NationStates Jolt Archive

There is a group of three people, we'll call them A, B, and C. One always lies, one always tells the truth, and one lies some of the time and tells the truth some of the time. You do not know which is which. They all know which is which.

Recently, you have been robbed, and you have a suspect, Mr. X. A, B, and C all know whether or not Mr. X was involved in the robbery as you suspect.

The problem is, they have decided you may only ask two questions. Not two questions to each of them, two questions total. Each question is directed at a single person, either A, B, or C, but not all of them. They must be yes-or-no questions.
What two questions do you ask?

You ask C whether Mr. X was involved in the robbery and then ask B whether C was telling the truth?

I'm usually bad at these things...

Do you know who's who?

Do you know who's who?
Oops, I forgot to state that, I need to edit that in.
No, you do not know which is which.

Oops, I forgot to state that, I need to edit that in.
No, you do not know which is which.

Okay. That makes it significantly more difficult. :D

They all answer your two questions right? So ask if Mr. X is guilty then ask if they told the truth. Maybe on Question#1 they'll all say yes or no and you'll know right then.

They all answer your two questions right? So ask if Mr. X is guilty then ask if they told the truth. Maybe on Question#1 they'll all say yes or no and you'll know right then.
I forgot to specify that each question may only be directed at one person. Let me edit that in.
*feels liek an idiot for leaving out such important stuff*

I torture all three of them until the answers seem genuine enough, or they die.

Do the three witnesses know who tells the truth, lies and does both?

Do the three witnesses know who tells the truth, lies and does both?
Yes, they do.

The inclusion of the third one makes it significantly more difficult...

The inclusion of the third one makes it significantly more difficult...
Yeah I strongly Agree

is there any reason why C will lie? (will he lie to keep the truth hidden or just arbitarily)

You ask C whether Mr. X was involved in the robbery and then ask B whether C was telling the truth?
That doesn't work. If C were the truth-teller, then B could be either the half-and-half or the liar, so there's a good chance the second question would be answered with a lie. Or, C might be the liar and B the half-and-half, or vice-versa.

is there any reason why C will lie? (will he lie to keep the truth hidden or just arbitarily)
You don't know which one C is. If he's the truth-teller, he will answer every single question truthfully. If he's the liar, he will give the wrong answer to every single question. If he's the half-and-hlaf, he'll lie some of the time, and tell the truth some.

(( This is what I figured out. It's not complete, and I'm stuck on what to do, but what I have so far sounds pretty reasonable. Tell me if I'm on the right track. ))

Ask A, "If I asked B whether or not Mr. X did it, what would he say?"

If B turned out to be truth/lie person, A could not answer the question in simply "Yes" or "No". Even if A was lying, he could still not answer with either of those two responses.

Now, if B wasn't that truth/lie person, we can safely continue to:

Ask B, "If I asked A whether or not Mr. X did it, what would he say?"

If A said Yes, and B said No, A is lying.
If A said No, and B said Yes, A is still lying.

Ask A, "If I asked B whether or not Mr. X did it, what would he say?"
That's not a yes-or-no question of the sort referred to. All you are allowed to ask is simple logical questions, such as 'Is it true that Mr. X was the thief?", or "Is C the truth-teller?".

EDIT:
Let me clarify a bit.
It has to be yes-or-no in the sense that you could feed it through logic gates. It can be a compound question, it doesn't have to be 'simple' as in one condition. Sorry if I confused anyone with my use of 'simple' where others may have a different definition of it than I.

Ask these two questions

would your freind (doesnt matter which one) be lying to me if he said mr. X was involved in the robbery.

Then you ask the person you asked the previous question about if they would be lying if they said mr. X was involved in the robbery.\

?????

are you ever planning to tell us the answer?

Ask these two questions

would your freind (doesnt matter which one) be lying to me if he said mr. X was involved in the robbery.

Then you ask the person you asked the previous question about if they would be lying if they said mr. X was involved in the robbery.\

?????
But if the one you first asked was the liar, he would say that the other person would be lying to you, even when the one being referred was the truth-teller. Among other things.

EDIT:
are you ever planning to tell us the answer?
Eventually.

But if the one you first asked was the liar, he would say that the other person would be lying to you, even when the one being referred was the truth-teller.

the idea is that there will always be one lie involved, so the answer will always come out as the opposite of the truth, the peoblem is if one of them is C and C is lying.


start a new thread with the answer on it

the idea is that there will always be one lie involved, so the answer will always come out as the opposite of the truth, the peoblem is if one of them is C and C is lying.
But one lie won't always be involved. You could get the truth-teller first, then the half-and-half telling the truth.

Ask A, "If I asked B whether or not Mr. X did it, what would he say?"
That's not a yes-or-no question of the sort referred to. All you are allowed to ask is simple logical questions, such as 'Is it true that Mr. X was the thief?", or "Is C the truth-teller?".

