# Is this a correct solution to determining which of two people is the liar using one question?

I was working my way through some Propositional Logic Questions in Discrete Maths by Rosen, when I came across the following question:

An explorer is captured by a group of cannibals. There are two types of cannibals—those who always tell the truth and those who always lie. The cannibals will barbecue the explorer unless he can determine whether a particular cannibal always lies or always tells the truth. He is allowed to ask the cannibal exactly one question.

Find a question that the explorer can use to determine whether the cannibal always lies or always tells the truth.

My Solution:

If I were to ask you whether you are a liar, would you answer "yes"?
- The honest person would say NO
- The liar would say YES (due to double negation)

Doubt:

Am I correct in saying my answer will work? It almost seems too simple

• There are interesting variants of this according to whether you define 'liar' as someone who always makes statements that are the exact opposite of the truth, or someone who always tries to mislead you, or something else. Martin Gardner has written some very interesting stuff on this, but I'm afraid I don't have a link for it (I read it in one of his books). Commented Dec 23, 2014 at 23:11

That works :)

For the question you are looking at, you must only determine if he is a liar or not, so as stated in your comment, objective questions such as "Is the Earth round?" are simple solutions.

Other similar riddles that you may come across, like the two paths problem, or the two guards, you must use double negatives, or have both people use a negative (ie. have the truth teller and liar lie). The reason being you need to figure out in one question if they are a liar or not and the solution to another question.

I can give an example if you want, or you can check out the two guards problem and give it a shot :)

Also, welcome to the Puzzling Beta!

• Hi , FreakyDan -- would an objective question like : Is the earth round ? -- also be enough . And thanks a bunch :) Commented Dec 23, 2014 at 15:59
• @pranav In this case yes, as you must only identify them. Good catch, I didn't think about that. Will edit answer to reflect. Commented Dec 23, 2014 at 16:04
• The other common strategy is to ask one something about what the other would answer to avoid the direct meta question. Commented Dec 24, 2014 at 0:03
• @FreakyDan Ofcourse being cannibals and all they might not know that the earth is round ;) Commented Dec 24, 2014 at 9:34