[wolfgang]

Three men, each one has money in his pocket.

The first one has 10$, the second one has 20$, and the third one has 30$.

Each one of them upon being asked the first( yes or no) question ,will randomly choose to be a truth teller or a liar.

And as he did he will be fixed to that persona and will not change it( i.e.If he tells the truth,will always tell the truth, if he lied,will always lie).

You are to ask only three ( yes or no ) questions.to any one of them at a time,or the same question to different persons..its up to you,in order to arrenge them in a row from the one with 10$ then 20$ then 30$.

so your goal is to arrenge them as follows:-

10$....20$....30$

[Guest]

Araver will be around soon to tell you that truth teller/liar doesn't matter, and thus the answer is very simple...

Edited December 3, 2010 by rajat_magic

[wolfgang]

Araver will be around soon to tell you that truth teller/liar doesn't matter, and thus the answer is very simple...

I hope so

Edited December 3, 2010 by wolfgang

[wolfgang]

I have to add,each of them knows who is who.

[Guest]

Hate to be trouble.. but I am a bit confused. Maybe its just me.. (these things happen! lol) but is there some information missing here?

You have already told us the order in which the money is given... First has $10, second has $20, and third has $30. Im not understanding where the truth teller and liar part is coming in. Sorry, I'm a bit new to the whole truth teller/liar riddles. Still learning I guess.

[Guest]

Hate to be trouble.. but I am a bit confused. Maybe its just me.. (these things happen! lol) but is there some information missing here?

You have already told us the order in which the money is given... First has $10, second has $20, and third has $30. Im not understanding where the truth teller and liar part is coming in. Sorry, I'm a bit new to the whole truth teller/liar riddles. Still learning I guess.

In addition to last post...

I could choose whomever I wanted to start the questions and decide... and do it again another time and get a different answer. Is this correct? I think I'm missing something here.. lol

[wolfgang]

Hate to be trouble.. but I am a bit confused. Maybe its just me.. (these things happen! lol) but is there some information missing here?

You have already told us the order in which the money is given... First has $10, second has $20, and third has $30. Im not understanding where the truth teller and liar part is coming in. Sorry, I'm a bit new to the whole truth teller/liar riddles. Still learning I guess.

Sorry...but I didn`t say they are standing in this arrengement...

there are six possiblities in this case as you know...

sorry again..and thanks

[wolfgang]

In addition to last post...

I could choose whomever I wanted to start the questions and decide... and do it again another time and get a different answer. Is this correct? I think I'm missing something here.. lol

I didn`t refer to the details,cuase this topic is well known to all members here.

I concider it as very easy one,you need maximal 5 min. to solve it..

[araver]

Araver will be around soon to tell you that truth teller/liar doesn't matter, and thus the answer is very simple...

If the world were that simple But in real life it does matter.

Because of the wording of the OP: "Each one of them upon being asked the first( yes or no) question ,will randomly choose to be a truth teller or a liar. And as he did he will be fixed to that persona and will not change it( i.e.If he tells the truth,will always tell the truth, if he lied,will always lie)." I am not sure that my previous trick could or could not work this time for the first question. It depends on when he decides: before/during the question.

However if the person knows before answering if he is forever going to be a truth-teller or forever going to be a liar then with some rewording:

Three persons A,B,C.

Q1) Ask A: "If I ask you in the next question if you have 10$ would you say yes?"

If A says Yes to Q1then he has 10$. Move to B and ask him: "If I ask you in the next question if you have 20$ would you say yes?". If B says yes he has 20$, C has 30$, else if B says no, then he has 30$ and C has 20$. Done in 2 questions.

If A says No to Q1, then he has either 20$ or 30$ and we ask him next question:

Q2) Ask A: "If I ask you in the next question if you have 20$ would you say yes?"

If A says Yes to Q2 then he has 20$. Move to B and ask him "If I ask you in the next question if you have 10$ would you say yes?". If B says yes he has 10$, C has 30$, else if B says no, then he has 30$ and C has 10$. Done in 3 questions.

If A says No to Q2, then he has 30$. Move to B and ask him "If I ask you in the next question if you have 10$ would you say yes?". If B says yes he has 10$, C has 20$, else if B says no, then he has 20$ and C has 10$. Done in 3 questions.

Edited December 3, 2010 by araver

[wolfgang]

If the world were that simple But in real life it does matter.

Because of the wording of the OP: "Each one of them upon being asked the first( yes or no) question ,will randomly choose to be a truth teller or a liar. And as he did he will be fixed to that persona and will not change it( i.e.If he tells the truth,will always tell the truth, if he lied,will always lie)." I am not sure that my previous trick could or could not work this time for the first question. It depends on when he decides: before/during the question.

However if the person knows before answering if he is forever going to be a truth-teller or forever going to be a liar then with some rewording:

Three persons A,B,C.

Q1) Ask A: "If I ask you in the next question if you have 10$ would you say yes?"

