Dario and Jean
On a foreign island, there are three islanders.
One is lying and the other two are telling the truth. One is named Dario and another is named Jean.
Who is Jean?
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15 solutions
I think you are correct, since we have found a consistent model. But is this the only consistent model? Is it not possible to have another arrangement of names such that the constraints still hold?
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We have shown that Jean must be the third islander. If the second islander is Dario, then both the first and third islanders are lying. Therefore, the only valid arrangement is that the first islander is Dario and the third is Jean.
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The problem lies, I think, in your formulation of proof -- in essence, you conflate sufficiency with necessity.
Your execution is, indeed, exhaustive of the possible outcomes, but the cost of calculation is only so low due to the extremely small size of a finite solution set; had the possible outcomes been even marginally greater (or, even better, an infinite set) the solution would require far more finesse to prove uniqueness.
More importantly than the outcome is how you get it. Your solution in this case is unique, but you fail to use this as the center point of your argument, leaving the uniqueness property a mere side-effect of the method rather than an intrinsic part of its composition.
i think it cannot be determined.cause of the statement of 3rd islander(dario is lying).....cause it is not clear,which one is dario,,,i mean the 3rd islander is saying "dario is lying"---this statement is for whom?,,1st islander or 2nd? can anyone clear me if i am wrong?
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The problem is asking who Jean is, not who Dario is.
The third islander is the one who is lying (apart from being Jean). In fact Dario is telling the truth, and is the first islander. We do not know the name of the second islander, but it is not Jean, and he is also telling the truth.
Dario shouldn't exist cause if we assume one of them as Dario this happens : let's say third guy is dorio,then we see dario says dario is lying which he cannot be right and wrong at the same time /
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İf we assume that the second guy is dario then he is telling the truth and first guy is telling a lie but third guy says dario is lying as we see he isn't
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Last of all if the first guy is dario then he is telling the truth by ''i am dario'' but the third guy is saying that ''dario is lying'' which ends up with all the senarios wrong
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- The 1st islander is Dario - Dario is telling the T r u t h .
- The 2nd islander's name is not Jean - They're telling the T r u t h .
- The 3rd islander is Jean - Jean is L y i n g about Dario.
If we assume the third guy is Dario, then the first guy is lying. Since there is only one liar, that means that Dario is telling the truth. But Dario claims that Dario is lying, a contradiction.
Basically the fact that the third guy claims that Dario is lying makes it impossible for him to be Dario. That doesn't mean "Dario doesn't exist" it just means that the third guy isn't Dario.
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If the third guy is Dario, then it seems unclear what he is referring to when he says "Dario is lying." If you say out load "I am lying", it has no meaning because there is no context. Lying about what? Actually all you are demonstrably doing is speaking. If he said "Dario is not speaking", then that is clearly a lie. It does seem we need to keep the scope small enough so the third islanders response is not meaningless.
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@Ian Leslie
–
If the 3rd islander were Dario, his statement would invoke the
Liar's Paradox
, which results in not being able to assign a truth value to the statement.
This problem states specifically that "One is lying and the other two are telling the truth", so we can eliminate all potential scenarios where a truth value cannot be assigned to a statement - Thus, Dario is not the 3rd islander.
The problem is asking who Jean is, not who Dario is. For the solution, islander one is truthful Dario, islander two is neither Jean nor Dario, and truthful, and islander three is Jean, lying about Dario.
Personal thought: If 3's claim that Dario is lying refers to 1 specifically (claimed Dario) as opposed to Dario (true identity) then 1 could be Jean also leaving it indeterminate
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I like the thought, but I don't think it works out that way. Islander 3's statement has to be demonstrably true, regardless of the other statements. He would either say "Islander 1", "The islander claiming to be Dario", or "Dario", since each of those has a relevant and distinct meaning. If Islander 3's statement, as presented, c o u l d apply to islander 1, then it would be impossible to maintain clarity in this sort of logic puzzle.
If Jean is islander 1, then that would make 2 people liars.
- Jean: "I am Dario" - L i e
- Dario: "I am not Jean" - T r u e
- Islander 3: "Dario is Lying" - L i e
Dario cannot be islander 3 because of the
Liar's Paradox
, which results in not being able to assign a truth value to the statement.
This problem states specifically that "One is lying and the other two are telling the truth".
