Monday, December 3, 2007

The liar, the witch & the truthteller

The unique town you came for an interview has all either liars or truthtellers , who seems to know each other. The Interviewer told you one more bizaare fact about the town that if a strangers asks more than one question in this town he is killed. He also tells you that, there are some wicked witches who sells poisonous food in town.

While coming back you were hungry and stopped in a food booth but you cannot make sure if the old lady sitting there is a witch or not ?
What will you do ?

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52 Comments:

Anonymous Joe in Hawaii said...

I'm not too sure how this works out, but I like the way it sounds. I would ask this question. "Is there another store in this town that sells poisonous food like you do?" This implies that the store already sells poisonous food. As a fact, there are definitely other stores that sell poisonous food. A liar would say no, there are no other stores, and they would also have to clarify whether or not they have poisonous food. If the liar says they do sell poisonous food, then they don't, and vice versa. If the town is full of truth tellers, the store owner will say yes, there are other stores in the town. And likewise, they'll say whether or not they sell poisonous food.

Full Scenario

You: "Are there other stores that sell poisonous food like this store?"

Liar 1:"No there are no other stores, nor do we sell poisonous food." (sells poison)

Liar 2:"No there are no other stores, but we do sell poisonous food." (feast)

Truth 1:"Yes, but we do not sell poisonous food."

Truth 2:"Yes, and we do sell poisonous food."

Makes sense to me. What do you think?

December 3, 2007 4:22 AM  
Anonymous HWDIV said...

ask her if she is one of those wicked witches. They only lie if you ask more than 1 question.

December 3, 2007 8:46 AM  
Anonymous GreenDrakeWeboen said...

I think HWDIV is misunderstanding the problem. The inhabitants of this town either are liars or truth tellers. Both exist in this town, not one or the other. I'm still trying to figure out the solution, but hopfuly this will help.

December 3, 2007 11:54 AM  
Anonymous Joseph V. said...

Say to her, I know you are either a liar or a truthteller. If I were to ask someone else in town who is the opposite of you in that regard whether you are a witch, what would they say?

If she responds they would say I'm a witch, then her food is safe to eat. If she responds they would say I'm not a witch, then don't eat her food.

Either the other person would be lying about her truthful self, or she would be lying about what the other truthful person would be saying. In either case you get a lie, so you do the opposite of it.

December 3, 2007 11:57 AM  
Blogger Jeff said...

Wait for someone to come around who lives in the town and tell them to ask the questions. Or make freinds with the old lady, so you are no longer a stranger, then ask her the questions.

December 3, 2007 2:10 PM  
Anonymous Joe in Hawaii said...

Green and Joe...

I don't think that BOTH exist in the town. The problem states that they are ALL either truthtellers or liars. That means it's only one, or the other. There would be no other person in a town opposite to another in that regard.

December 3, 2007 2:10 PM  
Anonymous Joe in Hawaii said...

The way you would have to solve this is to figure out the two facts with the one question. Is the town full of either truth tellers or liars. (The question does state that it is one or the other. Both would not be found in the town.) Then you'd have to find out if they are witches or not. You can reword my original scenario to say, "...are there any other witches in town like you," but i still think my original scenario covers all the angles, using just the one question allowed per person asked. Unless someone can come up with a better question, I think i already solved it.

December 3, 2007 2:21 PM  
Anonymous Joe in Hawaii said...

I just reread the question, and realized you can only ask one question in the town, and not the one question per person as i originally thought. this sucks really, because if the store does happen to be owned by a witch, then you're screwed, because you wouldn't be able to go to another store and ask another question. HMMMM....i'm hoping this is just a misunderstanding of the wording, otherwise, good luck to whoever can figure that out.

December 3, 2007 2:27 PM  
Anonymous Anonymous said...

you only asked one hypothetical question, which was, "If I were to ask someone else in town who is the opposite of you in that regard whether you are a witch, what would they say?" You don't have to actually ask someone else.

The only real problem with your solution, is if I were the store keeper, I would say, then you would be dead for asking more than one question.

