[rookie1ja]

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?

Spoiler for Solution:

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 Emanuel’s remark (that he does not know whether Hans is lying) is not true.

[s0079376]

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.

[rookie1ja]

Quote

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....cal_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....cal_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.]

[s0079376]

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

[fosley]

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.

[jmull747]

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.

[larryhl]

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.

[rookie1ja]

larryhl, of course, you are right

[comperr]

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.

[Numenor]

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