If A says Yes to Q1then he has 10$. Move to B and ask him: "If I ask you in the next question if you have 20$ would you say yes?". If B says yes he has 20$, C has 30$, else if B says no, then he has 30$ and C has 20$. Done in 2 questions.

If A says No to Q1, then he has either 20$ or 30$ and we ask him next question:

Q2) Ask A: "If I ask you in the next question if you have 20$ would you say yes?"

If A says Yes to Q2 then he has 20$. Move to B and ask him "If I ask you in the next question if you have 10$ would you say yes?". If B says yes he has 10$, C has 30$, else if B says no, then he has 30$ and C has 10$. Done in 3 questions.

If A says No to Q2, then he has 30$. Move to B and ask him "If I ask you in the next question if you have 10$ would you say yes?". If B says yes he has 10$, C has 20$, else if B says no, then he has 20$ and C has 10$. Done in 3 questions.

To ask them about(the next question),will not force them to tell the truth,they will remain totaly "at random" to the first question whatever it is.

[araver]

To ask them about(the next question),will not force them to tell the truth,they will remain totaly "at random" to the first question whatever it is.

That's why I said its not so clear.

However the trick should work because:

1) One decides whether he chooses to be a truth-teller or a liar before answering the question.

2) When evaluating/reading the question they know they are and forever will be either a truth-teller or a liar. This way, they are forced to answer to any question regarding the future, since they now their allegiance now (truth-teller, liar).

1 cannot be false since otherwise they cannot answer the first question as a truth-teller or a liar. They need to look and interpret the question.

2 cannot be false since it follows logically from 1 and the OP "And as he did he will be fixed to that persona and will not change it( i.e.If he tells the truth,will always tell the truth, if he lied,will always lie)"

Wolfgang, I understand you tried to create a random outcome of the first question but it's just not possible in the context of this OP.

They cannot at the same time be random for the first question AND decide to be truth-teller or liar for all eternity.

They need to look at the question and interpret/evaluate it before answering. There's no way to come up with a YES/NO answer without looking at the question.

- what if they choose No and the question is "Are you going to tell the truth forever?". Contradiction since both truth-teller and liars answer Yes to that question.

- what if they choose Yes and the question is "Are you going to lie forever?". Contradiction since both truth-teller and liars answer No to that question.

So, you cannot choose the answer randomly without looking at the question and afterwards claiming either to be a truth-teller or a liar (depending on the answer). You break consistency that way. They need to decide before answering and need to look and interpret the question.

Edited December 4, 2010 by araver

[wolfgang]

That's why I said its not so clear.

However the trick should work because:

1) One decides whether he chooses to be a truth-teller or a liar before answering the question.

2) When evaluating/reading the question they know they are and forever will be either a truth-teller or a liar. This way, they are forced to answer to any question regarding the future, since they now their allegiance now (truth-teller, liar).

1 cannot be false since otherwise they cannot answer the first question as a truth-teller or a liar. They need to look and interpret the question.

2 cannot be false since it follows logically from 1 and the OP "And as he did he will be fixed to that persona and will not change it( i.e.If he tells the truth,will always tell the truth, if he lied,will always lie)"

Wolfgang, I understand you tried to create a random outcome of the first question but it's just not possible in the context of this OP.

They cannot at the same time be random for the first question AND decide to be truth-teller or liar for all eternity.

They need to look at the question and interpret/evaluate it before answering. There's no way to come up with a YES/NO answer without looking at the question.

- what if they choose No and the question is "Are you going to tell the truth forever?". Contradiction since both truth-teller and liars answer Yes to that question.

- what if they choose Yes and the question is "Are you going to lie forever?". Contradiction since both truth-teller and liars answer No to that question.

So, you cannot choose the answer randomly without looking at the question and afterwards claiming either to be a truth-teller or a liar (depending on the answer). You break consistency that way. They need to decide before answering and need to look and interpret the question.

You know Dear Araver...intellegent people(like you),some times complicates a very simple situation.

Let me give you a hint...what about asking anyone of them a (yes)question?.

[Guest]

If we ask the first person: "do you know how much money I have in MY pocket" he will reveal whether or not he's lying or telling the truth (he can't know how much I have, so his answer is revealing).

Once we know that we ask the same person whether he has more money than the second person, and then ask the first person whether the second person has more than the third.

Knowing whether the first person is a liar or truth teller allows us to then order them appropriately.

[Guest]

Do they know how much $ each one of them has ? If Yes I think that simplifies the problem a lot.

[araver]

If we ask the first person: "do you know how much money I have in MY pocket" he will reveal whether or not he's lying or telling the truth (he can't know how much I have, so his answer is revealing).

Once we know that we ask the same person whether he has more money than the second person, and then ask the first person whether the second person has more than the third.

Knowing whether the first person is a liar or truth teller allows us to then order them appropriately.

If he's a truth-teller and says No to second question and Yes to third question you could be looking at either 20, 30, 10 or 10, 30, 20.

