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# In the Alps

## 33 posts in this topic

In the Alps - Back to the Logic Problems

Three tourists have an argument regarding the way they should go. Hans says that Emanuel lies. Emanuel claims that Hans and Philip speak the same, only doesn't know whether truth or lie. So who is lying for sure?

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In the Alps - solution

The only one who is lying for sure is Philip. Hans speaks probably the truth and Emanuel lies. It can be also the other way, but since Hans expressed himself before Emanuel did, then Emanuelâ€™s remark (that he does not know whether Hans is lying) is not true.

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This solution is wrong. Emanuel is the only one we can be certain is lying, because as rookie stated, Hans made his statement before Emanuel did, which means Emanuel must know whether Hans is lying or telling the truth. Therefore Emanuel is lying when he says he does not know. This means that both Hans and Philip are telling the truth when they agree that Emanuel lies.

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This solution is wrong. Emanuel is the only one we can be certain is lying, because as rookie stated, Hans made his statement before Emanuel did, which means Emanuel must know whether Hans is lying or telling the truth. Therefore Emanuel is lying when he says he does not know. This means that both Hans and Philip are telling the truth when they agree that Emanuel lies.

My solution should be correct. Check the following reasoning:

Hans speaks before Emanuel so Emanuel knows whether Hans is lying. The following was said:

Hans: "Emanuel lies."

Emanuel: "Hans and Philip speak the same but I don't know whether truth or lie."

If Hans speaks the truth then:

1. Emanuel lies = one part of Emanuel's sentence is a lie and the other one is truth OR both parts of the sentence are lies. For more on logical conjunction check http://en.wikipedia.org/wiki/Logical_conjunction

2. Emanuel knows if Hans is lying (second part is false) - for more check larryhl's explanation below [deleted=(second part is true) so the 1st part must be a lie = Philip lies.]

If Hans is lying:

1. Emanuel speaks the truth = both parts of Emanuel's sentence are true. For more on logical conjunction check http://en.wikipedia.org/wiki/Logical_conjunction

2. Emanuel knows if Hans is lying (second part is false) - for more check larryhl's explanation below [deleted=(second part is true) so the 1st part must be true as well = Philip lies.]

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My apologies, we were both incorrect. All factors in this problem can be determined with certainty. There is no "probably". Perhaps the problem is in the poor wording of the riddle.

Because Emanuel knows in the beginning whether Hans is lying, we know that Emanuel is lying when he says he does not know. In addition, we know that Hans is telling the truth when he says that Emanuel is lying.

However, I was incorrect when I stated that Hans and Philip agreed. Since we know that Emanuel lies, his first statement that "Hans and Philip speak the same" MUST also be a lie, so Philip must say "Emanuel tells the truth" which is also a lie.

Emanuel MUST be lying

Hans MUST be telling the truth

Philip MUST be lying

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Assuming the standard "everyone is either a liar or not", I've come to the conclusion that Hans tells the truth, Emanuel lies and Philip is unknown. You missed something critical here:

If Hans speaks the truth then:

1. Emanuel lies = one part of Emanuel's sentence is a lie and the other one is truth OR both parts of the sentence are lies.

2. Emanuel knows if Hans is lying (second part is true) so the 1st part must be a lie = Philip lies.

If Hans is lying:

1. Emanuel speaks the truth = both parts of Emanuel's sentence are true.

2. Emanuel knows if Hans is lying (second part is true) so the 1st part must be true as well = Philip lies.

Emanuel claims to NOT know, so if he knows, the second part is false--not true. Since Emanuel has to know, he has to be lying. Hans can't be lying because both parts of Emanuel's sentence can't be true. So Hans is speaking the truth. It's possible that Emanuel was telling the truth about the first part while lying about the second part, so we can't know for certain whether Philip lies or not.

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Three tourists have an argument regarding the way they should go. Hans says that Emanuel lies. Emanuel claims that Hans and Philip speak the same, only doesn't know whether truth or lie. So who is lying for sure?

If Hans is lying, then Emanuel is telling the truth, which means Philip lies.

