Logic puzzle
There are 5 men in front of you. One of them ALWAYS tells the truth, and the other 4 will alternate between telling the truth and lying. However, you do NOT know which state each of the 4 will start out. But, if they lie the first time, they MUST tell the truth the second time, and vice-versa.
The goal: Locate the one man who ALWAYS tells the truth.
The challenge: You are only allowed to ask two questions, and each question can only be asked to one man. No group questions. You may ask each question to a different man, or you may ask both questions to the same man.
The goal: Locate the one man who ALWAYS tells the truth.
The challenge: You are only allowed to ask two questions, and each question can only be asked to one man. No group questions. You may ask each question to a different man, or you may ask both questions to the same man.
>> #1 A1: 2345 A2: 1235 - this means #1 was a liar, but #4 is a truth teller
What if the answer was A1: 1234 A2: 1235 ?
What if the answer was A1: 1234 A2: 1235 ?
>What if the answer was A1: 1234 A2: 1235 ?
Couldn't happen with the rules. (We're asking #1 right now.)
Assume #1 is a liar. He can't say his number both times.
Assume #1 is truthful. He can't say his number at all.
Couldn't happen with the rules. (We're asking #1 right now.)
Assume #1 is a liar. He can't say his number both times.
Assume #1 is truthful. He can't say his number at all.
>> Assume #1 is a liar. He can't say his number both times.
Why not ? If he's lying, he can say anything he wants, as long as it's not the truth.
If 5 is the truth teller, then his first answer (1234) would be truthful, and his second answer (1235) would be a lie.
Why not ? If he's lying, he can say anything he wants, as long as it's not the truth.
If 5 is the truth teller, then his first answer (1234) would be truthful, and his second answer (1235) would be a lie.
That depends on the definition of a lie. These puzzles often confuse lying with saying the exact logical opposite of truth (the truth with a non-spoken logical “not” before the sentence). A lie more generally is a statement that is false, which is not the same thing.
If he couldn't include himself twice, then he couldn't include any liar twice, forcing answers like A1:4, A2:1235 — he can't include himself or the liar 2 in the first answer, because that information would not be a lie if provided alone...
(°v°)
If he couldn't include himself twice, then he couldn't include any liar twice, forcing answers like A1:4, A2:1235 — he can't include himself or the liar 2 in the first answer, because that information would not be a lie if provided alone...
(°v°)
Sorry, that was nonsense. All I wanted to say was that a lie is not necessarily a combination of false statements, only one needs to be false to make the whole statement false.
(°v°)
(°v°)
>> These puzzles often confuse lying with saying the exact logical opposite of truth
If that were the case, then you'd need only one question : "who is the truth teller ?"
If he points out 1 person, then he's telling the truth. If he points out 4 persons, then he's lying, and the one not mentioned is the truth teller.
If that were the case, then you'd need only one question : "who is the truth teller ?"
If he points out 1 person, then he's telling the truth. If he points out 4 persons, then he's lying, and the one not mentioned is the truth teller.
>> All I wanted to say was that a lie is not necessarily a combination of false statements, only one needs to be false to make the whole statement false.
Agreed.
Agreed.
Wouldn't
#1 A1: 1234 also be a lie?
#1 A1: 1234 also be a lie?
>> #1 A1: 1234 also be a lie?
If 5 is the truth teller, then 1234 would be a truthful answer to the question "who of you tell lies ?", no ? Am I missing something ?
If 5 is the truth teller, then 1234 would be a truthful answer to the question "who of you tell lies ?", no ? Am I missing something ?
^ therein lies the problem. Is each response (1&2&3&4) or the entire statement evaluated.
Even so then I'm with Infinity08 where A1: 1234 A2: 1235 means that #1 is a liar and #5 is truthful...Answer2 would be the truth.
Even so then I'm with Infinity08 where A1: 1234 A2: 1235 means that #1 is a liar and #5 is truthful...Answer2 would be the truth.
Maybe you consider "who of you tell lies ?" to be a different question than "who of you are capable of telling lies ?" ? To me, they are the same.
ASKER
"Even so then I'm with Infinity08 where A1: 1234 A2: 1235 means that #1 is a liar and #5 is truthful...Answer2 would be the truth."
Not so. Given Q1 & Q2 are both "who tells lies?" You have no way of distinguishing if A1 is true or A2 is true.
Consider: #5 is the one who always tells the truth (as you positted above).
A1 could equally be true and A2 could equally be a lie.
