Guest Posted September 24, 2010 Report Share Posted September 24, 2010 This paradox is a slight modification a logical puzzle here on BrainDen (thanks jazzship). This modification makes it a paradox. There are 15 people at a party. Each person is wearing a sticker with a different number from 1 to 15. Person 1 says: "There are zero honest people at this party." Person 2 says: "There is no more than one honest person at this party." Person 3 says: "There are no more than two honest people at this party." ... ... ... Person 14 says: "There are no more than thirteen honest people at this party." Person 15 says: "There are no more than fourteen honest people at this party." How many people are lying, and which ones are lying? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 24, 2010 Report Share Posted September 24, 2010 For a little help in seeing the paradox, here is the original logic puzzle: Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 25, 2010 Report Share Posted September 25, 2010 I'll try... person one says everybody is lying everybody else leaves the possibility that everyone is lying and that there is at least one honest person. so assume there are no honest people, then everybody could be telling the truth, but then they wouldn't be lying so assume all the people are honest, then everbody except person one could be telling the truth, but person one would have to be lying. so I am going to go with one is lying, and the liar is one. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 25, 2010 Report Share Posted September 25, 2010 I'll try... person one says everybody is lying everybody else leaves the possibility that everyone is lying and that there is at least one honest person. so assume there are no honest people, then everybody could be telling the truth, but then they wouldn't be lying so assume all the people are honest, then everbody except person one could be telling the truth, but person one would have to be lying. so I am going to go with one is lying, and the liar is one. If only person 1 is lying, then persons 2 through 15 are telling the truth. This gives 14 honest people (2 to 15). Person 2 says that there is at most 1 honest person though. If there are 14 honest people, then Person 2 must be lying because 14 is more than 1. This means that the original assumption that person 1 is the only liar cannot be correct. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 27, 2010 Report Share Posted September 27, 2010 (edited) This paradox is a slight modification a logical puzzle here on BrainDen (thanks jazzship). This modification makes it a paradox. There are 15 people at a party. Each person is wearing a sticker with a different number from 1 to 15. Person 1 says: "There are zero honest people at this party." Person 2 says: "There is no more than one honest person at this party." Person 3 says: "There are no more than two honest people at this party." ... ... ... Person 14 says: "There are no more than thirteen honest people at this party." Person 15 says: "There are no more than fourteen honest people at this party." How many people are lying, and which ones are lying? person 1 could be speaking as an outsider, many of us do this, we forget to include ourselves, in which case, technically, it would be a lie, to himself, he would be speaking truth. after all, what is "Honest" do you define it as someone who speaks the truth? and if so, how do you define "Truth"? is it fact? only that which is verifiable? or is truth the opposite of lie? in that it does not deceive? Is the atheist lying when he says there is no god? Is the christian lying when he says there IS a God? They each believe it to be true to their very core, so they are being honest with themselves, truth is relative in that it only means what you believe it to mean, so they could ALL be speaking truth, or ALL lying, we do not know the intent, besides, one could always tell the truth and be dishonest, maybe they are all thieves who tell the truth, and each know of some of the others' exploits, in which case, when saying "Honest" they could mean "non-thieves that I know of", in which case, it could mean they are all telling the truth, or conversely, perhaps they all mean to deceive you, in which case, they could all be lying, we know not the intentions of each, and so could not say which speak truth. as the late Robert Jordan wrote "the truth you hear may not be the truth you think it is" truth is relative, so it can be easily misinterpreted. so, because we don't know what context each is using for the word "Honest" and we don't know the intentions of each, there is no correct answer to the questions. After all, Honest and Liar are not opposites. Therefore, one can be honest, and also a liar, just in different contexts. Edited September 27, 2010 by Mayki Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 27, 2010 Report Share Posted September 27, 2010 person 1 could be speaking as an outsider, many of us do this, we forget to include ourselves, in which case, technically, it would be a lie, to himself, he would be speaking truth. after all, what is "Honest" do you define it as someone who speaks the truth? and if so, how do you define "Truth"? is it fact? only that which is verifiable? or is truth the opposite of lie? in that it does not deceive? Is the atheist lying when he says there is no god? Is the christian lying when he says there IS a God? They each believe it to be true to their very core, so they are being honest with themselves, truth is relative in that it only means what you believe it to mean, so they could ALL be speaking truth, or ALL lying, we do not know the intent, besides, one could always tell the truth and be dishonest, maybe they are all thieves who tell the truth, and each know of some of the others' exploits, in which case, when saying "Honest" they could mean "non-thieves that I know of", in which case, it could mean they are all telling the truth, or conversely, perhaps they all mean to deceive you, in which case, they could all be lying, we know not the intentions of each, and so could not say which speak truth. as the late Robert Jordan wrote "the truth you hear may not be the truth you think it is" truth is relative, so it can be easily misinterpreted. so, because we don't know what context each is using for the word "Honest" and we don't know the intentions of each, there is no correct answer to the questions. After all, Honest and Liar are not opposites. Therefore, one can be honest, and also a liar, just in different contexts. For the purpose of this thought exercise, it is meant for the reader to assume that by saying a person is honest or is a liar, we mean that his one statement at the party is true or false respectively. An honest person in this case has his/her one statement evaluate to true, while a liar in this case has his/her one statement evaluate to false. The goal of the reader here is to classify each person as being honest or dishonest in a logically consistent way. The paradox here is that there is no logically consistent way in which this can be done. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted February 5, 2011 Report Share Posted February 5, 2011 Isn't it just 9,10,11,12,13,14 and 15? 9 says that there are no more than 8, and there are 7, 10 says that there are no more than 9, and there are 7 etc. Also, what has the numbered stickers git to do with anything? It's not a paradox, isn't it identical to the other puzzle (more or less) I may be missing out on something here, not sure :S Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 20, 2011 Report Share Posted March 20, 2011 (edited) I have to ask the exact physical locations of all people at party.....thinking...thinking....there could be more or other horixontail types of laying-down there is going on???? LOL tell me your thoughts just trying to make you smile.... Edited March 20, 2011 by AshleyKanuckel Quote Link to comment Share on other sites More sharing options...
