The lie of the land: The Wknd Puzzle by Dilip D’Souza

Two tribes, two traditions, two replies. Your escape route depends on how well you can tell the truthers from the liars. Can you figure it all out with just one question?

Maybe you’ve heard of the mythical island populated with only two tribes: one that lies all the time and the other that compulsively tells the truth. This spot is an old staple of logic puzzles, which come in plenty of variations.

(Shutterstock)

In general, it goes like this: You’ve somehow parachuted onto this island and are wandering about, trying to figure out how to get off it. You are only allowed to ask one resident one question, and must choose your road based on her answer.

You come to a fork in the road. Previous visitors have told you that one of the forks leads to the airport and a helicopter that’s waiting to take you home. But the other fork leads straight to an alligator pit, where you’ll be eaten alive before you can think of turning away.

So it’s pretty important to take the correct road. Only, you have no idea which that is. Reading a newspaper at the fork is a resident of the island. You don’t know which tribe she’s from. And there’s a complication. Previous visitors have also told you that these residents answer questions from strangers with either of two phrases and nothing else: “Baar baar dekho” and “jaaneman jaaneman”. One means “yes” in the local lingo, the other means “no”, but you have no idea which means which.

Can you come up with just one question to ask the woman that will set you on the path to the helicopter and safety?

Hint: For the purpose of working this out, pick one road and assume it leads to safety. Also, think about whether you really need to know which phrase means what. In other words, how would you eliminate the need to know their meanings? One way to do that is to incorporate one of the phrases into your question.

Scroll down for the solution.

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Solution:

There are different questions you can ask. Here’s one: “If I ask someone from the other tribe if the left fork leads to the airport, will she answer with ‘baar baar dekho’?”

I’ll work through one of the possibilities here. Suppose the left road does lead to the airport, and suppose the woman reading her newspaper is a truther.

She knows that a liar will want to answer “no” to your question. If “baar baar dekho” means “yes”, the truther will say “jaaneman jaaneman” to indicate that the liar won’t want to say “yes”. But if “baar baar dekho” means “no”, the truther will still say “jaaneman jaaneman” (“yes”) to indicate that the liar will want to say “no”.

Work through the other three possibilities and you’ll see that the question leaves you with this much: If the woman answers you with “jaaneman jaaneman”, take the left fork. If she says “baar baar dekho”, take the right. Have a safe flight home!