Not so. Given Q1 & Q2 are both "who tells lies?" You have no way of distinguishing if A1 is true or A2 is true.
Consider: #5 is the one who always tells the truth (as you positted above).
A1 could equally be true and A2 could equally be a lie.
Question for you, exx1976 : do you know the solution ? Or are you also trying to find it ?
(fase statement and true statement) = false statement
(false statement or true statement) = true statement
(false statement or true statement) = true statement
ASKER
I do know the solution, yes.
>Given Q1 & Q2 are both "who tells lies?" You have no way of distinguishing if A1 is true or A2 is true.
Yep. See that now.
Yep. See that now.
"If my next question to you is 'who is a person of the same type as you?' what person could you indicate?"
Q1. Take the number of the person who tells the truth and multiply that number by one if you are telling the truth and by zero if lying. What is the result?
Q2. Take the number of the person who tells the truth and multiply that number by one if you are telling the truth and by zero if lying. What is the result?
Q2. Take the number of the person who tells the truth and multiply that number by one if you are telling the truth and by zero if lying. What is the result?
ASKER
You are allowed to ask questions, not ask them to perform mathematical calculations. In addition, you assume they are numbered. Let's call them Bill, Joe, Bob, Jim, and Julio.
Ask Bill this question twice : What would each of the others answer if I asked them whether 1 + 1 = 2 ?
If Bill is the truth teller, then he'll give the same answer twice for all 4 others.
If Bill is not the truth teller, then he'll give the same answer twice for 3 of the others, but will give different answers for the truth teller.
If Bill is the truth teller, then he'll give the same answer twice for all 4 others.
If Bill is not the truth teller, then he'll give the same answer twice for 3 of the others, but will give different answers for the truth teller.
I guess that won't work for the same reason I pointed out earlier.
Q1 If I were to ask the person who always tells the truth to tell me their name twice, what would those names be?
Q2 If I were to ask the person who always tells the truth to tell me their name twice, what would those names be?
Q2 If I were to ask the person who always tells the truth to tell me their name twice, what would those names be?
Also, about http:#33076455 A1:2 A2:3 — one answer was a lie...
I was thinking about this question: do you tell lies?
If not, the next answer will be truthful, so it's solved. If yes, the next will be a lie, but how to use that?
(°v°)
I was thinking about this question: do you tell lies?
If not, the next answer will be truthful, so it's solved. If yes, the next will be a lie, but how to use that?
(°v°)
A1 Joe/Joe
A2 Bob/bob
A2 Bob/bob
ASKER
Not so.
Consider: What if Bill initially lies, but the other 3 initially tell the truth? Since they have not been asked a question, they will still be willing to tell the truth.
You ask Bill, and he is a liar. So he says "They will all tell you that is incorrect." Now he tells the truth, so he says "They will all tell you that is correct."
The problem is that you don't know in what state each of the others will start (lie or truth), and they are independent of one another.
Consider: What if Bill initially lies, but the other 3 initially tell the truth? Since they have not been asked a question, they will still be willing to tell the truth.
You ask Bill, and he is a liar. So he says "They will all tell you that is incorrect." Now he tells the truth, so he says "They will all tell you that is correct."
The problem is that you don't know in what state each of the others will start (lie or truth), and they are independent of one another.
>> A1 Joe/Joe
>> A2 Bob/bob
That was in response to moorhouselondon btw.
>> A2 Bob/bob
That was in response to moorhouselondon btw.
ASKER
33076552 was in response to 33076512
>> Not so.
In http:#33076512, I forgot to explicitly specify something. The second question would not be exactly the same. I should have said :
Ask Bill the following two questions :
What would each of the others answer if I asked them whether 1 + 1 = 2 as their first question ?
What would each of the others answer if I asked them whether 1 + 1 = 2 as their second question ?
With the caveat that I think it's probably against the rules ...
In http:#33076512, I forgot to explicitly specify something. The second question would not be exactly the same. I should have said :
Ask Bill the following two questions :
What would each of the others answer if I asked them whether 1 + 1 = 2 as their first question ?
What would each of the others answer if I asked them whether 1 + 1 = 2 as their second question ?
With the caveat that I think it's probably against the rules ...
Q1 If I were to ask the person who always tells the truth to tell me their name twice, what would those names be?
Q2 What is the name of the person who tells the truth?
Q2 What is the name of the person who tells the truth?
>> Q1 If I were to ask the person who always tells the truth to tell me their name twice, what would those names be?
>>
>> Q2 What is the name of the person who tells the truth?
