[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]

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

[Guest]

It is your puzzle, sir, you get to be the judge.

My point is: if either 30-20-10 or 10-20-30 is an acceptable solution then my method will allow you to do one or the other, though you won't necessarily know which is which.

Taking your first example 10-30-20 and asking the first (10) if moving the third (20) would put them in order of money in pocket (high to low or low to high) then if he's a truth teller he'd say "yes". You'd then have another question to ask him and you could ask him if he had the most money and you'd know that it was 10-20-30, not the other way around.

If the original line up was 10-20-30, or 30-20-10 the truth teller would answer "no" twice (the liar "yes" twice) and you'd know they were in order, but wouldn't know whether it was lowest to highest or highest to lowest.

[wolfgang]

It is your puzzle, sir, you get to be the judge.

My point is: if either 30-20-10 or 10-20-30 is an acceptable solution then my method will allow you to do one or the other, though you won't necessarily know which is which.

Taking your first example 10-30-20 and asking the first (10) if moving the third (20) would put them in order of money in pocket (high to low or low to high) then if he's a truth teller he'd say "yes". You'd then have another question to ask him and you could ask him if he had the most money and you'd know that it was 10-20-30, not the other way around.

If the original line up was 10-20-30, or 30-20-10 the truth teller would answer "no" twice (the liar "yes" twice) and you'd know they were in order, but wouldn't know whether it was lowest to highest or highest to lowest.

I understand...Sorry firstly I thought you mean to move who has 30,but now it is clear...good job though!!

[Guest]

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$

Could you please post a spoiler because I don`t think there is a solution. In the first question you can find out if the person you are asking is a liar or one who tells the truth but you can`t find out with two questions who has how much even though you know that the person is lying or telling the truth. Or does it count as one question if you ask the three people the same question?

[wolfgang]

Could you please post a spoiler because I don`t think there is a solution. In the first question you can find out if the person you are asking is a liar or one who tells the truth but you can`t find out with two questions who has how much even though you know that the person is lying or telling the truth. Or does it count as one question if you ask the three people the same question?

you can concider them as one truth teller and two random(actually you don`t need them).

I said it doesn`t matter wether you can arrenge them ,10..20..30,,,or 30..20..10

all you can do is to ask the truth teller " do you have 20$?"

if YES,then put him in the middle.

if NO,ask him the second question"has the man in the middle the 20$?"

if YES,leave them as they are, if NO,the put the third man in the middle.

We can also solve it with Mathematical equations( I`ll leave it to my friend Araver )

[Guest]

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

Why not let them choose their persona at will, for every question?

Solution:

Observation 1: An alter-ego is a second self, a second personality or persona within a person, who is often (but not necessarily) oblivious to the persona's actions.

Observation 2: A normal person with a single personality (i.e. who does not naturally have an alter-ego) can imagine having an alter-ego.

Observation 3: Let's define the alter-ego of any man from the hypothesis as the same person in the alternative state. In other words, if the answerer chooses to be a liar, his alter-ego would be a truth teller and vice-versa. Being one self of a split personality, the alter-ego has access to all the knowledge of the person, including the amount of cash in his pocket.

Observation 4: A question that is forced through the mind of both a persona and its alter-ego always gives a lie.

In other words

* the truth of a lie is a lie and

* the lie of a truth is also a lie

The questions would be something like: What would your alter-ego answer to the question whether you have $x?

Knowing that the answer is a lie, you can easily determine who has which amount of money.

Compared to Araver's method, this avoids asking about the next question (which in case of Q3 would not exist!!), and also allows the men to change their persona at will between questions.

Edited December 8, 2010 by Kornrade

[Guest]

how about: You ask any one of the three, "do you have 40 dollars?"

I.) He says yes, and so is a liar. You know to consider the opposite of what he says to be the truth. Therefore you ask, (call him A):

1.) is B>C Ans: No

a.) is A>B, Ans: No solution: A=10, B=20, C=30

b.) is A>B, Ans: No solution: A=20, B=10, C=30

2.) is B>C Ans: Yes

a.) is C>A Ans: Yes solution: A=10, B=30, C=20

b.) is C>A Ans: No solution: A=20, B=30, C=10

Edited December 8, 2010 by IwantHATS

[wolfgang]

how about: You ask any one of the three, "do you have 40 dollars?"

I.) He says yes, and so is a liar. You know to consider the opposite of what he says to be the truth. Therefore you ask, (call him A):

1.) is B>C Ans: No

a.) is A>B, Ans: No solution: A=10, B=20, C=30

b.) is A>B, Ans: No solution: A=20, B=10, C=30

2.) is B>C Ans: Yes

a.) is C>A Ans: Yes solution: A=10, B=30, C=20

b.) is C>A Ans: No solution: A=20, B=30, C=10

If B>C and A>B (as in 1a),so A=30,B=20 and C=10....you chosse (No) for the 1st question to make him a truth teller.

