Truth-tellers and liars
✓ With solution
In a village where everyone always tells the truth or always lies, you hear just three sentences. Who is the liar?
In a strange village, everyone is either a truth-teller who always tells the truth, or a liar who lies every time. You meet three villagers: Samer, Rana and Jood. Samer says: "Rana is a liar." Rana says: "Exactly one of the three of us is a liar." Jood says: "Samer and Rana are not the same kind: one tells the truth and the other lies."
Who is lying?
- AOnly Samer
- BOnly Rana
- COnly Jood
- DSamer and Jood
Show the answer
Answer: A) Only Samer. Start with Jood. If Samer tells the truth, Rana is a liar as he says; if Samer lies, Rana tells the truth. Either way Samer and Rana are different kinds, so Jood's sentence is always true and Jood is a truth-teller. Now there is exactly one liar between Samer and Rana, and Jood is honest, so there is exactly one liar among the three. That is what Rana said, so Rana tells the truth. And since Rana is honest, Samer lied when he called her a liar. Only Samer is lying. The trap is believing the first thing you hear.
Never miss a puzzle
Subscribe to Khamantiq on YouTube and turn on the bell to get new puzzles first.