EDIT:
Let me clarify a bit.
It has to be yes-or-no in the sense that you could feed it through logic gates.

Then simply rephrase the question in the appropriate form, frex:

"If I asked B whether or not Mr. X did it, would he say 'yes'?"

When you say 'simple logical questions', does that include questions such as:

If I was to ask the other two people if Mr X is the guilty party, would both say 'yes'?

Then simply rephrase the question:

"If I asked B whether or not Mr. X did it, would he say 'yes'?"
You know, it seems like that might work...

EDIT:
When you say 'simple logical questions', does that include questions such as:

If I was to ask the other two people if Mr X is the guilty party, would both say 'yes'?
Yes.

if both A and B know that C will lie half the time, than they wont be able to answer maany of these questions effectivly

You know, it seems like that might work...

EDIT:

Yes.

So, the three people do know what answers the others would give, and know that one will always lie, one always tell the turth and the other 50/50?

So, the three people do know what answers the others would give, and know that one will always lie, one always tell the turth and the other 50/50?
They know which is which, but I don't know about them knowing which answer will be given in the case of the 50/50 guy.
Grr, monkey wrench.

I really like this tangent though. It seems quite close to finding an entirely different way to solve the problem than the solution I had in mind.

They know which is which, but I don't know about them knowing which answer will be given in the case of the 50/50 guy.
Grr, monkey wrench.


Does monkey wrench boy alternate between telling the truth and lying on a question per question basis? In other words, if we were able to ask him repeatedly 'Is the sky blue?' would he answer YNYNYNY or NYNYNYN?

Does monkey wrench boy alternate between telling the truth and lying on a question per question basis? In other words, if we were able to ask him repeatedly 'Is the sky blue?' would he answer YNYNYNY or NYNYNYN?
I had thought purely random, with a 50/50 chance.

I had thought purely random, with a 50/50 chance.

In that case I have a system which will allow us to ascertain Mr. X's guilt or not five sixths of the time. Hang on will I see if I can tweak it to 100%...

Since they all know who is who. I would ask these questions:

Question 1#: (Directly at C) Which one of you tells the truth all the time?

A lot of random things can come out of that, its 50/50 but its worth it. I'll just assume he says B tells the truth all the time.

Question 2#: (Directly at B) Is Mr.X guilty of stealing my stuff?

Problem solved.

Since they all know who is who. I would ask these questions:

Question 1#: (Directly at C) Which one of you tells the truth all the time?
That's not a yes-or-no question.

Since they all know who is who. I would ask these questions:

Question 1#: (Directly at C) Which one of you tells the truth all the time?

A lot of random things can come out of that, its 50/50 but its worth it. I'll just assume he says B tells the truth all the time.

Question 2#: (Directly at B) Is Mr.X guilty of stealing my stuff?

Problem solved.
Problems: Must be a y/n question, and you don't know which is which.

That's not a yes-or-no question.

Oh yea.

Lets retry that...

Question 1: (Directed at C) Does B tell the truth all the time? Yes or no?

I'll assume he says yes.

Question 2: (Directed at B) Did Mr.X steal by stuff? Yes or no?

Oh yea.

Lets retry that...

Question 1: (Directed at C) Does B tell the truth all the time? Yes or no?

I'll assume he says yes.

Question 2: (Directed at B) Did Mr.X steal by stuff? Yes or no?
But what C is the liar and B tells the truth?

As best I can figure it, the trick is to get the liar and the truth-teller to give the same answer to a question: we know that their response always follows a set of rules.

Here is the best I can do right now (I claimed earlier that I could do it 5/6 of the time, but actually it is only 2/3 of the time that I can get a definite result):

We ask two of the people "If I were to ask the other two 'did Mr. X do it' could both answer in the affirmative?"

If Mr. X did do it, then the truthteller would respond to 'did Mr. X do it' in the affirmative, while the liar would answer in the negative, and monkeywrench-boy would be either affirmative or negative.

Thus the truthteller would answer the asked question with a 'No', as would the liar, while MWboy would give either 'Yes' or 'No'.

We ask this question twice to different people and tabulate our results.

We can either get NN (truth & liar), NN (truth and MWboy 50% of the time), NN (liar and MWboy 50% of the time), NY (truth and MWboy 50% of the time), or NY (liar and MWboy 50% of the time).

So we have got a set of answers which are either NN or NY. Two thirds of the time we will have the answer NN, and one third of the time NY.

Okay...

So suppose that Mr. X didn't do it. What answers would we get then?

We can either get YY (truth & liar), YY (truth and MWboy 50% of the time), YY (liar and MWboy 50% of the time), NY (truth and MWboy 50% of the time), or NY (liar and MWboy 50% of the time).