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Yeah Liar's paradox is what makes this puzzle solvable otherwise it could go like this and you cant even know if multiple persons have same name( as only two names given and there is three persons):
- 1st Islander: "I am Dario" - LIE (then he could be Jean or not know person as there is two names and 3 person or there could be multiple people with same name)
- 2nd Islander: "I am not Jean" (then he could be Dario or not know person or something else if multiple person have same name)
- 3rd Islander: "Dario is lying" (if this is referring to first person and he is lieing then stament is true but if there is multiple persons with same name then he could be referring with anybody)
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@Jarkko Hietala
–
The problem does also state that "One is named Dario", so it's implicit that neither of the other 2 are named Dario.
"another is named Jean" is slightly less explicit, but the word 'another' is typically used with a singular noun.
So we can conclude that there is 1 Dario, 1 Jean, and 1 person not named Dario or Jean.
@Jarkko Hietala – If you had two Darios, the "Dario is lying" statement would have to apply to both people named Dario (right?). It would require the first two islanders to be Dario, and truth-tellers, since neither Dario the liar nor Dario the truth-teller could make the third Islander's statement.... which would also result in the third islander being Jean. Dario 1 tells the truth, Dario 2 tells the truth, and Islander 3 tells the lie, and is Jean.
This may have been obvious to everyone but me, but for this problem to make sense, the third islander must speak after Dario. I initially looked at 1, 2, and 3 as just labels. Clearly (to me anyway) if Islander 3 were to speak first then whole problem would be nonsense, since there would be no lying or truth telling for him to be responding to. I give credit to my wife for pointing out this requirement to me.
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Now that I've thought about it more, the order is of speaking has to be 1, 2, 3 in order for there to be this puzzle, or to satisfy constraints. If the spoken order was 1,3,2, then clearly 3 can only be referring to 1 when he speaks. So 1 must be Dario, 3 is lying and must be Jean, and 2 is perhaps Bob or Wally! If the spoken order was 2,3,1 then 2 must be Dario, again by necessity for 3 to be referring to something said, so 3 is lying and so is 1. This violates the two truth tellers and one liar condition. As I said above, 3 can't be first because it would be meaningless. I think that covers everything.
Suppose the first islander is lying - this implies both other islanders are telling the truth, and that one of them must be dario. Yet the third islander says that dario is lying, which implies that one of them is lying, which is a contradiction, since beacuse islander 1 is lying they cannot be dario
Thus the first islander must be telling the truth, and is dario, which tells us that the tird islander is lying, which means that the second islander is telling the truth.
From this we know that Jean cannot be any of the first two islanders, which leaves only the third islander.
If the first islander is Jean, then he is lying and the other two are telling the truth. The first one is jean, but he states he is dario after he claims to be dario, the thrid person being the real dario states that dario is lying...meaning the one who proclaimed to be dario. And thus the 2nd is telling the truth because he is not jean...thus islander one is jean.
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Suppose that the third islander does not know the first islander's true identity. Then the third islander cannot truthfully state anything about the first islander's statement, "I am Dario" (because he does not know the 1st islander's identity).
Now suppose that the 1st islander is lying and the 3rd islander does know the 1st islander's identity. Then the 3rd islander, telling the truth, would not refer to the 1st islander as "Dario."
Thank you! This is the only real proof (as yet) on here.
@Mike, Your answer is the clearest, but I have one hurdle I can't quite get over. If the third islander is Dario, then what does "Dario is lying" even mean. Lying about what? If he is Dario, then all he is doing is speaking. He could have said "Dario is telling the truth". The truth about what? There seems to be some sort of condition that needs to be included, such as, "Each statement must contribute to the solution of the problem."
if the 1st is lying we don't learn any information so there would be no reason for him to lie to us. if two is lying then we know who the Jean is. Although, three is saying one is lying but we know he is telling the truth. So three must be lying making him Jean as one is Dario.
If we assume that the third islander is lying then he is in fact Jean which means that the first and second islanders are telling the truth...All the requirements are therefore satisfied.
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Satisfaction is far from necessity.
You have proven the,specific, but can you prove the general?
There are three islanders but only two known names. Therefore the first islander could be lying about being Dario and still not be named jean.
You assume importance of information when there is no reason to. The reasoning arrives at the correct conclusion, but only by happy accident.
Failure to prove on principles is as good as guessing...