0 Guest Posted March 22, 2011 Report Share Posted March 22, 2011 If only person 1 is lying, then persons 2 through 15 are telling the truth. This gives 14 honest people (2 to 15). Person 2 says that there is at most 1 honest person though. If there are 14 honest people, then Person 2 must be lying because 14 is more than 1. This means that the original assumption that person 1 is the only liar cannot be correct. but just because number 1 is lying doesn't necessarily mean everyone else is honest because the truth isn't the exact opposite of what the lie was, so he might be lying as well as someone else... Quote Link to comment Share on other sites More sharing options...
0 Guest Posted April 9, 2011 Report Share Posted April 9, 2011 Well, I haven't read the original post, but I've developed the answer on my own. Person two is the only one telling the truth. That's the only possible result (unless I'm wrong) Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 21, 2011 Report Share Posted July 21, 2011 I agree with Q-Cumber Person 2 is the only one telling the truth by saying that there is only one person telling the truth (himself) Say for instance, Person three says no more than 2 are telling the truth. That means that everyone ahead of him is telling the truth. (No morethan)Which means that person three can't be telling the truth! Same with Person 4, 5, 6, ect. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted July 21, 2011 Report Share Posted July 21, 2011 Sorry there's no spoiler FORGOT Quote Link to comment Share on other sites More sharing options...
0 fabpig Posted July 21, 2011 Report Share Posted July 21, 2011 (edited) I agree with Q-Cumber Person 2 is the only one telling the truth by saying that there is only one person telling the truth (himself) Say for instance, Person three says no more than 2 are telling the truth. That means that everyone ahead of him is telling the truth. (No morethan)Which means that person three can't be telling the truth! Same with Person 4, 5, 6, ect. That would mean that persons3 onwards are also telling the truth (1 is "no more than" 2, etc) Edited July 21, 2011 by fabpig Quote Link to comment Share on other sites More sharing options...
0 Guest Posted August 8, 2011 Report Share Posted August 8, 2011 assume person 9 is telling the truth. then 9-15 are telling the truth and that's 7 honest people. but this means that person 8 is telling the truth thus making there be 8 honest people which makes person 8 a liar. therein lies the paradox. you have to remember that if person n is telling the truth then so is person n+1. so no number below 8 works as the first truth teller. This results in person n telling the truth implying that person 16-n lying and vice versa. thus person 8 telling the truth is equivalent to him lying. this is really similar to russel's paradox. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted September 17, 2011 Report Share Posted September 17, 2011 It's definitely a paradox. If people 8-15 are telling the truth, then the statement of person 8, "there are no more than 7 honest people at this party" would be incorrect since everyone including and after 8 would have to be counted as honest, meaning that there are 8 honest people, which then nullifies 8's statement, making 8 one of the liars. But if people 9-15 are telling the truth, at first glance it appears that this can fit, as 9 states "there are no more than 8 honest people at this party" - which at first glace appears to be fitting, as people 9-15 would all be then truthtellers, and each correct..... BUT that would make a total of exactly 7 honest people at the party, which would in turn change 8 from a liar into a truthteller (as 7 honest people fits with Person 8's statement), thus making it 8 honest people and again nullifying 8 as a potential truthteller. Total paradox. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted October 19, 2011 Report Share Posted October 19, 2011 I agree with the original answer Quote Link to comment Share on other sites More sharing options...
Question
Guest
This paradox is a slight modification a logical puzzle here on BrainDen (thanks jazzship).
This modification makes it a paradox.
There are 15 people at a party.
Each person is wearing a sticker with a different number from 1 to 15.
Person 1 says: "There are zero honest people at this party."
Person 2 says: "There is no more than one honest person at this party."
Person 3 says: "There are no more than two honest people at this party."
...
...
...
Person 14 says: "There are no more than thirteen honest people at this party."
Person 15 says: "There are no more than fourteen honest people at this party."
How many people are lying, and which ones are lying?
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