December 3, 2007 2:53 PM  
Anonymous Anonymous said...

My question is if the person that told you if a stranger asked more than one question he was killed and that there are wicked witches that sell poison is a citizen of the town. If he was, he might be a liar, and therefore you could be ask as many questions as you want and not worry about poison.

December 3, 2007 4:05 PM  
Blogger phil said...

Well how bout asking them a question like a math question as in 2+2. the liars would tell some other number and the truth people would say 4 and then you would see on the last people preferably 2 the questions that the first post has. if i'm wrong then correct me please, i don't like to be wrong or yelled at for being wrong.

December 3, 2007 9:34 PM  
Anonymous Anonymous said...

As a member of the town, everything the interviewer says is either a lie or the truth. If he's telling the truth about the witches and poison, then it means everyone else in town must also tell the truth. If he's lying about the witches and poison, then it means that everyone in town is a liar, but that there are no witches or poisoned food.

Simply ask anyone "Where can I find unpoisoned food?"

It it's a truthfull town, they will tell you a good place to eat. If it's a lying town, then there are no witches or poison, but they will tell you that all the food is poisoned. In that case, you can eat wherever you want.

I'm assuming that the statement "all either liars or truthtellers" is true no matter what, since it doesn't say that you got that information directly from the interviewer.

December 3, 2007 11:28 PM  
Anonymous Anonymous said...

It says what will you do. So what i would do is ask no questions. I would get a bucket of water and lob it over her, if she melts, shes a witch and i run off with food, if not then kill her anyway and run off with the food.

December 4, 2007 9:28 AM  
Anonymous Rob said...

There is a simple solution to this situation.

When you approach the purveyor of sustenance, start a conversation without asking any questions.

You: I am in town for an interview. I became hungry, so I figured I would stop in hear for something to eat. Only thing is, the interviewer told me some unnerving information.

Witch or not: Oh really! Just what did your interviewer tell you?

You: Well, he said "...all (persons in the town are) either liars or truthtellers". He also told me, "...that if a strangers asks more than one question in this town he is killed." Then he told me, "...there are some wicked witches who DO NOT sells poisonous food in town."

Witch or not: You don't say!

You: Now I am hungry and I do not know if the food is safe to eat.

Witch or not: All my food is safe to eat.

You: Hearing that,I must ask you a question. Was the interviewer telling the truth?

If the Witch or not says yes, you know the Witch is lying since you changed the wording of the interviewer's comments. With that knowledge, you also know the interviewer was lying as well.

If the Witch or not says no, you know she is telling the truth, and so was the interviewr.

Since she already said her food was safe to eat, you need ask no more questions. Go ahead and feed you face.

December 4, 2007 9:00 PM  
Anonymous Rob said...

Then again, if the interviewer WAS lying, then his statement that "... all either liars or truthteller", is a lie as well.

So are they-
All neither liars or truthtellers?
All both liars or truthtellers?
Few either liars or truthtellers?

December 4, 2007 9:14 PM  
Blogger Daniel said...

I was meditating on this question today, and I came on to pretty much post the same as joseph v.

I'm also very releived to see that Joe in Hawaii has returned to the blog; for a moment I thought he'd been scared away, but his string-posts make it clear that this is in fact not the case.

I beleive Joseph V. is correct, and I think the key is Raj's note in the question that everyone in the town "know(s) each other". By asking what an opposite person would say (in all of these type problems) you can guarantee a lie.

A truthful person will tell you what liars would say, and a liar will tell you what a truthful person would NOT say.

"I know that you're either a liar or a truthteller; if I were to ask someone who is the opposite of you if your food was poisonous, what would they say?"

There are four possibilities: Witch or Not Witch, Liar or Truthteller, and their responses are as follow:

WL: My opposite (TT) would say my food is safe. (lie)
WT: My opposite (L) would say my food is safe.
NWL: My opposite (TT) would say my food is poisonous. (lie)
NWT: My opposite (L) would say my food is poisonous.

