Truth and Lie Puzzles in Reasoning: Who Is Telling the Truth Questions with Solved Examples for SSC

In truth and lie puzzles, some persons make statements about each other, and you find who tells the truth and who lies. You solve them with one method: assume one statement is true and check whether all the other statements agree. These truth and lie puzzle tricks for SSC give the rules, the method and solved examples.

Rules

• A truth-teller always speaks the truth, and a liar always speaks a false sentence.
• If a statement is true, its opposite is false, and the other way round.
• If two statements directly contradict each other, at most one of them can be true.
• If the puzzle says "exactly one is lying", the others are all truthful.

Method: Assume and Check

1. Pick one person and assume that he speaks the truth.
2. Use his statement to decide about the others.
3. Check all the other statements. If any statement is against the assumption, the assumption is wrong.
4. Try the opposite assumption (the person is lying) and check again.
5. The case with no contradiction is the answer.

Solved Examples

Example 1. A says, "B is lying." B says, "C is lying." C says, "A and B are both lying." Who tells the truth?
Assume A is truthful: then B is lying, so C is truthful (B’s statement is false). But C says that A is lying, which is against the assumption. Not possible.
Assume B is truthful: then C is lying. A says B is lying, which is false, so A is lying. C says "A and B both lie", which is false because B is truthful, so C is lying. All is consistent. Only B tells the truth.

Example 2. Three friends P, Q and R say: P: "Q is lying." Q: "R is lying." R: "P is telling the truth." Exactly one of them is lying. Who is lying?
If P is lying: Q is truthful, so R is lying. That makes two liars. Not possible.
If R is lying: Q is truthful, and P’s statement "Q is lying" is false, so P is lying too. Two liars. Not possible.
If Q is lying: P is truthful (his statement is true) and R is truthful (Q’s statement is false), and R says P is truthful, which is true. Only one liar. Q is lying.

Example 3. A says, "B is lying." B says, "A is lying." How many are truthful?
If A is truthful, B is lying (and B’s statement is false, which is consistent). If A is lying, B is truthful. In both cases exactly one of them is truthful. Who it is cannot be found.

Example 4. One person always tells the truth and another always lies. Both are asked, "Are you a truth-teller?" What do they say?
Both say "Yes". This is a famous trick.

Tips

• Start with the person whose statement has the most details.
• A person who says "I always lie" is impossible, because it is a paradox.
• Write T for truth and L for lie next to each name while you check.

Quick Tips

• Assume one case and check all the statements.
• If you meet a contradiction, the assumption is wrong.
• Use "exactly one" or "only one" in the question to cut the cases.
• Write T and L next to the names.

Quick Revision Points

• A truth-teller always tells the truth.
• A liar always makes a false statement.
• Two contradictory statements cannot both be true.
• Assume and check is the key method.
• Both a truth-teller and a liar say "Yes" to "Are you a truth-teller?".

Practice Questions With Answers

1. What does a liar answer to "Are you a truth-teller?"
   Answer: Yes
2. What does a truth-teller answer to "Are you a truth-teller?"
   Answer: Yes
3. A says "B is lying" and B says "A is lying". How many are truthful?
   Answer: Exactly one
4. A: "B is lying." B: "C is lying." C: "A and B are both lying." Who tells the truth?
   Answer: B
5. P: "Q is lying." Q: "R is lying." R: "P is telling the truth." Exactly one is lying. Who?
   Answer: Q
6. Can a person say "I always lie" and be a liar who always lies?
   Answer: No, it is a paradox
7. If two statements contradict each other, how many can be true?
   Answer: At most one
8. Can both "A is guilty" and "A is not guilty" be false?
   Answer: No, exactly one of them is true
9. What is the first step in the assume and check method?
   Answer: Assume that one statement is true
10. What do you do if you find a contradiction?
    Answer: The assumption is wrong, so try the opposite case

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Logical Reasoning notes page, read the previous topic Passage Reasoning and the next topic Logical Reasoning Syllabus and Tricks. Also read the Reasoning notes. Also read Puzzle Reasoning.

Frequently Asked Questions

What are truth and lie puzzles?

They are puzzles in which people make statements about each other, and you find who is truthful and who is lying.

What is the best method to solve them?

Assume one statement is true and check all the other statements.

What if two statements contradict each other?

At most one of them can be true.

What does a liar say if asked "Are you a liar?"

A liar says "No", since the truth is "Yes".

What does "exactly one is lying" mean?

It means all the others are telling the truth.

Can a person truthfully say "I am lying"?

No, it is a paradox.

What if the assumption gives a contradiction?

The assumption is wrong, so try the opposite one.

Is this topic asked in SSC exams?

It appears in some SSC and other reasoning papers as a type of puzzle.

How much time should I take?

About 60 to 90 seconds.

What are the common mistakes?

Not checking all the statements and stopping at the first consistent case.

How can I practise?

Make puzzles with 3 friends and solve them with the assume and check method.

Is a truth and lie puzzle the same as a normal puzzle?

It is a special kind of puzzle that uses the truth values of the statements.