# Lying guard

You are traveling in a land where every inhabitant either always lies or always tells the truth. You come across two caves: in one lies treasure and in the other lies certain death. There is a guard in front of the caves, and a sign announcing that the guard will answer one yes/no question to any traveler.

You don't know whether the guard tells the truth or lies - what single yes/no question should you ask the guard if you want to find the treasure? (Or try to show that it is impossible for you to determine which cave has the treasure.)

###### I thought of this independently, but presumably someone has come up with this problem before.

Note by Maggie Miller
4 years, 10 months ago

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is there more then one cave with treasure?

- 3 years, 9 months ago

"If I ask you whether the left cave has treasure, would you answer Yes?"

- 4 years, 9 months ago

That's what I was thinking! :)

- 4 years, 9 months ago

Choose a random route, and ask him : You people have two kinds of folks, liars and truthful. If I asked one of the other kind of people if this is the right way he would say yes. Am I right?

If it was the right way: Liar: No Truthful: No

if it was the wrong way: Both will say yes.

- 4 years, 10 months ago

Oh, I didn't think about just reducing it to two guards. That does the care of the problem, though.

- 4 years, 10 months ago

I don't really get what you mean by reducing it to two guards but yea I think this works out the problem. Took me a while though haha

- 4 years, 10 months ago

Well, there's a very famous problem where there are two guards: one who lies and one who tells the truth. The strategy there is to ask one guard what the other would say if asked if the left cave had treasure - which is essentially your answer here

- 4 years, 10 months ago