I beleive this is based on a sort of multiplication principle that a negative times a positive makes a negative. Along those same lines you could ask "if i asked someone who is the same as you, what would they say" should always yield the truth, but I can't be certain.

December 5, 2007 12:03 AM  
Anonymous Johnny in Oklahoma said...

It seems clear from the statement "either liars or truthtellers, WHO SEEMS TO KNOW EACHOTHER" that there are BOTH liars and truthtellers in the town and everyone knows whether every other person is a liar or truthteller.

Since I know the person I'm asking is either a liar or truthteller, and also may or may not be a witch, the question I would ask is simple: "If I asked someone else like you if their food is safe, what would they say?" This would guarantee a truthful answer. If she says yes, eat up; if she says no, throw water on her and enjoy the show.

The logic is simple: there are four possible types of people in town: witch/liar (WL), witch/truthteller (WT), nonwitch/liar (NWL), and nonwitch/truthteller (NWT). By asking her what someone else like her would say, it keeps it simple (they're both the same).

The four possible responses are:

WT: Both tell the truth: "it's not safe". Better find a Denny's instead.

WL: Both lie: 2nd person says "it's safe" so she lies and says "they would say it's not safe." Hope there's a McDonalds close by.

NWT: Both tell the truth: "it's safe" so eat all you want.

NWL: Both lie: the 2nd person says "it's not safe", so she lies and says "they would say it's safe". Dinner time.

One final thought comes to mind: if I ever find myself at an interview in a town where psychotic witches sell poisoned food, a town inhabited by manic, bipolar sociopaths who kill normal people for asking two questions but don't do anything about the homicidal witches even though they know who they are, I am NOT going to be provoking them with silly word games and hanging around eating dinner with them!

December 5, 2007 3:22 AM  
Anonymous Mememememeeee said...

I'd ask:
If I ask you the others if your food is ok to eat, what would they say?

Then I'd only eat from the person that says "it's poisened"

December 5, 2007 7:52 AM  
Anonymous peji said...

either everyone lies or tells the truth.

if everyone tells the truth the interviewer is correct that some witches sell poison. ask the witch if it is poisonous, she will tell the truth

if everyone lies, then he is lying - there arent witches that sell poisonous food so you are safe

:)

December 5, 2007 1:14 PM  
Anonymous James said...

Several other people reached my conclusion before me. I think I'd just change the tone of my question; I'd be at once more specific and more flattering - making sure to introduce a hypothetical person that is similar to her only in her habits of factuality:

ME: Were I to ask an enchanting young woman as honest as yourself if the food you serve is free of poison, what would she say, hm?

Food is poisoned. If she's an honestant, a similarly truthful person would say "no," a fact she would likewise verify. But if she's a swindlecant, a similarly false person would say "yes," a truth she would be incapable of relating. Hence:

HER: No.

Food is not poisoned. Same logic as above but with the "no"s and "yes"s reversed:

HER: Yes.

ME: Marvelous! Then can I get the green curry with one star and a bottomless chai, please?

HER: That's two. Take him away.

ME: What? Wait, no! (being dragged away to the place of execution) No, I meant "Give me a green curry and chai!" That's not a question; it's a command! I demand food! Give me curry! Stop executing me!

Yeah, obviously I wouldn't last long. If I'm good enough to go without food after discovering the place sells poison, I'm good enough to go without food. Then I'll save my one question for finding out the next train out of town. No doubt this is the same detestable place that manufactures "use and throw" knives.

December 6, 2007 2:19 PM  
Anonymous Skrewston said...

well, i think the answer to this is everyone in town is a truth teller. reason y is cuz the interviewer stated a fact.

"The Interviewer told you one more bizaare 'FACT' about the town that if a strangers asks more than one question in this town he is killed."

December 6, 2007 7:33 PM  
Anonymous Anonymous said...

I give up. Can we please just have the answer already???

December 7, 2007 3:03 AM  
Anonymous Joe in Hawaii said...