If Hans is telling the truth then Emanuel is lying, which means Philip lies.

Hans and Emanuel could both either lie or tell the truth, but Philip can only be a liar.

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rookie1ja, your logic is flawed. take a look at logical conjunctions again. if both p and q are true, then the statement is true. otherwise, the statement is false.

therefore, if hans is speaking the truth:

1. emanuel lies, so either the first or second part of his statement is false, or both are false.

2. the second part of his statement must be false because he knows if hans lied (due to his speaking after hans.)

3. the first part of his sentence can be true or false. if true, philip also speaks the truth. if false, philip lies.

if hans is lying:

1. emanuel speaks the truth, so both statements must be true!

2. error in logic - he must know if hans lied, so the second part of his statement is false.

3. EMANUEL IS THE DEFINITE LIAR!

unfortunately, the solution given is incorrect. the correct solution should be: hans speaks the truth, emanuel lies, and philip can be either.

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larryhl, of course, you are right

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A first statement does not indicate precedence over the second so if the first is lying then you don't know anything and if the first is telling the truth then you know that Emanual is lying. It is impossible to solve this riddle.

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As far as I see it:

If Hans is telling the truth, then Emanuel is lying and that Hans and Philip are saying different things. Since Hans would be telling the truth, Philip would have to be lying.

If Hans is lying, then Emanuel is telling the truth and that Hans and Philip are saying the same thing. Since Hans is lying, then Philip would have to be lying as well.

But when you think about it, what has Philip said in this argument? He can't lie if he doesn't say anything

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That's what I've been thinking the whole time I'm reading over the arguements over whether or not the solution is correct...Philip never said anything...so how is he lying??

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Ummm... I have a question.

WHAT ARE YOU GUYS SAYING? CAN YOU EXPLAIN VERY SIMPLY PLEASE?

Thank You!!!!!

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Ummm... I have a question.

WHAT ARE YOU GUYS SAYING? CAN YOU EXPLAIN VERY SIMPLY PLEASE?

Ok, here we go:

"Three tourists have an argument regarding the way they should go. Hans says that Emanuel lies. Emanuel claims that Hans and Philip speak the same, only doesn't know whether truth or lie. So who is lying for sure?"

If Hans tells the truth, then that means that Emanuel does in fact lie. If he lies, then his statement about "Hans and Philip speak the same" must be false. So Hans and Philip must have spoken differently. So if Hans spoke the truth, the Philip spoke the opposite, which is a lie.

The opposite is that Hans lied. That makes his statement that "Emanuel lies" false. So Emanuel speaks the truth. Then that means that Hans and Philip spoke the same. So since Hans lied, so did Philip.

In both scenarios, Philip had to have lied.

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if "three tourists are arguing..." then none of them agree with eachother...therefore emanuel must be lying because he says that hans and phillip agree...

poor wording of the riddle...

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Read the riddle again, it initially says the three are arguing about which way to go, the riddle occurs at the end of the argument. Phillip likely said something during the argument to warrant the statements made by Emmanuel and Hans. So just because Phillip didn't say anything regarding who was lying or not, does not exclude him from being in the original argument.

I agree with the people who are saying it must be Emanuell lying:

Emanuell spoke AFTER Hans, so he would know FOR A FACT whether or not what Hans said ABOUT HIM was truth or lie. Now just because Emanuell is lying does not mean Phillip is as only one part of his statement has to be a lie in order for the statement as a whole to be considered a lie. So Emanuell could have been telling the truth about Hans and Phillip speaking the same, which would be both truth, or he could've lied about that also and they speak differently, meaning Phillip is lying. Bottom line is phillips position can not be determined

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This is very simple.

The key is that each individual know whether or not he is a liar or telling the truth, so therefore:

Emanuel is lying.

Hans claims that Emanuel is lying, but this statement is really negligable.

Emanuel on the other hand lumps Phillip and Hans together as either lying or telling the truth, but says he doesn't know which one. This is the lie.

Emanuel - Liar = Hans/Phillip -Truthteller(s)

Emanuel - Truthteller = Hans/Phillip - Liar(s)

Therefore Emanuel lied when he said he didn't know which one they were.