[wolfgang]

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

Why not let them choose their persona at will, for every question?

Solution:

Observation 1: An alter-ego is a second self, a second personality or persona within a person, who is often (but not necessarily) oblivious to the persona's actions.

Observation 2: A normal person with a single personality (i.e. who does not naturally have an alter-ego) can imagine having an alter-ego.

Observation 3: Let's define the alter-ego of any man from the hypothesis as the same person in the alternative state. In other words, if the answerer chooses to be a liar, his alter-ego would be a truth teller and vice-versa. Being one self of a split personality, the alter-ego has access to all the knowledge of the person, including the amount of cash in his pocket.

Observation 4: A question that is forced through the mind of both a persona and its alter-ego always gives a lie.

In other words

* the truth of a lie is a lie and

* the lie of a truth is also a lie

The questions would be something like: What would your alter-ego answer to the question whether you have $x?

Knowing that the answer is a lie, you can easily determine who has which amount of money.

Compared to Araver's method, this avoids asking about the next question (which in case of Q3 would not exist!!), and also allows the men to change their persona at will between questions.

Thank you dear Kornrade...but each question has its limits and its own idea.

when I write a new topic ,I take it to my own level of thinking( )and I am for sure not so intellegent like you.

[Guest]

how about: You ask any one of the three, "do you have 40 dollars?"

I.) He says yes, and so is a liar. You know to consider the opposite of what he says to be the truth. Therefore you ask, (call him A):

1.) is B>C Ans: Yes(Truth is no)

a.) is A>B, Ans: Yes solution: A=10, B=20, C=30

b.) is A>B, Ans: No solution: A=20, B=10, C=30

2.) is B>C Ans: No

a.) is C>A Ans: Yes solution: A=20, B=30, C=10

b.) is C>A Ans: No solution: A=10, B=30, C=20

Edited December 14, 2010 by IwantHATS

[Guest]

Present all questions if the format "If I asked you if you had X how would you respond?" In either case the answer would be true.(Right?)

Ask the first about the largest amount[Q1].

If Q1 is yes the first has $30 so ask the second about the smallest amount[Q2a].

-----If Q1 is yes and Q2a is yes the second has $10 the third has $20 and the first has $30.

-----If Q1 is yes and Q2a is no the third has $10 the second has $20 and the first has $30.

If Q1 is no ask the first about the smallest amount[Q2b].

-----If Q1 is no and Q2b is yes then the first has $10 so ask the second about the largest amount[Q3].

----------If Q1 is no, Q2b is yes and Q3 is yes then the first has $10 the third has $20 and the second has $30.

----------If Q1 is no, Q2b is yes and Q3 is no then the first has $10 the second has $20 and the third has $30.

-----If Q1 is no and Q2b is no then the first has $20 so ask the second if he has the largest amount[Q3].

----------If Q1 is no, Q2b is no and Q3 is yes then the third has $10 the first has $20 and the second has $30.

----------If Q1 is no, Q2b is no and Q3 is no then the second has $10 the first has $20 and the third has $30.

[wolfgang]

Present all questions if the format "If I asked you if you had X how would you respond?" In either case the answer would be true.(Right?)

Ask the first about the largest amount[Q1].

If Q1 is yes the first has $30 so ask the second about the smallest amount[Q2a].

-----If Q1 is yes and Q2a is yes the second has $10 the third has $20 and the first has $30.

-----If Q1 is yes and Q2a is no the third has $10 the second has $20 and the first has $30.

If Q1 is no ask the first about the smallest amount[Q2b].

-----If Q1 is no and Q2b is yes then the first has $10 so ask the second about the largest amount[Q3].

----------If Q1 is no, Q2b is yes and Q3 is yes then the first has $10 the third has $20 and the second has $30.

----------If Q1 is no, Q2b is yes and Q3 is no then the first has $10 the second has $20 and the third has $30.

-----If Q1 is no and Q2b is no then the first has $20 so ask the second if he has the largest amount[Q3].

----------If Q1 is no, Q2b is no and Q3 is yes then the third has $10 the first has $20 and the second has $30.

----------If Q1 is no, Q2b is no and Q3 is no then the second has $10 the first has $20 and the third has $30.

You can not depend on answer anyone of them ,since they are all (randomly answerer) to the first question asked.

so you have to ask one of them a (yes) question,then continue asking him the other two questions.