Posted: 12/2/2004 4:56:30 AM EDT
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In a certain mythological community, politicians never tell the truth, and non politicians always tell the truth. A stranger meets three natives and asks the first of them, "Are you a politician?" The first native answers the question. The second native then says, "The first native denied being a politician." The third native says that the first natives is a politician. How many of the three natives are politicians? (i'll post my response once i have time to think it over) |
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So native number 1 answers but we do not know the answer. Number two tells us that number 1 denied being a politician, and the third native says that the first is a politician. Hmmm... Sounds like numbers 2 and 3 are more politician-like than number 1 who answered and shutup. |
+1. But if you really want to be sure, you'll weigh each of them against a duck... |
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The 1st two are politicians. Call them A, B, C If A says "Yes I am" Then B says "he said he isn't" and C says "He's a politician" In this scenario then all A and B are politician. Remember if he says he is one he's lying so if he says he is then he would say he isn't. (This is the right one I think) If A says "No I'm not" Then B says "he said he isn't" and C says "He's a politician" In this scenario then you can eliminate B since as a politician since he told the truth but A and C cannot be conclusively eliminated since if he's lying he is a politician and then he's the only one but if he's not lying then C is the politician. Of course I've always been bad at these so feel free to tell me I've screwed up something 
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 btw, I dont know the answer.. the question was posed by an instructor of mine. Im leaning towards the first and second being politicians because the first obviously denied being a politician.. the second ratted him out and the second just simply said that person #1 is a politician. |
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Ok, we need to break this down logically to get the answer. First, all of them will deny being a politician. The politician will lie and say he is not, and the non-politician will tell the truth, and say he's not. Therefore we know that person A denied being a politician. From this information, we can deduce that person B is NOT a politician, because he told the truth in stating that peroson A denied being a politician. Follow me so far? Now, we're left with 4 options: 1 - both persons A and C are politicians, 2 - both persons A and C are not politicians, 3 - person A is a politician and person C is not a politician, or 4 - person A is not a politician and person C is a politician. We can rule out #1 and #2 from person C's answer. We know that person A denied being a politican (see above.) Now, if A is truly not a politician, then C is lying by claiming that A is a politician. Conversly, if A is a politician, and is lying about it, then C is telling the truth. Therefore, we know that B is a non-politician, and we know that either A or C is also not a politician. So the answer is one of the natives is a politician. |
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One is a politician, and two are not. Person 1 had to have answered "No" to the question, because if he were a politician, he would lie, and if he weren't, he would tell the truth. Therefore, he definitely would always say "No", no matter whether he were a politician or not. Case 1: Person 1 is a politician. Person 2 told the truth, so he is not a politician. Person 3 also told the truth, so he is not a politician. Case 2: Person 1 is not a politician. Person 2 told the truth, so he is not a politician. Person 3 told a lie, so he is a politician. So either way, there is one poliician and there are two non-politicians. ETA: Greymage beat me to it. 
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This is why you're wrong - A can't say he's a politician. If he's a politician then he told the truth and if he's not he lied. Therefore, A must say that he's not a politician, whether or not he is one. B told the truth, so he's not a politician. C may or may not be a politician. If he's not, A is. If C is a politician, then A is not. Therefore: There is one politician and it is either A or C. Shoot them both and have a beer with B. |
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Question posed to natives: "Are you a politician?" If native #1 is a politician he would not say "yes". If native #1 is not a politician he would not say "yes". If native #1 is a politician he would say "no". If native #1 is not a politician he would say "no". Therefore, native #1 would not answer "yes" to the question in any case. We are given as fact that native #1 did answer and from the above we see he answered "no". Native #2 stated, "The first native denied being a politician." From the above we know native #1 denied being a politician, therefore, native #2 spoke the truth, hence native #2 is not a politician. Native #3 states that, "the first native is a politician". This is a lie. From the above we know native #1 responded to the question with "no". Therefore native #3 is a politician, because only politicians lie. |
How do you know it's a lie? It's only a lie if he isn't a politician. How can you prove that he isn't one? Remember, he didn't claim Man #3 said he was a politician, but that he was a politician. |
I think A cannot have answered that he was a politician because if he IS a politician and they always lie he would have had to say that he ISNT a politician. Also if he isnt a politician then he can't have said he was because non politicians always tell the truth. So A answered NO that he isnt a politician. Lie or not he answered no. B says that A denied being a politician. We just determined that to be true so B is NOT a politician. C says A is a politician. If A was telling the truth and is not a politician then C is lying and there is ONE politician. If A was lying and really is a politician then C is telling the truth and there is still one politician. Which one the politician is I dont know but that wasnt the question. |
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I've heard another simalar question. A man goes into a jungle and is met by natives who decide to execute him. They tell him that he has to make a statment, if it's false he gets shoves off a cliff. If it's true he gets his head cut off. What does the man say? ANSWER: He says, "you will throw me off a cliff." |