So we have got a set of answers which are either YY or NY. Two thirds of the time we will have the answer YY, and one third of the time NY.

Thus, by asking this same question twice we can two-thirds of the time determine if Mr. X is guilty or not. If we get a NN set of answers then he is guilty, whereas if we get a YY set of answers he is innocent.

Unfortunately, one third of the time we will get a NY set of answers which does not allow us to determine his guilt.

EDIT: Edited by mistake when I meant to quote part of my own text.

Bump, I guess, for Neo-Anarchists' analysis.

Since I want to hear the answer to this, I'll bump it and suggest my own two questions.

Question #1: To person A: "Is person C capable of telling me that Mr X took my things?"

Question #2: To person B: "Is the person who tells the truth one of either person A or person C?" (just say yes if the truth-teller is one of them, no if its not)

If the answers are "No, Yes", then Mr X did do it, because you'll have identified the truth sayer to be either A or C, which means that since A claims that C is not able to say it, either A is lying or C would have to lie. If the answers are "Yes, Yes" then Mr X did not do it under the same logic. If the answers are "No, No" then Mr X did not do it, and the logic for that is quite abstract and possibly incorrect, but it's basically stating that either person C isn't capable, A is telling the truth and therefore person C would not be capable of telling the truth, thus proving that X didn't do it, or that person A is lying, therefore presuming that person C can say it and since A lied, we can use the "no" answer to question 2 to assume that person C would also lie and is therefore capable of doing so, meaning that Mr X would not do it. A "Yes, No" answer similarly means that Mr X did do it by the same reasoning.

Does that work? *Shrug* I just wanna hear the answer. >_<;

By way of a further bump...

Here is the best I can do right now (I claimed earlier that I could do it 5/6 of the time, but actually it is only 2/3 of the time that I can get a definite result):

We ask two of the people "If I were to ask the other two 'did Mr. X do it' could both answer in the affirmative?"

If I was allowed to ask this question three times, then I would be able to determine Mr. X's guilt beyond a shadow of a doubt 100% of the time -

If he were guilty I'd get NNN or NNY answers.

If he were innocent I'd get YYY or YYN answers.

I really like this tangent though. It seems quite close to finding an entirely different way to solve the problem than the solution I had in mind.

The "If I would ask blabla what his answer would be" approach ? That is the main solution for the famous, simpler version of this riddle, where there are only 2 persons (truthteller and liar) and 1 question. The other one is based on adding an additional condition to the question, like "if I had asked you yesterday if..."

I've never seen this 3 person version before. It's intruiging *is trying to find a nice solution*

Yeah. Orrrrr, you could take my solution, stop playing word games with neurotic criminals, and just torture them. Torture works. Torture is a good reason why questions like these are silly.

No one wants non-clever solutions, though.

Yeah. Orrrrr, you could take my solution, stop playing word games with neurotic criminals, and just torture them. Torture works. Torture is a good reason why questions like these are silly.

No one wants non-clever solutions, though.
Non-clever solutions are underrated. *points shotgun at person C*

Can you ask a different second question depending on the answer to your first question?
I'm trying to work on a solution including the question 'can the 50/50 person tell me mr. x is guilty', which must be answered yes to be true.

There is a group of three people, we'll call them A, B, and C. One always lies, one always tells the truth, and one lies some of the time and tells the truth some of the time. You do not know which is which. They all know which is which.

Recently, you have been robbed, and you have a suspect, Mr. X. A, B, and C all know whether or not Mr. X was involved in the robbery as you suspect.

The problem is, they have decided you may only ask two questions. Not two questions to each of them, two questions total. Each question is directed at a single person, either A, B, or C, but not all of them. They must be yes-or-no questions.
What two questions do you ask?

I shoot A in the kneecap with my 45, and say to the group, "Tell me what I want to know."

If I don't get a satisfactory answer, I repeat this with B.

I don't think it will take more than that.

*Pokes the thread with a stick, causing it to jump in pain to the front page*

Last time, I promise, but hurry up and answer it! >_<;

As best I can figure it, the trick is to get the liar and the truth-teller to give the same answer to a question: we know that their response always follows a set of rules.

Here is the best I can do right now (I claimed earlier that I could do it 5/6 of the time, but actually it is only 2/3 of the time that I can get a definite result):

We ask two of the people "If I were to ask the other two 'did Mr. X do it' could both answer in the affirmative?"

If Mr. X did do it, then the truthteller would respond to 'did Mr. X do it' in the affirmative, while the liar would answer in the negative, and monkeywrench-boy would be either affirmative or negative.

Thus the truthteller would answer the asked question with a 'No', as would the liar, while MWboy would give either 'Yes' or 'No'.

We ask this question twice to different people and tabulate our results.

We can either get NN (truth & liar), NN (truth and MWboy 50% of the time), NN (liar and MWboy 50% of the time), NY (truth and MWboy 50% of the time), or NY (liar and MWboy 50% of the time).

