I’d like to share a small but interesting puzzle from my new book Mental Mosaics: A Unique Collection of 200 Puzzles on Logic, Lies, and the Limitless. This puzzle is called “A Curious Greeting” and is taken from the chapter “Liar Liar,” the first chapter in the book.
A Curious Greeting
You’ve just stepped off the boat onto an island populated by people who either always tell the truth or always lie. The first person to greet you shakes your hand and says:
“I said this exact sentence yesterday and I’m saying it today; I’m one of the honest people on this island.” Can you tell if this person is a truth teller or a liar, and if so, how?
Hint: The island has two types of people. Would both types be able to say this sentence without contradiction?
Answer: This person is definitely a liar.
Explanation: When the person states, “I said this exact sentence yesterday,” the sentence includes that phrase itself, which means they are claiming they also said “I said this exact sentence yesterday” on the previous day. That implies they said this exact sentence the day before, and the day before that, and so on. There can never be a day on which they first made this statement, so it cannot be true.