2 questions mean 4 possibilities. There are 6 possible arrangements. 4 possibilities cannot determine uniquely 6 possible arrangements.

Edited December 5, 2010 by araver

[wolfgang]

Do they know how much $ each one of them has ? If Yes I think that simplifies the problem a lot.

Yes they do..

[araver]

You know Dear Araver...intellegent people(like you),some times complicates a very simple situation.

Let me give you a hint...what about asking anyone of them a (yes)question?.

Thank you for the compliment.

But the beauty of proposing a puzzle on BD is that people usually come up with ideas/answers/strategies different than your own. This is why you should read their arguments or at least comment if you accept their answers. My argument is that considering the first answer is completely random breaks the consistency assumption mentioned in the puzzle. You have chosen neither to approve nor deny that. But if it's true, it makes my solution valid, and your previous response "To ask them about(the next question),will not force them to tell the truth,they will remain totaly "at random" to the first question whatever it is." false.

Secondly, for your hint

Asking the same person three questions means 8 possible outcomes (from Yes/Yes/Yes to No/No/No).

There are 6 possible arrangements of 10,20,30 and two possibilities for that person (truth-teller/liar). Combined they give 6x2=12 possibilities.

8 outcomes cannot uniquely determine 12 possibilities so there's no way you can know both the arrangement and what the person is after 3 questions.

[phaze]

Is 30, 20, 10 considered to be the mirror image of 10, 20, 30 (or 10, 20, 30 seen from other side)?

Is either way applicable for the solution or just one?

[wolfgang]

Is 30, 20, 10 considered to be the mirror image of 10, 20, 30 (or 10, 20, 30 seen from other side)?

Is either way applicable for the solution or just one?

It makes no differemce..it is the same so or so.

[Guest]

It makes no differemce..it is the same so or so.

[wolfgang]

Thank you for the compliment.

But the beauty of proposing a puzzle on BD is that people usually come up with ideas/answers/strategies different than your own. This is why you should read their arguments or at least comment if you accept their answers. My argument is that considering the first answer is completely random breaks the consistency assumption mentioned in the puzzle. You have chosen neither to approve nor deny that. But if it's true, it makes my solution valid, and your previous response "To ask them about(the next question),will not force them to tell the truth,they will remain totaly "at random" to the first question whatever it is." false.

Secondly, for your hint

Asking the same person three questions means 8 possible outcomes (from Yes/Yes/Yes to No/No/No).

There are 6 possible arrangements of 10,20,30 and two possibilities for that person (truth-teller/liar). Combined they give 6x2=12 possibilities.

8 outcomes cannot uniquely determine 12 possibilities so there's no way you can know both the arrangement and what the person is after 3 questions.

Thank you Dear araver...

You know...If I`ve said each one has a different underware color( e.g.), so no one can solve it !!

but I said ( money ),,and fixed amount...a+b+c=60...

what can I say more?

[Guest]

Ask number 1 if he knows how much I have in my pocket to reveal whether he speaks the truth or lies. Regardless of whether he's a liar or truth teller, ask him if moving #3 to the middle would put them in correct order. Then ask him if moving himself to the middle would put them in correct order. This should allow you to order them correctly, but you wouldn't know whether it was 10-20-30 or 30-20-10

[wolfgang]

Ask number 1 if he knows how much I have in my pocket to reveal whether he speaks the truth or lies. Regardless of whether he's a liar or truth teller, ask him if moving #3 to the middle would put them in correct order. Then ask him if moving himself to the middle would put them in correct order. This should allow you to order them correctly, but you wouldn't know whether it was 10-20-30 or 30-20-10

If they were:

10,,20,,30

so by moving 30 to the middle,will get 10,,30,,20 and you will get (no) answer.

and by moving himself to the middle,will get either 20,,10,,30 OR 10,,30,,20 in both cases you get(no) again.

[Guest]

If they were:

10,,20,,30

so by moving 30 to the middle,will get 10,,30,,20 and you will get (no) answer.

and by moving himself to the middle,will get either 20,,10,,30 OR 10,,30,,20 in both cases you get(no) again.

[Guest]

Yes, if he's a truth teller and responds with "no" twice, you know they're already in order. If he's a liar and responds with "yes" twice, you know they're in the correct order. In fact if you get lucky and on the second question you learn that moving 3 would put them in order then on the next question you could find out whether it's 10-20-30, or 30-20-10.

[wolfgang]

Yes, if he's a truth teller and responds with "no" twice, you know they're already in order. If he's a liar and responds with "yes" twice, you know they're in the correct order. In fact if you get lucky and on the second question you learn that moving 3 would put them in order then on the next question you could find out whether it's 10-20-30, or 30-20-10.

See the order 10,,30,,20 will give you 2 times(no) also if you were asking the 10.

and the same with 30,,10,,20 and 30,,20,,10 if you were asking the 30