Seek the truth: The Wknd Puzzle by Dilip D’Souza
Purva has stumbled into that mythical land beloved of puzzle-setters everywhere, Trulia. You know, the country whose citizens are all either liars or truth-tellers. But not, of course, both.
One evening, she sits down to dinner with three silent Trulians: Edmond, Luboš and Yuji. Conversation is non-existent, until Purva asks: “Dudes, please tell me something about yourselves!” That perks up the trio.
Edmond says: “Exactly one of us is a liar.”
Luboš says: “Exactly two of us are liars.”
Yuji says: “Exactly three of us are liars.”
Question 1: Can you help Purva find out who’s lying?
Hint: Clearly only one of the three can be telling the truth.
Question 2: Replace “Exactly” with “At least” in all three cases. Can you help Purva find out who’s lying?
Hint: Let’s say Edmond is a liar. For “At least one of us is a liar” to be a lie, all three have to be telling the truth. Impossible. So Edmond is a truth-teller. Go on from there.
Bonus: What links those three names? (Not Purva).
Scroll down for the answers.
Answer 1: Edmond and Yuji are lying.
Answer 2: It’s impossible to tell who’s lying; the three statements are logically inconsistent.
Bonus: The first names of three men who have comets named after them: Edmond Halley, Luboš Kohoutek, Yuji Hyakutake.