Puzzles
What you'll learn
- Identify truth-tellers and liars from their contradictory statements
- Build a grid and use elimination to solve logic puzzles
- Apply the process of elimination systematically
- Handle "alternator" characters who switch between truth and lies
Key concepts
Type 1 — Truth-Teller and Liar Puzzles
In these puzzles, people make statements. Truth-tellers always tell the truth; liars always lie. Your job is to figure out who is who.
Core principle:
- If a truth-teller says "A is a liar," then A IS a liar.
- If a liar says "A is a liar," then A is actually a truth-teller.
- Two truth-tellers will ALWAYS agree with each other.
- A truth-teller and a liar will ALWAYS disagree with each other.
Worked Example: A says: "B is a liar." B says: "A is a liar."
Both accuse each other — this is the classic setup. It means exactly one of them is a truth-teller and one is a liar. You cannot determine which without more information.
Worked Example 2 (with 3 people):
- A says: "B is a truth-teller."
- B says: "C is a liar."
- C says: "A is a liar."
Test Case: Assume A is a truth-teller.
- A's statement is true → B is a truth-teller.
- B's statement is true → C is a liar.
- C's statement is false (C is a liar) → A is NOT a liar → A IS a truth-teller. ✓ Consistent.
Test Case: Assume A is a liar.
- A's statement is false → B is a liar.
- B's statement is false → C is a truth-teller.
- C's statement is true → A IS a liar. ✓ Also consistent.
Lesson: Some puzzles have two valid solutions unless additional constraints are given. Always check both cases.
Type 2 — Grid-Based Logic Puzzles
You are given a set of people, attributes (color, job, pet, etc.) and clues. Build a grid where rows = people and columns = attributes.
Example setup: Four friends — Ananya, Rohan, Priya, Dev — each prefer a different sport: Cricket, Tennis, Badminton, Hockey.
Clues:
- Ananya does not play Cricket or Hockey.
- Rohan plays Tennis.
- Dev does not play Badminton.
Grid:
| Cricket | Tennis | Badminton | Hockey | |
|---|---|---|---|---|
| Ananya | ✗ | ? | ? | ✗ |
| Rohan | ✗ | ✓ | ✗ | ✗ |
| Priya | ? | ✗ | ? | ? |
| Dev | ? | ✗ | ✗ | ? |
From Rohan = Tennis → remove Tennis from all others. Ananya = not Cricket, not Hockey → Ananya = Badminton (only option left). Dev = not Badminton (now taken) → Dev = Cricket or Hockey. Priya gets whatever Dev doesn't. Dev ≠ Badminton (✗) → Dev = Cricket or Hockey → Since Ananya already took Badminton, Dev = Cricket or Hockey. No more constraints → try: Dev = Cricket, Priya = Hockey. ✓
Final: Ananya=Badminton, Rohan=Tennis, Dev=Cricket, Priya=Hockey.
Process of Elimination — 4 Rules
| Rule | How to apply |
|---|---|
| 1. Direct placement | If only one option is possible for a cell, confirm it. |
| 2. Unique in column | If an attribute belongs to only one person in the column, assign it. |
| 3. Unique in row | If a person has only one unassigned attribute, assign it. |
| 4. Pair exclusion | If two people can only have two attributes between them, no one else can have those. |
Never guess. Every cell you fill must be justified by at least one clue. If you're guessing, step back and re-read the clues.
Type 3 — Alternator Puzzles
An alternator tells the truth on odd-numbered statements and lies on even-numbered ones (or vice versa).
Strategy: Test both "truth first" and "lie first" for the alternator and see which is consistent with the other characters' statements.
Writing Out Reasoning
For complex puzzles, write each step as a sentence:
- "Rohan plays Tennis (from Clue 2)."
- "Since Rohan plays Tennis, he cannot play anything else — mark ✗ in all other sport cells for Rohan."
- "Since Tennis is taken, remove it from all other rows."
This prevents errors and makes your work checkable.
Quick check
- A says "I am a liar." Is this statement possible? What can you conclude?
- In a truth-teller/liar puzzle with 3 people, if all three say "I am a truth-teller," how many truth-tellers can there be?
- In a grid puzzle with 4 people and 4 colors, if you know 3 colors, how do you find the 4th?
- What does it mean when a liar says "X is honest"?
- Give one real-life situation where process-of-elimination logic is used.
Open the Practice tab for graded questions on Logical Puzzles.
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