Daniel, glad you appreciate my string of blabbering on. makes me feel wanted. my only question for your post is how exactly are you to distinguish between the liar and truthteller, since the answers are the same? and if you were to ask "if i ask someone opposite of you..." how do you distinguish if the person they might be talking about is a truthteller or a liar. ALSO, whether or not there are only liars, truthtellers, or BOTH, my line of questioning still works, based on the answers strictly given from the storeowner. Johnny, you run into a problem with guaranteed truthful answer, since there are liars in town, if you must insist that there are both. Considering that my question works either way, I still i got it. bwahaha.

and just so we're clear, here's the problem with asking that whole "if i ask someone opposite of you...", or even "if i ask a liar about you..." a liar who sells poisonous food will say the same thing as a truthteller who doesn't sell food. how would you distinguish between the two? hmmmmm???? again, that is something that NONE OF YOU have done.

December 7, 2007 8:01 PM  
Anonymous Joe in Hawaii said...

crappity crap crap crap. nvm. damn it. i have too much fun, and very stubborn. i MIGHT be wrong. but i will never be scared away daniel. bwahahaha.

December 7, 2007 8:14 PM  
Anonymous Joe in Hawaii said...

defensive even, obviously bored out of my mind, so yeah, sorry about that. =) =) =). hahaha. bring on another one.

December 7, 2007 8:20 PM  
Anonymous Erika said...

It was not read carefully. You cannot ask some "opposite" of a person because the statement says, "ALL either liars or truthtellers"
This means that the town has only liars and liars alone, with some witches.
OR
The town has only truthtellers along with some witches.

December 7, 2007 11:59 PM  
Anonymous Hoskri said...

I think a lot of people are leaving out a key phrase in the question of are there only liars or truth tellers. The sentence goes, all either liars or truth tellers, who seems to know each other. The each other hints that there are both.
You know for a fact that the town has both of these people, because it never states that the interviewer tells you that fact. He only tells you that if you ask more than one question you'll be killed, and that there are witches who serve poisoness foods. He never states that there are witches that don't, stating that all the witches serve poisoness foods. Now, to what I would do...
I would look at the menu, expecting to see what goes into each meal in the description. Obviously if they don't sell poisoness foods then there won't be poison on the menu, and if they do, then they'll lie, and not include it on the menu. Then, I'll order something, making note of all the ingredients listed. Say I order chili, and the ingredients include onion, garlic, chili powder, etc.
Now, when I recieve my order, I will be sure I can see the onion. Then I'll look up and ask the woman, is there onion in this? If she replies no, then she is a liar, meaning that there is poison in it, because it wasn't on the menu. If she replies yes, then I am safe.

December 8, 2007 9:36 AM  
Anonymous Anonymous said...

Could you ask the witch a question that you know to be true and depend on her response to tell you whether or not she lies?

Example: Hold up something that is red and ask...Is this item red?

By definition, the liar could not say "yes" or they would be telling the truth. They would have to say "no". If that was the case, the food would be safe because the interviewer is a liar as well.

The person telling the truth would have to say "yes". That would imply that the interviewer was telling the truth.

Since the actual question is "What will you do?" and not whether or not the food is poisoned. You should probably not buy any food from the person.

Probably way off base but it is fun thinking about it.

December 8, 2007 11:12 AM  
Anonymous AJ said...

I THINK I HAVE HALF A SOLUTION FOR THIS ONE, IT'S QUITE SIMPLE, BUT PLEASE READ TO UNDERSTAND WHY I BELIEVE IT'S A LITTLE HELPFUL, YET NOT FULL


case 1: the guy was a liar, u ask the lady are you a witch? since he was a liar then there are no witches in town so her answer will definitely be "YES" since she's not a witch and she's a liar as well.


case 2: he was a truth teller, now the lady is either a witch or not. ask the same question and if she says "YES", then she is a witch for sure. he was telling the truth and so is she. if she is not she will say "NO" I am not. the guy was telling the truth about the existance of such witches and she is telling the truth about not being one... hence that you got a "NO" for a case of a good food and 2 "YES"s. one for good food, one for poisoned

so yeah, it's half an answer. you ask that question and if you get a "NO" then ur free to eat. yet if u get a "YES", u can't really tell. so there's probably a better answer

December 8, 2007 2:17 PM  
Anonymous Anonymous said...

i would be headed for another town...