So we have got a set of answers which are either NN or NY. Two thirds of the time we will have the answer NN, and one third of the time NY.

Okay...

So suppose that Mr. X didn't do it. What answers would we get then?

We can either get YY (truth & liar), YY (truth and MWboy 50% of the time), YY (liar and MWboy 50% of the time), NY (truth and MWboy 50% of the time), or NY (liar and MWboy 50% of the time).

So we have got a set of answers which are either YY or NY. Two thirds of the time we will have the answer YY, and one third of the time NY.

Thus, by asking this same question twice we can two-thirds of the time determine if Mr. X is guilty or not. If we get a NN set of answers then he is guilty, whereas if we get a YY set of answers he is innocent.

Unfortunately, one third of the time we will get a NY set of answers which does not allow us to determine his guilt.

EDIT: Edited by mistake when I meant to quote part of my own text.
Hmm... Interesting. It does appear to work 2/3 of the time.
Since I want to hear the answer to this, I'll bump it and suggest my own two questions.

Question #1: To person A: "Is person C capable of telling me that Mr X took my things?"

Question #2: To person B: "Is the person who tells the truth one of either person A or person C?" (just say yes if the truth-teller is one of them, no if its not)
But you could get the truth-teller as person A, the liar as person B, and the half-and-half guy as person C. In that case, the answer to the first question would be "yes" whether or not Mr. X was really involved. Then, B would answer the second question as a negative, being a liar and such. So whether or not Mr. X was really involved, in that situation you'd get two "No"s.

Hmm... Interesting. It does appear to work 2/3 of the time.

And you have a 100% method involving only two questions?

There is a group of three people, we'll call them A, B, and C. One always lies, one always tells the truth, and one lies some of the time and tells the truth some of the time. You do not know which is which. They all know which is which.

Recently, you have been robbed, and you have a suspect, Mr. X. A, B, and C all know whether or not Mr. X was involved in the robbery as you suspect.

The problem is, they have decided you may only ask two questions. Not two questions to each of them, two questions total. Each question is directed at a single person, either A, B, or C, but not all of them. They must be yes-or-no questions.
What two questions do you ask?
This sounds like the investigation in the Jon Benet Ramesy murder.

And you have a 100% method involving only two questions?
Yes, I do.

Yes, I do.
I think I can do it in one question.

Pick one of the men and ask, "If I were to ask you whether Mr X was the burglar, and you chose to answer that question with the same degree of truth as you answer this question, would you then answer 'yes'?"

The truthteller will say "yes" if Mr X was the burglar and "no" otherwise. The liar will answer the same, since he will lie about Mr X, and he will lie about lying. The third man may either lie or tell the truth about this one question, but either way he is behaving like either the truthteller or the liar and thus must correctly answer the question about Mr X.

Okay, it's a compound question. But I think it's right!

I think I can do it in one question.

Pick one of the men and ask, "If I were to ask you whether Mr X was the burglar, and you chose to answer that question with the same degree of truth as you answer this question, would you then answer 'yes'?"

The truthteller will say "yes" if Mr X was the burglar and "no" otherwise. The liar will answer the same, since he will lie about Mr X, and he will lie about lying. The third man may either lie or tell the truth about this one question, but either way he is behaving like either the truthteller or the liar and thus must correctly answer the question about Mr X.

Okay, it's a compound question. But I think it's right!
Interesting. I'll have to ponder that. I'm trying to work out ther third guy's reaction still. It appears to work for the truthteller and the liar though.

ask one of them the answer that would be given by another and go with the opposite answer (this, i think is the answer to another question similar to this but i'll try it anyway). if all else fails perform chinese water torture

Ask one person if they comitted the crime. If yes or no, then ask them did Mr. X commit the crime.


It's that wishy washy guy that's throwing me for a loop.

ask one of them the answer that would be given by another and go with the opposite answer (this, i think is the answer to another question similar to this but i'll try it anyway).
What if you ask the half-and-half guy referring to the liar? You could get a lie and a lie. It doesn't work.

I would start with asking A "Is B more likely to tell me the truth than C?"

If A's answer is 'yes', and:
A always tells the truth, then B is 50/50 guy and C is the liar
A always lies, then B is 50/50 guy and C the truth teller
A is the 50/50 guy, then C is either the truth telling one or the liar

-->: T,50/50,L
L,50/50,T
50/50,-,T/L
So C can't be the 50/50 guy



If A's answer is 'no', and:
A always tells the truth, then B is the liar and C is the 50/50 guy
A Always lies, then B is the truth telling guy and C the 50/50 guy
A is the 50/50 guy, then B is either the truth teller or the liar

-->: T,L,50/50
L,T,50/50
50/50,T/L,-
So B can't be the 50/50 guy


If I'm right thus far, I now know who the tricky 50/50 guy IS NOT. (If the answer was 'yes'
- it can't be C; if 'no - it can't be B)

*gawd, my head hurts!*





So, my second question would be to either B or C:

"If I asked you if Mr. X was guilty, would you say 'yes'?"

