logic problem

[dr432]

there are two hamburgers. one is poisoned. there are two guards in front of them. they both know which had been poisoned, but one of the guards (you don't know which) is a liar and always lies, the other always tells the truth. you can ask only one of the guards a single question.

 

what question can you ask to know for certain which hamburger is poisoned?

Edited August 7, 2009 by dr432

[DJBruce]

Ask one of the guards which hamburger will the other guard tell me to pick. If you ask the liar he will tell you the poison hamburger as he is lying. If you ask the truthful one the liar will pick he will tell you the truth and show you the poison hamburger. So ask that question then pick the opposite hamburger.

[dr432]

yep, that's correct. also, my psychic powers tell me you live in michigan.

[iNow]

So ask that question then pick the opposite hamburger.

But the OP states there is only one hamburger. Was the OP misworded, since he confirmed you were correct in your response? Should there have been two burgers?

[dr432]

ok the original problem was with two doors and for some reason i decided to misword it to be one hamburger

 

ok here i'll reword it so that bruce's solution fits.

[DJBruce]

But the OP states there is only one hamburger. Was the OP misworded, since he confirmed you were correct in your response? Should there have been two burgers?

 

I am not sure normally puzzles similar to this has two choices: heaven or hell, life or death, path of enlightenment or path of darkness, etc, but I don't think it matters all that much. If you rephrase the question, would the other guard say the hamburger is poisoned? I think you get the same results.

 

If the hamburger is poisoned and you ask the liar knows the truth-teller will say yes and therefore says no, if you ask the truth-teller he knows the liar will lie and say no so he tells you no.

 

If the hamburger is not poisoned and you ask the liar he knows the truth-teller will say no and therefore says yes, if you ask the truth-teller he knows the liar will lie and so says yes.

 

So by asking that question then and then only eating the burger if you are answered yes you should be safe. I hope that makes sense I could not think of how to make a truth table for it.

[D H]

Ask one of the guards which hamburger will the other guard tell me to pick.

There's only one hamburger, but you are on the right track.

 

Edit

dr432, he didn't answer your original question!

[dr432]

no he did get ther right answer, just look... ok cause i changed the question kind of before he answered it, but it doesn't matter: either "which hamburger is poisoned" or "is the hamburger poisoned" because asking "which hamburger is poisoned" is the same as asking "is the hamburger on the left side poisoned" you know?

 

in any way both guards are involved so it has to be a lie whoever you ask...

[D H]

If you rephrase the question, would the other guard say the hamburger is poisoned?

That is the question.

 

So by asking that question then and then only eating the burger if you are answered yes you should be safe. I hope that makes sense I could not think of how to make a truth table for it.

 

 

There are four cases: The hamburger is poisoned or safe to eat; you ask the liar or truth teller.

 

1. Poison, liar. The other guard tells the truth: the hamburger is poisoned. The one you asked will say it is safe.

 

2. Poison, truth teller. The other guard will lie, saying the hamburger is safe. The one you asked will report this honestly (safe).

 

3. Safe, liar. The other guard will say it is safe. The one you asked will say it is poisoned.

 

4. Safe, truth teller. The other guard will say it is poisoned. The one you asked will say it is poisoned.

 

So, ask a guard whether the other guard will say the hamburger is safe or poisoned. Eat the hamburger if the answer is poisoned. Do not touch it if the answer is safe.