December 8, 2007 2:23 PM  
Anonymous jimmy dean in maine said...

i agree with Joe in hawaii

December 8, 2007 4:30 PM  
Anonymous Anonymous said...

I would simply ask her if she sells foods. If she replies yes, she is a witch if she replies no she is a liar

December 9, 2007 8:36 AM  
Anonymous supratik said...

if the interviewer belongs to that town...
mind it there is no feasible answer...
since he may be a liar or a truthteller!!!

December 9, 2007 10:34 AM  
Anonymous Cressa said...

go back to the interviewer and ask that question "Does 2+2 equal 4?" if he says no he is a liar, if yes, he is a truthteller. If he's a truthteller then say, "Tell me the names of the witches." If he's a liar, there are no witches. You escape with your life and your one question and you get something to eat.

December 9, 2007 4:11 PM  
Blogger drsnowman said...

i think... what you do is bring in a few people with you, you ask the lady behind the counter if she is a witch, then ask "p1" (p and then the number is just easier than writing person everytime..lmao..i know i know i am a lazy mofo..lmao) to ask the lady if she is lying, then ask p3 if to ask the question .. so on and so forth...

but i just read Cressa's answer and it seems to be the faster and smarter way to do this..lmao...
remind me to invite you to come along with me if i ever need to go to a place like this..lmao

December 11, 2007 4:12 AM  
Anonymous the great one said...

I'd leave and go to a different town that has a mcdonald's

December 11, 2007 3:07 PM  
Anonymous AJ said...

I HAVE IT THIS TIME...

YOU GET ANOTHER PERSON FROM THE SAME TOWN, SAY TOM, AND ASK HIM TO ASK HER IF SHE'S A WITCH AND THEN COME TELL YOU WHAT SHE SAID:

1 - SHE'S A LIAR >> INTERVIEWER IS A LIAR >> NO WITCHES >> SHE'LL SAY YES I AM A WITCH (lie), AND TOM WILL COME TELL YOU SHE SAID NO SHE ISN'T A WITCH (lie), CAUSE HE'S A LIAR AS WELL
(NOT A WITCH, ANSWER IS NO)

2 - SHE'S A TRUTHTELLER / NOT A WITCH >> SHE WILL TELL TOM NO, I'M NOT A WITCH (truth)>> TOM WILL TELL YOU SHE SAID NO SHE ISN'T A WITCH (truth) CAUSE HE'S NOW A TRUTHTELLER LIKE THEM.
(NOT A WITCH, ANSWER IS NO)

3 - SHE'S A TRUTHTELLER / WITCH >> SHE WILL TELL TOM SHE IS A WITCH (truth) >> TOM WILL TELL YOU SHE SAID YES (truth).
(WITCH, ANSWER IS YES)


YES for witch, and NO for non witch

and the Oscar goes to....? X)

December 12, 2007 8:53 AM  
Anonymous AJ said...

I HAVE IT THIS TIME...

YOU GET ANOTHER PERSON FROM THE SAME TOWN, SAY TOM, AND ASK HIM TO ASK HER IF SHE'S A WITCH AND THEN COME TELL YOU WHAT SHE SAID:

1 - SHE'S A LIAR >> INTERVIEWER IS A LIAR >> NO WITCHES >> SHE'LL SAY YES I AM A WITCH (lie), AND TOM WILL COME TELL YOU SHE SAID NO SHE ISN'T A WITCH (lie), CAUSE HE'S A LIAR AS WELL
(NOT A WITCH, ANSWER IS NO)

2 - SHE'S A TRUTHTELLER / NOT A WITCH >> SHE WILL TELL TOM NO, I'M NOT A WITCH (truth)>> TOM WILL TELL YOU SHE SAID NO SHE ISN'T A WITCH (truth) CAUSE HE'S NOW A TRUTHTELLER LIKE THEM.
(NOT A WITCH, ANSWER IS NO)

3 - SHE'S A TRUTHTELLER / WITCH >> SHE WILL TELL TOM SHE IS A WITCH (truth) >> TOM WILL TELL YOU SHE SAID YES (truth).
(WITCH, ANSWER IS YES)


YES for witch, and NO for non witch

and the Oscar goes to....? X)

December 12, 2007 8:58 AM  
Anonymous Anonymous said...