I think both the liar and the truth telling guy would answer this question the same way.
The truth telling guy would of course say how it is; 'yes' if X was guilty - 'no', if X was innocent.
The liar would say 'no' if he was innocent - 'yes', if he was guilty.

If the answer to this is 'yes', then X is guilty, if 'no', then he is innocent.


Please let this be right... or even close... (and let the alignment be ok...)

Ask one person if they comitted the crime. If yes or no, then ask them did Mr. X commit the crime.
Huh? Ask a person if that person whom you are asking committed the crime?
What does that accomplish?

Huh? Ask a person if that person whom you are asking committed the crime?
What does that accomplish?
If they are lying. The liar will say yes, the truthteller no.

(Could use a bit more sleep >. >)

I would start with asking A "Is B more likely to tell me the truth than C?"

If A's answer is 'yes', and
A always tells the truth, then B is 50/50 guy and C is the liar
A always lies, then B is 50/50 guy and C the truth teller
A is the 50/50 guy, then C is either the truth telling one or the liar

-->: T,50/50,L
L,50/50,T
50/50,-,T/L
So C can't be the 50/50 guy



If A's answer is 'no', and
A always tells the truth, then B is the liar and C is the 50/50 guy
A Always lies, then B is the truth telling guy and C the 50/50 guy
A is the 50/50 guy, then B is either the truth teller or the liar

-->: T,L,50/50
L,T,50/50
50/50,T/L,-
So B can't be the 50/50 guy.
Err, how can you disqualify people from being one thing or another when the original question is looking for something that works 100% of the time (I.E. with each possible combination of people). It is a part of the condition that B or C could be the 50/50 guy, so your thing there can't work. Can it?
:confused:

If they are lying. The liar will say yes, the truthteller no.

(Could use a bit more sleep >. >)
Ooh. Tricky.
I see what you mean about the 50/50 guy messing it up for you then.

Err, how can you disqualify people from being one thing or another when the original question is looking for something that works 100% of the time (I.E. with each possible combination of people). It is a part of the condition that B or C could be the 50/50 guy, so your thing there can't work. Can it?
:confused:
Well, I certainly thought I could eliminate the 50/50 guy with my 1st question. Maybe I didn't explain well enough how I came to my conclusion. Please, give it another look. I need a break. :)

Well, I certainly thought I could eliminate the 50/50 guy with my 1st question. Maybe I didn't explain well enough how I came to my conclusion. Please, give it another look. I need a break. :)
Ooh, I understand what you meant now. You didn't mean that all situations would be identical.

Your idea might work. I'm not positive about it, but it seems to.

Okay, it's a compound question. But I think it's right!

I ran into problems when I was trying to build compound questions, as it isn't entirely clear if the liar will lie about multiple levels of a question. IF we were to build a compound question which was effectiovely comprised of a series of truth gates, then would the liar determine the correct answer to each initial choice and carry its negation on to the next stage, or would he perform the entire compound operation faithfully and then only negate the final answer?

__________

Side issue:

If we ask "Is your answer to this question 'yes'?" then how does the liar answer?

If he answers 'no' then he is telling the truth.
If he answers 'yes' then he is telling the truth.

Ooh, I understand what you meant now. You didn't mean that all situations would be identical.
The first question is to determine who to ask the 2nd question to, and I certainly don't want to ask the 50/50 guy. I think the question I presented is sufficient to determine that.

The second question is worded the way that both liar and the truth guy would answer the same way.

I thought I nailed it. (but it wouldn't be the first time I thought wrong)

I ran into problems when I was trying to build compound questions, as it isn't entirely clear if the liar will lie about multiple levels of a question. IF we were to build a compound question which was effectiovely comprised of a series of truth gates, then would the liar determine the correct answer to each initial choice and carry its negation on to the next stage, or would he perform the entire compound operation faithfully and then only negate the final answer?
He will negate the final answer.
Side issue:

If we ask "Is your answer to this question 'yes'?" then how does the liar answer?

If he answers 'no' then he is telling the truth.
If he answers 'yes' then he is telling the truth.
Huh, that's wierd.

Interesting. I'll have to ponder that. I'm trying to work out ther third guy's reaction still. It appears to work for the truthteller and the liar though.

It depends on whether the Monkey Wrench Guy is actually capable of or willing to follow the stipulation 'and you chose to answer that question with the same degree of truth as you answer this question'. I've been working under the assumption that he is just randomly generating yes or no answers without examining the questions any further than to determine if they are actually coherent questions. Thus, faced with a question like this he would pause, construe the question as a valid one, and then either metaphorically or literally flip a coin and answer according to its fall.