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I think the main issue is just that people are making assumptions. If you make the assumption that Emmanuel hears what Hans said, then yes Emmanuel must be lying about something. However, for those people, like me, who didn't assume that Emmanuel heard Hans, then the only logical answer is that Philip is always a liar.

The problem is too ambiguous to solve.

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This is a logic problem, so ignore the story. It is just there to make the problem more interesting.

There is no "who said what first", the timing of the events doesn't matter.

The liar always lies.

The truthsayer always speaks the truth.

There are possibilities to look at:

If Hans speaks the TRUTH -> then Emanuel lies.

Emanuel lying means Hans and Philip must speak opposite. Since we assumed in this case that Hans is speaking the truth; PHILIP LIES.

If Hans LIES -> then Emanuel speaks the truth.

Emanuel is speaking the truth, then both Hans and Philip speak the same. Since Hans is a liar is this assumption, so is Philip.

The matter of Emanuel knowing or not knowing if they speak the truth or not doesn't matter.

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This riddle sucks.

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The responses of Han and Emanuel are probably about the argument on where to go. If so the original solution is correct.

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Perhaps the quality of the riddle could be improved by Emanuel instead saying "Either both Hans and Phillip are lying or both Hans and Phillip are not lying." If this statement is false, then one is lying, and one is not. For an illustration of what I just said, you can look at the truth table in this spreadsheet file (easier than posting in here, sorry): [url:23592]http://www.box.net/shared/static/s5mypr3nua.xls. You will notice the file extension is .xls--this is not a virus. [Also note: I'll keep the file available for another few weeks, then I'll take it down. In the mean time, if anyone knows of a better way to show this in here, tell me]

This is originally how I interpreted the riddle. As far as I can tell, this resolves the issue of whether Emanuel hears what Hans says before he speaks (as some others said before, going by Emanuel's original statement, we could say he is always lying). I think the key thing is that Hans is making a statement about the truth of Emanuel's statement, and this narrows it down to two scenarios (scenarios 2 and 4), and in both cases, Phillip is lying.

I think my reasoning is right, but check.

.

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Let's assume you believe that Emanuel is the liar, and you assmue that both his statements are lies (A. the others both say the same thing, and B. he is unsure of whether or not they are truthful). Just because A is a lie, are we sure that they say the opposite? Why can't one say "Emanuel is a liar" and the other say "I have no knowledge of Emanuel's integrity." Can't both statements be true?

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Wait.

Hans says that Emanuel lies.

Emanuel says that hans and philip are either both liars are both truth tellers but he doesn't know which. But he does know that Hans called him a liar. This means he does know whether Hans is telling the truth or not. Since he says he doesn't, he must be lying. This is consistent with what Hans said, and so Hans is a truth teller. We also know that Hans and Emanual can't be the same (becuase a liar said they were) and so Philip must also be a liar. If you take a lie to require only lying about one part of the conjunction then you don't know for sure about philip. Either way it is Emanual who is the liar.

In the Alps - Back to the Logic Problems

Three tourists have an argument regarding the way they should go. Hans says that Emanuel lies. Emanuel claims that Hans and Philip speak the same, only doesn't know whether truth or lie. So who is lying for sure?

In the Alps - solution

The only one who is lying for sure is Philip. Hans speaks probably the truth and Emanuel lies. It can be also the other way, but since Hans expressed himself before Emanuel did, then Emanuelâ€™s remark (that he does not know whether Hans is lying) is not true.

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Some of the problem rest on the abiguity on whether or not everything a liar says has to be a liar or whether every statement a liar says has to be a liar on the whole.

Fore example: Could a Lair say: Two plus two equals five and a triangle has three sides. By the rule of conjuntion if either part is a lie then the whole statement is.

But, one would interpret that a every statement a liar makes is a lie, and thus when emanuel says that he does not know if H&P are liars, but he knows they are the same then we must know that philip is different because both parts have to be a lie.

I am not sure if all these riddles are consistent in the way they they assume Liars behave.