Ask her if she will taste the fruit !!!!!!

December 13, 2007 9:33 PM  
Anonymous Anonymous said...

we gonna get the definitive solution on this one?

December 14, 2007 2:47 PM  
Anonymous amanda said...

Just ask "are you a lying witch?"
if she says yes, then don't buy from her... if no then you're all set :)

December 19, 2007 11:11 PM  
Anonymous Jénova said...

You could ask the woman an obvious question that both you and her know the answer to, i.e What is the colour of your hair?
If she tells the truth - she's not a liar and you can have your supper.

December 22, 2007 10:19 PM  
Anonymous Jénova said...

I completely forgot about the poison... ignore that

December 22, 2007 10:22 PM  
Anonymous Anonymous said...

ask a passer by...

If i ask the seller if she a witch, what would she say?

eat if the answer is no

December 23, 2007 2:18 AM  
Anonymous erwally said...

Ask the lady if she knows you. She can only answer yes or no. If she says Yes...The whole town are liars, and the Interviewer was one as well. EAT UP!! If she says NO....then the interviewer was telling the truth and you should leave hungry.

December 28, 2007 9:39 AM  
Anonymous CMOY said...

I've got the answer... It took a while but I think I figured it out... ask the woman if she'll eat the food first... If she does then you're safe.

December 28, 2007 2:54 PM  
Anonymous hairy.hippo.nuts said...

ok i dont know if anyone else as posted this becuase i got tired of reading all those answers.

my answer is: i would tell the lady my name and shake her hand
then ask all the questions i want

December 28, 2007 5:09 PM  
Blogger Rajesh Lal said...

ANSWER
----------------------
The trick is to ask two direct questions( Are you a truth teller ? and Is the women wicked ?) as one
indirect question.

SOLUTION
----------------------
Stop a passerby and ask the following question:-

If i will ask you about the old women what will you say ?

Four Scenarios

1
----------------------
The women is a witch
The passerby is a truth teller

Answer: I will say the women is a witch

2
----------------------
The women is a witch
The passerby is a liar

Answer: I will say the women is a witch

because actually he will say the women is not a witch, he has to lie twice

3
----------------------
The women is NOT a witch
The passerby is a truth teller

Answer: I will say the women is NOT a witch

4
----------------------
The women is NOT a witch
The passerby is a liar

Answer: I will say the women is NOT a witch because he will actually say she is a witch ( he has to lie twice )



GOT RIGHT
-------------------------------
a number of good analysis, Danile, Joe

December 28, 2007 6:48 PM  
Anonymous Anonymous said...

Wait can i ask one question though?
if the town is full of truthtellers and liars, whos to say that the interviewer wasnt a liar and lied about the whole thing?

December 28, 2007 8:15 PM  
Anonymous Fardin said...

Because

"The Interviewer told you one more bizaare FACT about the town that if a strangers asks more than one question in this town he is killed"

he is stating a fact so he is a truth teller IMO

December 28, 2007 9:22 PM  
Anonymous Anonymous said...

k...here's the best answer...the puzzle says you're hungry...not starving to death. screw all these nut-job liars and witches. they can all sit around eating their poisonous food together. just keep walking. there's bound to be a normal town nearby. even if it wasn't poisoned, the food isn't that good anyhow. ;)

January 2, 2008 9:39 PM  
Anonymous alex said...

next time pack ur own lunch then u wont have to worry

January 3, 2008 5:40 AM  

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