So, my second question would be to either B or C:

"If I asked you if Mr. X was guilty, would you say 'yes'?"

I think both the liar and the truth telling guy would answer this question the same way.

The truth telling guy would of course say how it is; yes if X was innocent, 'no', if X was guilty.

You have slipped up here:

Q: If I asked you if Mr X was guilty, would you say 'yes'?

True Answer: (if Mr X is guilty) Yes.
True Answer: (if Mr X is not guilty) No.

False Answer: (if Mr X is guilty) No.
False Answer: (if Mr X is not guilty) Yes.

However, if you are certain that you have identified the 50/50 guy and aren't asking him the question, then you could ask 'If I asked the other guy who isn't the 50/50 dude if Mr X was guilty, would he say 'yes'?'

If Mr X is guilty, the truthteller would say 'no'.
If Mr X is innocent, the truthteller would say 'yes'.

If Mr X is guilty, the liar would say 'no'.
If Mr X is innocent, the liar would say 'yes'.

The pair would both answer in the same way: if they say 'no' then X is guilty, if they say 'yes' he is innocent.

You have slipped up here:

Q: If I asked you if Mr X was guilty, would you say 'yes'?

True A: (if Mr X is guilty) Yes.
True A: (if Mr X is not guilty) No
Oh, right. Sorry. 3 am here. :)

Will edit it.

Interesting. I'll have to ponder that. I'm trying to work out ther third guy's reaction still. It appears to work for the truthteller and the liar though.
This is where I've pinned down the third guy. Or so I claim. You decide.

... and you chose to answer that question with the same degree of truth as you answer this question ...


That's kind of why the question came out as such a mouthful.

Oh, right. Sorry. 3 am here. :)

Will edit it.

I've given you a version that would work as a second question in my edit to the post up the page...

http://forums2.jolt.co.uk/showpost.php?p=8937730&postcount=66

It depends on whether the Monkey Wrench Guy is actually capable of or willing to follow the stipulation 'and you chose to answer that question with the same degree of truth as you answer this question'. I've been working under the assumption that he is just randomly generating yes or no answers without examining the questions any further than to determine if they are actually coherent questions. Thus, faced with a question like this he would pause, construe the question as a valid one, and then either metaphorically or literally flip a coin and answer according to its fall.
Damn. This makes the situation far more complicated.

Now I'm confused, as this is one I don't know the answer to. And apparently a very important one.

I would think that it would make sense to specify that he lies or does not lie based on the random chance, but does not purely answer 'yes' or 'no' randomly, but I'm not sure whether that really makes sense or not.

Damn. This makes the situation far more complicated.

Now I'm confused, as this is one I don't know the answer to. And apparently a very important one.

Shifting sands. I love 'em.

Shifting sands. I love 'em.
This is a logic problem. You have to bound it somewhere.

I've given you a version that would work as a second question in my edit to the post up the page...

http://forums2.jolt.co.uk/showpost.php?p=8937730&postcount=66
Thanks. I'm sure I could make it work, but at the moment I'm so tired I'm afraid I've butchered it with my editing. I'm looking forward reading this thread tomorrow.

And your question is what I was after. :D

This is a logic problem. You have to bound it somewhere.

Indeed. I'm sure I don't need to talk to you about black swans. The question is whether the original formulation is rigorous enough to allow a solution to be clearly understood as a correct one of not.

I would start with asking A "Is B more likely to tell me the truth than C?"

...

If I'm right thus far, I now know who the tricky 50/50 guy IS NOT. (If the answer was 'yes'
- it can't be C; if 'no - it can't be B)

Goddamnit. This actually works.

Indeed. I'm sure I don't need to talk to you about black swans. The question is whether the original formulation is rigorous enough to allow a solution to be clearly understood as a correct one of not.
Sure, you're right. I just decided to bound my own problem. It's a lot tougher if you leave the wildcard guy with no constraints. I don't know if two questions would solve that case. Kinda like thermodynamics where defining the system the right way makes the answer real easy or real hard.

Sure, you're right. I just decided to bound my own problem. It's a lot tougher if you leave the wildcard guy with no constraints. I don't know if two questions would solve that case.

I think Bunnyducks has cracked it.

First:

I would start with asking A "Is B more likely to tell me the truth than C?"

...

If I'm right thus far, I now know who the tricky 50/50 guy IS NOT. (If the answer was 'yes'
- it can't be C; if 'no - it can't be B)

If the answer is yes, we ask C "'If I asked B if Mr X was guilty, would he say 'yes'?"

If the answer is no, we ask B "'If I asked C if Mr X was guilty, would he say 'yes'?"

If their answer is no, then Mr. X is guilty.
If their answer is yes, then Mr. X is innocent.