A1 : Joe/Joe
A2 : Bob
>>
>> Q2 What is the name of the person who tells the truth?
A1 : Joe/Joe
A2 : Bob
ASKER
Re: 33076581
Indeed, you're simply proxying 5 questions through one individual.
Additionally, you are working under the assumption that Bill knows in which state the others will start. What if he only knows WHO will lie, but not if they start lying or telling the truth?
Re: 33076588
A1: Joe/Joe
A2: Julio
How does that help?
Indeed, you're simply proxying 5 questions through one individual.
Additionally, you are working under the assumption that Bill knows in which state the others will start. What if he only knows WHO will lie, but not if they start lying or telling the truth?
Re: 33076588
A1: Joe/Joe
A2: Julio
How does that help?
My first reaction was in fact:
Q: Will you answer my question with a lie?
A: no
The answer “yes” would be a paradox, hence forcing liars to start with the truth. But I could not find a similar trick to force a lie out of liars.
(°v°)
Q: Will you answer my question with a lie?
A: no
The answer “yes” would be a paradox, hence forcing liars to start with the truth. But I could not find a similar trick to force a lie out of liars.
(°v°)
>> Additionally, you are working under the assumption that Bill knows in which state the others will start.
I indeed assumed that each of the 5 would know the start states of all of the others. I guess that's not the case. That complicates (or simplifies depending on pov) things.
I indeed assumed that each of the 5 would know the start states of all of the others. I guess that's not the case. That complicates (or simplifies depending on pov) things.
ASKER
Well, your assumption may or may not be true. The fact of the matter is that the initial question gave all information that is known for certain, so anything else would be a gamble.
If they don't know that, they might not be able to answer with the truth or with a lie, something the problem states they must do. If asked something they don't know ("will Bob lie to me?"), they can only answer "I don't know", the truth, because the answers "yes" or "no" might be a lie or the truth. When they are forced to produce a lie, they need to know the truth. Or is that flawed somehow?
Ah, yes. The truth-sayer can be totally ignorant and answer "I don't know" to any question asked. It's so much easier to be honest...
(°v°)
Ah, yes. The truth-sayer can be totally ignorant and answer "I don't know" to any question asked. It's so much easier to be honest...
(°v°)
ASKER CERTIFIED SOLUTION
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Sounds good. It's silly: I had discarded "show me a liar" to use the lie, but I can't remember why. Thanks, I can go sleep now! — (^v°)
Ask any of them "do you ever lie?"
Answer Yes - Can't come from truth teller so it's a 50:50er you're asking and their next answer must be a lie so ask them to point to a 50:50er and they'll point to the truth teller.
Answer No must come from a 50:50er and their next answer must be tru so ask them to point to the truth teller.
Answer Yes - Can't come from truth teller so it's a 50:50er you're asking and their next answer must be a lie so ask them to point to a 50:50er and they'll point to the truth teller.
Answer No must come from a 50:50er and their next answer must be tru so ask them to point to the truth teller.
Scratch that, and Ozo's already answered it.
Yours is still valid, andyalder.
Yes, it's right but 3rd paragraph is a bit mis-worded, should say whether it comes from truth teller or 50:50er they'll still point to the truth teller when asked to do so.
yep :)
ASKER
Well done, guys. The solution I came up with was similar:
Q1: Are you the truthteller?
A1: Yes - is either a lie or you have asked the truthteller. This means that the next answer will be truthful, so
Q2: Who is the truthteller?
A1: No - You asked a 50/50 and he told the truth. The next question will be a lie, so
Q2: Which man is NOT the truthteller?
Points to ozo.
Q1: Are you the truthteller?
A1: Yes - is either a lie or you have asked the truthteller. This means that the next answer will be truthful, so
Q2: Who is the truthteller?
A1: No - You asked a 50/50 and he told the truth. The next question will be a lie, so
Q2: Which man is NOT the truthteller?
Points to ozo.
I have Puzle on the file atached can somoene help to find out the meaning of this
Puzle.docx
Puzle.docx
Micolo try this link to post your question
Just posting here and in the closed Geocaching thread limits your audience to participants in these threads
(You might also want to check why no number in your list is bigger than 26)
Just posting here and in the closed Geocaching thread limits your audience to participants in these threads
(You might also want to check why no number in your list is bigger than 26)
Q1: Which of you tell lies?
Q2: Which of you tell lies?
#1 A1: 2345 A2: 2345 - this means #1 is the truth teller
#1 A1: 2345 A2: 1235 - this means #1 was a liar, but #4 is a truth teller