94 replies to this topic

[ShawnInToronto]

Ask person A the first question:

"Would you currently answer yes to the statement 'I sometimes tell the truth and sometimes lie' ?"

If A is the truth teller, he will truthfully say no.
If A is the liar, he would say yes to 'I sometimes tell the truth and sometimes lie', but will lie about his agreement, answering no.
If A is the random in the truth-telling mood, he would truthfully answer yes.
If A is the random in the lying mood, he would not answer yes to 'I sometimes tell the truth and sometimes lie', but will lie and say he would, answering yes.

If A answered yes, we know he is random. We then ask B a second question 'Would C say that you are a liar ?'. If B says yes, he is the truth-teller and C is the liar; if he says 'no' he is the liar and C is the truth-teller. In this case we know the identies of all three with two questions.

If A answered no, we know he is either the truth-teller or the liar. Ask him a second question 'Would B or C ever agree that you are a liar ?". If yes , A is the truth-teller. If no, A is the liar. Know we know whether A is a liar or truth-teller with one question left. Ask him the last question, 'Is B random ?'.

If A is the truth-teller, yes implies B random, C liar. No implies B liar, C random.

If A is the liar, yes implies B liar, C random. No implies C liar, B Random.

All three identies known with only 3 yes / no questions.

[Prime]

This is a very interesting problem. After checking the posts, I see that Writersblock had solved it a year ago. The solution that I found is the same in essence. Though, I found a different kind of relation between the three men (other than LEFT RIGHT).

Spoiler for Another relation:

Let's designate the men as 1, 2, and 3. There are six possible arrangements for them to be Truth-teller (T), Liar (L), and Random R:

1 2 3
T L R
T R L
L T R
L R T
R T L
R L T

The first question must get rid of Random in one of the positions, otherwise the problem is unsolvable. So you ask the man 1:
1) Is it possible for 2 to tell truth more often than 3?
T in the first arrangement would answer "NO". T in the second arrangement would answer "YES".
L in the 3rd arrangement would answer "NO". L in the 4th arrangement would answer "YES".
(For it is not possible for R to tell truth more often than T, and for L more often than R.)
And we don't care what Random would answer, for her answer gives no useful information.

Thus "YES" leaves us with 4 possible arrangements:
1 2 3
T R L
L R T
R T L
R L T
Here man 3 can only be either L or T, but not R.

"NO" will leave for us:
1 2 3
T L R
L T R
R T L
R L T
Where man 2 can only be L or T, but not R.

The second question would be directed to the man who can be only T or L:
2) Are you a Random-teller? To which T answers "NO" and L answers "YES".
And the third final question to the same man would be:
3) Is man 1 a Random-teller? Which would narrow your choice to just one possible arrangement.

Edited by Prime, 16 August 2008 - 05:47 PM.

[aly410]

i have a solution too and it seems simple:D

so:
we have 1 2 3
We ask 1:" do i have 5 figers at one hand?" ( and i do ) )
He answers: NO => 1 = L
then i ask 1 : " is 2 random?" => he answers yes =>2= T and 3 = R
no => 2 = R ; 3 = T

He answers YES: => 1 = T or R
then i ask 2" is 1 L?" => YES => 2 = L then i ask 2" is 1 T?" => YES => 1= R and 3= T
NO => 1= t and 3= R
=> NO => 2 = R or T and 3 = L ; so i ask 3 "if 1 is T?" = > YES => 1=R and 3=T
NO => 1= T and 3 = R

Is it OK ?

[achemaromba]

establish which man is the truth-teller. ask man1(m1) if he always speaks truth. if he replys no ask m2 the same question. if he replys no, u know m3 is the truth-teller. ask him if the man to his left (or right) always lies. weather he replies yes or no you can deduce who the remaining 2 men are. if u find the truth teller on the first question u can find out in 2 questions

[Martini]

establish which man is the truth-teller. ask man1(m1) if he always speaks truth. if he replys no ask m2 the same question. if he replys no, u know m3 is the truth-teller.

That won't work; two men can't answer that question with a "no".

[Phatfingers]

i have a solution too and it seems simple:D

so:
we have 1 2 3
We ask 1:" do i have 5 figers at one hand?" ( and i do ) )
He answers: NO => 1 = L
then i ask 1 : " is 2 random?" => he answers yes =>2= T and 3 = R
no => 2 = R ; 3 = T

He answers YES: => 1 = T or R
then i ask 2" is 1 L?" => YES => 2 = L then i ask 2" is 1 T?" => YES => 1= R and 3= T
NO => 1= t and 3= R
=> NO => 2 = R or T and 3 = L ; so i ask 3 "if 1 is T?" = > YES => 1=R and 3=T
NO => 1= T and 3 = R

Is it OK ?

You have a problem if 1 is Random. He might answer "NO".

[Phatfingers]

There is a truth teller (always tells the truth), a liar (always lies), and one that sometimes answers truthfully and sometimes lies. Each man knows who is who. You may ask three yes or no questions to determine who is who. Each time you ask a question, it must only be directed to one of the men (of your choice). You may ask the same question more than once, but of course it will count towards your total. What are your questions and to whom will you ask them?

