, revisit all clues to ensure no conflict. | If we place “red” at seat 2, check all colour clues. |
| 7. Keep a Working Hypothesis | When stuck, assume a possibility, test it, and backtrack if needed. | Assume “X drinks water” → see if it breaks any rule. |
| 8. Time Management | Allocate 1–2 minutes for each puzzle. | 30 puzzles → 60–90 min → 2–3 min/puzzle average. |
3. Worked Example – “The Five Houses” (Zebra‑Style)
Puzzle Statement
Five houses are painted red, green, yellow, blue, and white (from left to right).
The owners are English, Spanish, Italian, German, and Norwegian.
Drinks are tea, coffee, milk, juice, and water.
Pets are dog, cat, bird, fish, and horse.
No two adjacent houses share the same pet, drink, or owner nationality.
The English owner lives in the red house.
The Spanish owner drinks coffee.
The Italian owns a dog.
The German drinks milk.
The Norwegian lives in the first house.
The green house is immediately to the right of the white house.
Who owns the fish?
(Answer: German – we will show the reasoning.)
Step 1: Create the Grid
| Position | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Colour | |||||
| Nationality | |||||
| Drink | |||||
| Pet |
Step 2: Place Fixed Information
| Clue | Action |
|---|---|
| “Norwegian lives in the first house.” | Position 1 = Norwegian |
| “English lives in the red house.” | Red house somewhere |
| “Green house is immediately right of White house.” | White at 1‑4, Green at 2‑5 |
| “German drinks milk.” | German → Milk |
| “Spanish drinks coffee.” | Spanish → Coffee |
| “Italian owns dog.” | Italian → Dog |
| “No two adjacent houses share same pet, drink, or nationality.” | Important for elimination |
Step 3: Deduce Positions
- White & Green: If White is at 4 → Green at 5.
→ Leaves 1–3 for other colours. - **