Logic/probability riddle

Question

The Island of Zombies: On a certain island, some of the residents have been turned into zombies, but they act just like normal people except that they only lie. The humans on the island only tell the truth. This sounds like a knight-knave situation, but the reality is more complicated: the islanders understand English, but they can only speak in their native tongue which has not yet been translated. When you ask them a yes or no question, they respond with “Gha” or “Jal.” One means yes, and the other no, but you don’t know which. You arrive on the island and are immediately captured. The leader of the Island points to a card written in English above his head. It says: “You may ask the leader any one question. If he answers “Gha” then you may visit the island peacefully, if he answers “Jal” then you will be transformed into a zombie and forced to live out your days on the island. What do you ask the leader, given that you don’t know whether he is a human or a zombie and given that you would prefer not to be a zombie? Explain your answer.

I started by thinking of asking, "is the meaning of 'gha' no?" In this case, the zombies would say "gha" which is good, but the humans would say "jal" which is what we don't want.

Answer 1

Are you human and 'Gha' means yes, or are you a zombie and 'Gha' means no?

We want our captor to say 'Gha'. If 'Gha' means yes and our captor is human, we want the answer to our question to be yes. If 'Gha' means no and our captor is human, we want the answer to be no. If 'Gha' means yes and our captor is a zombie, we want the answer to be no, because then the zombie will lie and say 'Gha', which means yes. If 'Gha' means no and our captor is a zombie, we want the answer to be yes, because the zombie will lie and say 'Gha.' The question "Are you human and 'Gha' means yes, or are you a zombie and 'Gha' means no?" will have the desired answer in each situation.

Answer 2

Would you have said Gha or Jal if I became like you?

• The human can only answer Gha because he tells the truth.
• The zombie can not answer answer Jal because he lies.

Answer 3

A standard template to deal with knights and knaves, is to ask this:

What would you say if I ask you [question]?

A knave would have to lie twice and therefore tell the truth -- i.e. he would lie about the [question] if you had asked him directly, so since you asked indirectly he would have to lie about the fact he would lie about [question]. This gets rid of all knight/knave issues.

(In a sense, it is sad such a template exists, coz now most knight/knave puzzles are not fun any more.)

It only remains what [question] should be. In the classic escape example, [question] would be "Is this the door to escape?" In your example, the [question] would be "Does Gha mean Yes?" The best thing about the template is that, since we got rid of the knight/knave issue, all you need to check is that a knight will answer Gha in both cases.

Credit: IIRC I read about the template from one of the logic puzzle books by Raymond Smullyan.