Spoiler for Yet another solution...

1. Ask A if C is Random
2. Ask B if C could affirm that A's answer was truthful.
If both give the same answer, then C is non-random, otherwise A is non-random.
3. Ask the non-random person if 0+1=1.

If the answers to questions 1, 2, 3 are:

NNN: A=Random, B=Truthteller, C=Liar
NNY: A=Liar, B=Random, C=Truthteller
NYN: A=Liar, B=Truthteller, C=Random
NYY: A=Truthteller, B=Random, C=Liar
YNN: A=Liar, B=Truthteller, C=Random
YNY: A=Truthteller, B=Random, C=Liar
YYN: A=Random, B=Truthteller, C=Liar
YYY: A=Random, B=Liar, C=Truthteller

[Prime]

Spoiler for Yet another solution...

1. Ask A if C is Random
2. Ask B if C could affirm that A's answer was truthful.
If both give the same answer, then C is non-random, otherwise A is non-random.
3. Ask the non-random person if 0+1=1.

If the answers to questions 1, 2, 3 are:

NNN: A=Random, B=Truthteller, C=Liar
NNY: A=Liar, B=Random, C=Truthteller
NYN: A=Liar, B=Truthteller, C=Random
NYY: A=Truthteller, B=Random, C=Liar
YNN: A=Liar, B=Truthteller, C=Random
YNY: A=Truthteller, B=Random, C=Liar
YYN: A=Random, B=Truthteller, C=Liar
YYY: A=Random, B=Liar, C=Truthteller

Just looking at your first case, NNN could mean A=Truth-teller, B=Random, C=Liar; or A=Random, B=Truth-teller, C=Liar. So those three questions do not resolve who is who. Correspondingly, your arrangement for the YNY implies that the Truth-teller lied to the first question. As well the YNN arrangement implies that the Liar answered the first question truthfully...

Edited by Prime, 20 January 2009 - 08:11 AM.

[Phatfingers]

Just looking at your first case, NNN could mean A=Truth-teller, B=Random, C=Liar; or A=Random, B=Truth-teller, C=Liar. So those three questions do not resolve who is who.

If A is Random, then his "No" answer to Q1 is a lie.
If C is Liar, then his affirmation of Q2 would be "Yes".
B therefore must answer yes, making "NNN" an impossibility for combination RTL.

Correspondingly, your arrangement for the YNY implies that the Truth-teller lied to the first question. As well the YNN arrangement implies that the Liar answered the first question truthfully...

Got me there. I originally solved it where A and C were asked the questions of B and I tried to swap them in my head as I was transcribing. Let's see if it was a transcription error or a logic error:

YNY should imply:
A is determined non-random, therefore A is asked second question, and proven truthful.
Truthful A claimed C is Random, so C is Random and B is Liar.
YNY should have equated to A=Truthteller, B=Liar, C=Random

YNN should imply:
A is determined non-random, therefore A is asked second question, and proven a liar.
Liar A claimed C is Random, so C is Truthteller and B is Random.
YNN should have equated to A=Liar, B=Random, C=Truthteller

Yup. I shouldn't try to sort and copy at the same time... I still assert (randomly?) that the logic is sound. The questions are sufficient to determine who's who.

[IDoNotExist]

There is a truth teller (always tells the truth), a liar (always lies), and one that sometimes answers truthfully and sometimes lies. Each man knows who is who. You may ask three yes or no questions to determine who is who. Each time you ask a question, it must only be directed to one of the men (of your choice). You may ask the same question more than once, but of course it will count towards your total. What are your questions and to whom will you ask them?

Spoiler for Answer<br />

First, have them stand next to each other facing you, 1,2,3. Ask (2) if there is a liar or a truth teller on either side of him.

Spoiler for If (2) answers 'yes:

than (2) is either a truth teller or random. Realign the men so that the original middle guy, (2), is now on the outside, such as (2),(3),(1). Ask (3) if there is a truth teller or random on either side of (3).

Spoiler for If (3) answers 'yes:

Than you know (3) is either a truth teller or random, making the other man, (1), the liar by process of elimination. Point to one of the men you know to be either a truth teller or random, at this point in the example either (2) or (3), and ask the liar, (1), if the man you are pointing to is a truth teller. If the liar says no, the man you are pointing to is a truth teller. If the liar says yes, than the man you are pointing to is random.

If (3) answers 'no' than (3) is the Liar. Point to one of the men you know to be either a truth teller or random, at this point in the example either (2) or (1), and ask the liar, (3), if the man you are pointing to is a truth teller. If the liar says no, the man you are pointing to is a truth teller. If the liar says yes, than the man you are pointing to is random.

If (2) answers 'no' than (2) is the liar. Point to one of the men you know to be either a truth teller or random, at this point in the example either (1) or (3), and ask the liar, (2) if the man you are pointing to is a truth teller. If the liar says no, the man you are pointing to is the type of man you asked about. If the liar says yes, than he is the other man.