I say they are all guilty and throw them into prison. Problem solved.

I do believe Bunnyducks' method works.
It works on a similar principle to the one I had in mind, yet it's done in a much simpler method. And apparently it still works.

EDIT:
BWO, I think your summary of the method is a bit off.
If the answer is yes, we ask C "'If I asked B if Mr X was guilty, would he say 'yes'?"

If the answer is no, we ask B "'If I asked C if Mr X was guilty, would he say 'yes'?"
Isn't that involving the 50/50 guy, because all you know is that either C isn't it or B isn't it?

I say they are all guilty and throw them into prison. Problem solved.

And thence to a three-way prisoners' dilemma* no doubt.





*trilemma?

I do believe Bunnyducks' method works.
It works on a similar principle to the one I had in mind, yet it's done in a much simpler method. And apparently it still works.

Time for you to spill your beans.

Time for you to spill your beans.
My method was this:
The question I would ask once I knew I had the liar or the truth-teller is this.
"Is it the case that the statements that you are a truth-teller and Mr. X was involved are either both true or both false?"
This question forces the liar and the truth-teller to both give the same answers.
Like this.
If A is a liar, and Mr. X is guilty, it is the case that both are false. So A lies, and says "Yes."
If A is a liar, and Mr. X is innocent, then it is the case that one is true and the other false. So A lies, and says "No".
If A is a truth-teller, and Mr. X is guilty, then both are true, so A answers "Yes".
If A is a truth-teller, and Mr. X is innocent, then one is false and one true, so A answers "No.
So if the answer is "No", then Mr. X is innocent, if "Yes", then he is guilty.

So, how is it that I will narrow it down to knowing that a certain person is either the liar or the truth-teller, so that I may ask him the question?

With a similar question.
"Is it the case that the statements that you are a truth-teller and C is the 50/50 guy either both true or both false?"
If I ask either the liar or the truth-teller, I get a correct answer as to whether or not C is the 50/50 guy.
So what happens if the one I pick to ask is the 50/50 guy?
It doesn't matter, because no matter what he answers, it will lead me to picking one of the others, who will both answer the same.

So here's my method.

First question, directed at A: "Is it the case that the statements that you are a truth-teller and C is the 50/50 guy either both true or both false?"
If "Yes", then I ask B the next question.
If "No", then I ask C the next question.

Second question: "Is it the case that the statements that you are a truth-teller and Mr. X was involved are either both true or both false?"
If "Yes", then Mr. X is quilty. If "No", then Mr. X is innocent.


Wow, my method is much too long-winded.

EDIT:
Argh, I must sleep now. I will be back sometime tomorrow.

I think Bunnyducks has cracked it.

First:



If the answer is yes, we ask C "'If I asked B if Mr X was guilty, would he say 'yes'?"

If the answer is no, we ask B "'If I asked C if Mr X was guilty, would he say 'yes'?"

If their answer is no, then Mr. X is guilty.
If their answer is yes, then Mr. X is innocent.

The more I look at it, the more I think Bunny Ducks is right, too. The word "likely" just doesn't sit well and I cannot find a reason why it's wrong. That even sits worse :).

Good job.

Thanks for clearing my second question BWO. I could make it work in Finnish, but something went wrong when I wrote my answer in English. :)

Hmmm... maybe the word 'likely' isn't the best possible Myrmidonisia (I couldn't tell), but no worries, you can substitute it with something else. "Is it probable that B will answer more thruthfully than C?" perhaps ;)

Did you make this question up by yourself N-A? ...Or is there an article or a site I can find the solution/more about this?

Furthermore, can you determine who is who (of the witnesses) with less than three yes/no questions? I seem to need 3 questions to be 100% sure. (maybe I need to be tired when doing this)

Thanks for clearing my second question BWO. I could make it work in Finnish, but something went wrong when I wrote my answer in English. :)

No, I'm afraid I mangled it in later versions too - I kept on assuming that we knew which of B and C were which. We do need to ask it in the form:

"If I asked the other man who isn't the 50/50 guy if Mr X was guilty, would he say 'yes'?"

and not

"If I asked B if Mr X was guilty, would he say 'yes'?"

Right you are. I kinda ran out of steam after I figured out how to eliminate the 50/50 guy.

About that question of mine (how to determine who is who)...
Asking the first Q, 'Is it probable that B will answer more thruthfully than C?' to exclude the 50/50 guy, and then asking something simple like 'Is the chair you sit on blue?' would do it with 2 questions, right?

EDIT: Damn! No... I would just know if he was the compulsive liar or the truth telling guy - nothing about the two other guys...
Thus third question is needed. If he answered 'yes', he is the truthteller and I can ask him directly 'is that guy 50/50?'. If 'no' I ask him the same and just distrust his answer...

