[Guest]

Hi,

I got this question from friend and i don't know the solution for this (And i don't think there is any rule saying that - you should not post the puzzles for which you don't know the answers). If someone can answer this puzzle, would be helpful

The puzzle is:

There are 4 persons in a room excluding you. Out of which 2 persons always tell truth and 2 persons always lies. And every single person knows the behaviors of other 3 persons (I mean he knows which person tells what, either truth or lie). And everyone will give you only YES/NO answers. So you should ask questions in a manner that they can answer it either YES or NO

You can ask maximum of 2 questions and after asking the 2 questions, you should determine which persons are telling truth and who all are telling lies.

FYI, i am again mentioning that i don't know the solution for this.

Thanks

Shravan

[bonanova]

six ways four persons can be assigned truthteller and liar status on a 2-2 basis.

Two yes/no questions can distinguish four cases.

That's an interesting challenge.

[Guest]

ask person 1, "can you point to a truth teller?" if he says no, then he is a liar, if he says yes, and does so, then you have both your truth tellers after one question, and from that the other 2 are the liars......if person 1 said no, then use your second question on person 2 and ask the same thing, if he says no, then you know both of the liars...

[Guest]

ask person 1, "can you point to a truth teller?" if he says no, then he is a liar, if he says yes, and does so, then you have both your truth tellers after one question, and from that the other 2 are the liars......if person 1 said no, then use your second question on person 2 and ask the same thing, if he says no, then you know both of the liars...

But if person 1 is a liar, they can say 'Yes' and point the other liar. What if we ask any 2 people the same question, "How many of you are in this room?" No matter who you pick, the truth tellers will say "4" and the liars will say something else like "green".

[Guest]

But if person 1 is a liar, they can say 'Yes' and point the other liar. What if we ask any 2 people the same question, "How many of you are in this room?" No matter who you pick, the truth tellers will say "4" and the liars will say something else like "green".

But i mentioned that they can answer only yes/no. Even if the first person tells truth and says yes when you ask the question, he can not point to anyone else. You can ask something like does person 2 tells truth then he can say yes/no.

[Guest]

But i mentioned that they can answer only yes/no. Even if the first person tells truth and says yes when you ask the question, he can not point to anyone else. You can ask something like does person 2 tells truth then he can say yes/no.

How about just asking , "Are there 4 people in this room?" The truth tellers will say yes and the liars will have to say no.

[Guest]

Are you allowed to ask the questions to the group or do the questions have to be asked to individuals. It seems like Wingless' solution would be right if you could ask the group like that but I also feel like that would be to easy of a riddle.

[Guest]

No possible solution.

[Guest]

How about just asking , "Are there 4 people in this room?" The truth tellers will say yes and the liars will have to say no.

Ya... you can ask these questions as the person can answer it in yes/no format

[Guest]

Are you allowed to ask the questions to the group or do the questions have to be asked to individuals. It seems like Wingless' solution would be right if you could ask the group like that but I also feel like that would be to easy of a riddle.

I am sorry...I did not get what you are saying over here. But if you are going to ask a question to a group, i wonder how they can answer it in yes/no format simply. If you are going to ask question to 2 people, then you get two answers (one from each) and i think this will be counted as equivalent to asking 2 questions.

[Guest]

May be we can have an assumption that the people can answer anything (not only yes/no). Although this is not the correct assumption. But just wanted to build this solution in step-wise (may be it will help us in final solution). Once we got the number of answers for this, then we can try to see whether we can have a solution if they can answer only yes/no.

[Guest]

How about just asking , "Are there 4 people in this room?" The truth tellers will say yes and the liars will have to say no.

If you ask a liar first and a truthteller second you will only know what two of the people are. The other two will not have been identified.

[Guest]

Maybe by arranging them in some order then asking a question. Then rearranging them and asking the same person. It seems like there is a solution just out of reach. Or maybe it's just one question away.

[Guest]

I am sorry...I did not get what you are saying over here. But if you are going to ask a question to a group, i wonder how they can answer it in yes/no format simply. If you are going to ask question to 2 people, then you get two answers (one from each) and i think this will be counted as equivalent to asking 2 questions.

So if I am understanding what you are saying from your last line. If I were to ask a yes/no question that all 4 people in the room answer then you consider that asking 4 questions. Therefore the solution of just asking everybody a simple question such as "Are there four people in the room?" returns 4 results meaning 4 questions were asked. Is my thinking on this correct?

[Guest]

But if person 1 is a liar, they can say 'Yes' and point the other liar.

A liar wouldn't be able to say yes...no matter who he plans on pointing at, he would be telling the truth by saying "yes I can point to a truth teller"(since both you and him know that he knows what the other 3 are)...which he can't do...the deception would come after he answered the question...so a liar would be forced to lie and say no to the question...maybe I have a short circuit in my logic today..

What if we ask any 2 people the same question, "How many of you are in this room?" No matter who you pick, the truth tellers will say "4" and the liars will say something else like "green".

this way only identifies 2 people for certain...if you get lucky and both are either a liar or truth teller, then you can figure out the other 2....but if one is a liar and the other is a truth teller...the other 2 people are either a liar or truth teller, but you couldn't tell which is which..

[Guest]

I thought the riddle said we can ask 2 questions, but it didn't specify we had to individually ask them up to 2 questions. If we can get away with the group question, "Are there 4 people in this room?" it'll work. But if we limit it to 2 questions total to ask any 2 individuals once or any one twice, we'll need to come up with a whole new set of questions. I'm still trying to figure this one out, its driving me nuts! Where's that John Forbes Nash guy from Beautiful Mind when you need him.