There are 2 situations the third islander can be lying or telling the truth. From there we can deduce whether the other 2 are lying. Finally only one of these situations satisfies the condition that only one of them is lying
3rd islander - T F
1st islander - F T
2nd islander - F T
Only one liar - F T
Our goal is to try to find who is lying. We will prove that the third islander is a liar. Now assume that he is telling the truth. So accordinrcwg to him, Dario is lying. If the first islander is Dario, his lying speech w
I'll be using A,B and C to refer the three islanders.
C's statement establishes the fact that C is not Dario. Otherwise he will contradict his own statement. His statement would then be a truth and a lie at the same time.
Now we approach the problem by assuming one of them is a liar and then determining if the truth of the other two contradicts that assumption.
- Assuming A is lying. That means that B and C are telling the truth. But that will be contradicted by C. As B, who will be Dario , will be saying truth and a lie at the same time.
- Assuming B is lying. Then B is Jean and A is Dario , which is again impossible as A's statement will be a truth and a lie at the same time.
- Assuming C is lying. This means, A is actually Dario and B is not Jean and also that Dario is NOT lying. That deduces that C is Jean .
Hence the Third islander is JEAN.
Lmao I just guessed that the lier is lying. Ez.
Third islander I got it correct
If no1 lies, he is not Dario which does not correspond with no3; so no1 or no3 is Jean.
If no2 lies, no1 is Dario which is in conflict with no3, and implies that two of them lie and no2 or no3 can be Jean.
If no3 lies, no1 is Dario, no2 is not Jean and therefore no3 must be Jean.
First and third cannot both be telling the truth and the third must be the liar. Since there is only one liar, second is telling the truth like the first. The third must be Jean.
Let first islander be incorrect. Then 2 and 3 islanders are true. Which implies that second islander is Dario but Third islander rejects that which contradicts our assumption. Let second islander be incorrect. Then first and Third contradict each other's sentence. Lastly let Third islander be incorrect. which suggest s that first one is Dario and second is not Jean so this is Jean and since Third is lia. So Dari. Isn't wrong
Can be done without writer. 2nd Islander said "I am not Jean" first Islander never said he is jean. Naturally, third Islander is Jean which is the answer to question. You ignored him saying truth or lie.
Make a table, 1,2,3 across the top, then next 3 rows, t,t,f; f, t,t, last row t, f,t you see from table only scenario that fits is first row. I.e 3rd islander is Jean.
there's a Liar there's Dario (Not liar!) and there's Jean (Not liar!)
Scenario 1:
1st Islander = Jean. Jean says hes Dario. Jean is lying there fore he can not be Jean.
Scenario 2:
2nd Islander = Jean Jean says hes not Jean. Jean is lying there fore he can not be Jean.
Scenario 3:
3rd Islander = Jean Jean says Darius is lying. Jean is not lying???
Well no Jean is still lying because Darius is not a liar!
Solution:
Jean can't be any of them as each one would make him the liar.
Nothing says Jean or Dario can't be the liar.
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Then they are all Jean!
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One of them is could be also named Dario, and maybe all 3 are one person then Dario Jean Lying-pants the first.
In a situation like this, it is important we start our reasoning from the most certain response. But unfortunately we have two, but according to law of non-contradiction, if 1st Islander is lying and 3rd Islander still refers to him as Dario, then there's a contradiction.
However if we assume 1st Islander says the truth then we accept that 3rd Islander is lying so there is no contradiction. Which implies 2nd Islander is saying the truth leaving only one choice, 3rd Islander is Jane.
i think it cannot be determined.cause of the statement of 3rd islander(dario is lying).....cause it is not clear,which one is dario,,,i mean the 3rd islander is saying "dario is lying"---this statement is for whom?,,1st islander or 2nd? can anyone clear me if i am wrong?
The 3rd islander says Dario is lying. The truth of his statement cannot be determined. Neither is he referring to the first islander as Dario, but just says that Dario is lying. Coming from a point where I don't know who Dario is, nor any characteristics of Dario, nor any third party that can confirm who Dario is, I cannot assume that the 1st islander is telling the truth. So I think it cannot be determined.
If the first islander is Jean, then he is lying, so the other two, including Dario , are telling the truth. But the third islander says that Dario is lying, which is a contradiction.
If the second islander is Jean, then he is lying, so the other two are telling the truth. However, these two cannot be telling the truth at the same time (if the first islander is truthful, this means he is Dario, but the third islander says that Dario is not truthful).
The third islander must be Jean. If the first islander is Dario, then all the requirements are met.