Right you are. I kinda ran out of steam after I figured out how to eliminate the 50/50 guy.

About that question of mine (how to determine who is who)...
Asking the first Q, 'Is it probable that B will answer more thruthfully than C?' to exclude the 50/50 guy, and then asking something simple like 'Is the chair you sit on blue?' would do it with 2 questions, right?

EDIT: Damn! No... I would just know if he was the compulsive liar or the truth telling guy - nothing about the two other guys...
Thus third question is needed. If he answered 'yes', he is the truthteller and I can ask him directly 'is that guy 50/50?'. If 'no' I ask him the same and just distrust his answer...

Hmmm. I'll have a think about this one.

In the meantime...

What happens if we ask the question?:

"Can the other two men answer this question in the affirmative?"

(actually we can ignore the existence of the 50/50 dude for this one and just consider the truthteller and the liar on their own being asked the question "can the other man answer this question in the affirmative?")


EDIT:

Here's a bit of a cheating way to determine who is who in only two answerable questions -

We ask A "Can the other two men answer this question in the affirmative?" If he is able to answer this question then he is the 50% dude, if he isn't then we haven't actually asked an answerable question. A question which cannot be answered by any means is not a question, and so if he doesn't answer we haven't used up a question. We repeat this for B and if he answers he is 50% dude. If he doesn't then we know that C is 50%.

Then we ask one of the men we know not to be 50% dude this question "Is your answer to thie question 'yes'?" If he is able to answer it, then he is the turthteller.

Thus we could determine who is whom without actually getting an answer to any questions if we are lucky enough to put these questions to them in the correct order...

Shameful, I know.

Shameful, I know.
LOL
I love it! It's kinda like when a Genie tells you that you only have three wishes - Now, what's your first wish?" ...And you immediately wish for infinite amount of wishes.

Don't know about that "can the other man answer this question in the affirmative?" though. My english must fail me. It seems like a non-question to me... please elaborate.

LOL
I love it! It's kinda like when a Genie tells you that you only have three wishes - Now, what's your first wish?" ...And you immediately wish for infinite amount of wishes.

Don't know about that "can the other man answer this question in the affirmative?" though. My english must fail me. It seems like a non-question to me... please elaborate.

"Could the other two men answer this question with 'yes'?" - if we aren't ignoring the 50% dude.

"Could the other man answer this question with 'yes'?" - if we are ignoring his existence for the moment to make the paradox clearer.

If the liar says 'yes', then the truthteller also has to say 'yes', which means the liar must actually say 'no', which means the truthteller has to say 'no', which means the liar has to say 'yes'...

Oh, right. If we aren't ignoring the 50/50 guy, it wouldn't work, would it..? We don't know wether we are asking the liar or the truthteller...

But if we ignore him... then...yes... seems to work.
Must.Do.Calculations.

EDIT: Umm...we'd find out who the one this questions is directed to is. But how could we determine who the other two are from this? Seems to me like a third question is still needed... (now i know why this is better to be done in the wee hours of the night; something distracts me every 5 minutes!)

Oh, right. If we aren't ignoring the 50/50 guy, it wouldn't work, would it..? We don't know wether we are asking the liar or the truthteller...

But if we ignore him... then...yes... seems to work.
Must.Do.Calculations.

It is a question that only the 50% dude can provide an answer to, as he is not actually constrained by rules of logic, but just randomly generates a Yes or No response.

A-ha! You are playing that card again. :D
Very clever approach, I must admit.

EDIT: I have to say I never thought of constructing a question only the 50/50 guy could answer. I just thought of him like something I must get rid of in order to reach a solution of some kind. Well done sir/ma'am! Opened my eyes.

Bump for Neo-Anarchists and Myrmidonisia to rip my ploy to shreds.

Did you make this question up by yourself N-A? ...Or is there an article or a site I can find the solution/more about this?
I wish I had come up with it. I read about it a few months ago in a book, and it rendomly popped into my memory again recently.
It may have a name or something, I'm really not sure.
"Could the other two men answer this question with 'yes'?" - if we aren't ignoring the 50% dude.

"Could the other man answer this question with 'yes'?" - if we are ignoring his existence for the moment to make the paradox clearer.

If the liar says 'yes', then the truthteller also has to say 'yes', which means the liar must actually say 'no', which means the truthteller has to say 'no', which means the liar has to say 'yes'...
Interesting idea. I wouldn't have thought of trying to actually utilize the 50/50 guy.

Interesting idea. I wouldn't have thought of trying to actually utilize the 50/50 guy.

It doesn't directly help us to acertain Mr. X's guilt (or not) in less than two questions, unless we are lucky enough to put the first question to the 50/50 dude (1/3 chance) and then the second question to the liar (1/2 chance). 1/6 of the time we could determine his guilt getting an answer to only one question though...