[Guest]

lets say the 4 people are called A, B, C, and D. ask person A if person B would say person C is a liar. If person A says yes, then person B and person A must both be the same. in that case C and D are the same. ask any1 if there are 4 people in the room and you will be able to deduce what everyone is. If person A says no, then person A and person B must be opposite. in that case ask person B if C is a liar. if person B says no, then A was telling the truth making A and D truthers and B and C liars. If person C says yes. then that makes person A and C the liars, making B and D the truthers.

im sorry if this is confusing i wish i could make a flow chart but alas, i'm too lazy to.

Edited July 29, 2009 by sparx1

[Gmaster479]

lets say the 4 people are called A, B, C, and D. ask person A if person B would say person C is a liar. If person A says yes, then person B and person A must both be the same. in that case C and D are the same. ask any1 if there are 4 people in the room and you will be able to deduce what everyone is. If person A says no, then person A and person B must be opposite. in that case ask person B if C is a liar. if person B says no, then A was telling the truth making A and D truthers and B and C liars. If person C says yes. then that makes person A and C the liars, making B and D the truthers.

im sorry if this is confusing i wish i could make a flow chart but alas, i'm too lazy to.

If the order goes LTLT or TLTL then A would answer no, and you know they alternate and if they answer yes then the 2 are next to eachother.

But what if the order went TLLT. Then the answer would be no because player A would say the truth which is that Player B would say that Player C isn't a liar even though he is. From there you have 3 possibilities. LTLT, TLLT, TLTL. From there you would have to get lucky so it isn't exactly correct, but works more often then most other ones.

Also is he answered yes the 3 possibilities would be TTLL, LLTT, or LTTL. .

[Guest]

If the order goes LTLT or TLTL then A would answer no, and you know they alternate and if they answer yes then the 2 are next to eachother.

But what if the order went TLLT. Then the answer would be no because player A would say the truth which is that Player B would say that Player C isn't a liar even though he is. From there you have 3 possibilities. LTLT, TLLT, TLTL. From there you would have to get lucky so it isn't exactly correct, but works more often then most other ones.

Also is he answered yes the 3 possibilities would be TTLL, LLTT, or LTTL. .

actually you are right, i didn't consider the LTTL case. back to the drawling board!

[Guest]

I might be wrong again but i think this is kind of impossible because there are only 4 possible combos based on the OP with whic u should determine which of 6 situatiosn it is. BUT if the OP actually allows you to, you can simply solve this with a paradox. lets say you ask person person A "if i ask person a and b this question will they both say the same thing?". in the case they are both truthers, they shall say yes. if they are both liars, they will keep quiet because no matter what they say, at least one of them will be telling the truth. if one is a liar and one a truther the truther will say no and the liar yes. then ask the same thing of C concerning A and C. if c is quiet, then A and C are liars. if C says yes, then A and B are truthers. If A was quiet in the first place then he and B are liars. IF A says no then C says yes, C and B are liars. I know this is even more confusing but its basically possible because there are now 3 possible responses.

QED!!!!

Edited July 30, 2009 by sparx1

[Guest]

I might be wrong again but i think this is kind of impossible because there are only 4 possible combos based on the OP with whic u should determine which of 6 situatiosn it is. BUT if the OP actually allows you to, you can simply solve this with a paradox. lets say you ask person person A "if i ask person a and b this question will they both say the same thing?". in the case they are both truthers, they shall say yes. if they are both liars, they will keep quiet because no matter what they say, at least one of them will be telling the truth. if one is a liar and one a truther the truther will say no and the liar yes. then ask the same thing of C concerning A and C. if c is quiet, then A and C are liars. if C says yes, then A and B are truthers. If A was quiet in the first place then he and B are liars. IF A says no then C says yes, C and B are liars. I know this is even more confusing but its basically possible because there are now 3 possible responses.

QED!!!!

If A answers "yes," you have no idea if A and B are truthers, or if A is a liar and B a truther. Oh, but then you just ask the same question to A and C, and that'll get you the answer.

Holy crap... bravo man. You solved it... I've been banging my head against this for hours, trying to figure out how to get past the seeming impossibility of getting 6 from 4.

Turns out it IS impossible, and you gotta cheat with the silence thing.

Goddang... that's something.

[Guest]

So if I am understanding what you are saying from your last line. If I were to ask a yes/no question that all 4 people in the room answer then you consider that asking 4 questions. Therefore the solution of just asking everybody a simple question such as "Are there four people in the room?" returns 4 results meaning 4 questions were asked. Is my thinking on this correct?

Yes... you are correct. It results in 4 questions

[Guest]

[spoiler=correction ]In response to my previous post. you would have to ask them if they both would answer no not if they both would answer yes ( 2 truthers could both say yes or both say no. same concept though 2 liars say yes, 2 truthers keep silent and if a liar and a truther the truther would say no and the liar would still say yes.

[Scudo]

The question should be asked twice to two different people about the same person. For intance A about B and C about B or D about B. Would he say you are a truth teller? Truthe sayers would say about truth sayers "yess". Truth sayers would say about liars "No". Liars would say about truthsayers "yes" and Liars would say about liars "No". So you know that person being spoken of is a liar if the answer is "No" and a truth sayer if the answer is "Yes", but you do not know what the answereer is. Now if you know what that person is, ask the same question about him to another person. This will not only give you the the identity of the person your asking but also the first person you asked leaving the fourth person to default classification.

I know this is confusing but test my logic and let me know if I did ok.

[Scudo]

The second question should be of the person already discerned about one of the other two. From this you will know what persuasion two are and discern the persuasion of the first person you asked. having 3 the other is default.

[Scudo]

It does work if you ask the same person the question about 2 seperate people.