D'kian Posted June 24, 2008 Report Share Posted June 24, 2008 We're all familiar with the contrived, highly unlikely or outright fantastic scenarios meant to expose ethical contradictions. Well, there are some that do well as logic problems. I suppose many here know them, neverhteless here go two: 1) You need to extract an important piece of information from an individual named Zathras, let us say he knows whether the price of a stock will go up or down. The thing is Zathras will lie once in every interrogation, but only once. You can ask him two questions. What would you ask? (this is a very easy one). 2) You face a chioce between two doors, labeled A and B. One leads to freedom, the other leads to a dungeon. Naturally you don't know which is which. Each door has a guard. One guard always lies, the other always tells the truth. Again you don't know which is which. You are allowed only one question to either guard (one question total). What do you ask? Hint: it doesn't matter which guard you choose, whether the liar or the other, the question works for both. Answers later, assuming no one knows it already or figures it out. Quote Link to comment Share on other sites More sharing options...
EC Posted June 24, 2008 Report Share Posted June 24, 2008 I figured out the answer's, but I don't see how these are similar to the scenario's meant to expose ethical contradictions. In the ethical scenario's the people that are posing the questions simply don't understand (or choose to evade) that a proper ethical foundation doesn't include emergency situations. But these just seem like exercises to hone one's use of logic, like sodoku puzzles, etc. Quote Link to comment Share on other sites More sharing options...
D'kian Posted June 24, 2008 Author Report Share Posted June 24, 2008 (edited) The similarity is in the contrived, unlikely and fantastic nature of the scenarios. The logic problems can be fun to figure out and they do excercise logical thinking. That's it. edited to add: They're like math problems. Here's one, BTW. what's the highest number you can build using the numerals 1, 1, 1 and 1 and any mathematical notations or symbols? Example 11+11=22, 11*11=121, 11^11=285,311,670,611. You musy use all the numerals. Edited June 24, 2008 by D'kian Quote Link to comment Share on other sites More sharing options...
JMeganSnow Posted June 24, 2008 Report Share Posted June 24, 2008 1. Is your name Zathras? Will the stock go up? If he answers "yes" to the first one, you know that his answer to the next question is a lie. If he answers "no", you know that his answer to the next question is the truth. 2. Ask one of the guards (it doesn't matter which one) "Which door would the other guard tell me to go through?" then take the opposite of the answer. Quote Link to comment Share on other sites More sharing options...
athena glaukopis Posted June 24, 2008 Report Share Posted June 24, 2008 The second one is used in the movie Labyrinth ^^ O the memories!! Quote Link to comment Share on other sites More sharing options...
eriatarka Posted June 24, 2008 Report Share Posted June 24, 2008 (edited) 1. Is your name Zathras? Will the stock go up? If he answers "yes" to the first one, you know that his answer to the next question is a lie. If he answers "no", you know that his answer to the next question is the truth. 2. Ask one of the guards (it doesn't matter which one) "Which door would the other guard tell me to go through?" then take the opposite of the answer. Applying your second answer to the first problem, surely you only need to ask Zathras one question rather than two ("if my next question is 'will the stock go up?' then what will you tell me?'). Edited June 24, 2008 by eriatarka Quote Link to comment Share on other sites More sharing options...
eriatarka Posted June 24, 2008 Report Share Posted June 24, 2008 (edited) edited to add: They're like math problems. Here's one, BTW. what's the highest number you can build using the numerals 1, 1, 1 and 1 and any mathematical notations or symbols? Example 11+11=22, 11*11=121, 11^11=285,311,670,611. You musy use all the numerals. 11 ↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑↑(etc) 11 where the ↑ is the Knuth Up Arrow? Its a bit of an ambiguous question though because theres a lot of pretty obscure math things you could use if 'symbols' allows pre-defined functions. A(11,11) where A is the Ackermann function for instance. Or B(1111) where B is Busy Beaver Edited June 24, 2008 by eriatarka Quote Link to comment Share on other sites More sharing options...
D'kian Posted June 24, 2008 Author Report Share Posted June 24, 2008 11 || 11 where the '|' is the Knuth Up Arrow? Its a bit of an ambiguous question though because theres a lot of pretty obscure math things you could use. A(11,11) where A is the Ackermann function for instance. Before my head explodes, the largest number is infinity. You get at it thus: ((((((1,111!)!)!)!)!)!.....!) Where 1,111!= 1,111*1,110*1,109*1,108.*...11*10*9*8*7*6*5*4*3*2*1 The second parenthesis would be something like (1.6185630726417858745547823350912e+2903)! which is already ridiculously high Quote Link to comment Share on other sites More sharing options...
Matus1976 Posted June 24, 2008 Report Share Posted June 24, 2008 1. Is your name Zathras? Will the stock go up? If he answers "yes" to the first one, you know that his answer to the next question is a lie. He would answer "NO, its ZaathhruUus, not ZaAathhruus" which to the interregator would sound exactly the same, thus diffusing the logical trap! (Babylon 5 reference) Quote Link to comment Share on other sites More sharing options...
D'kian Posted June 24, 2008 Author Report Share Posted June 24, 2008 He would answer "NO, its ZaathhruUus, not ZaAathhruus" which to the interregator would sound exactly the same, thus diffusing the logical trap! (Babylon 5 reference) Actually he'd say "It's un-stock in time." Now pardon me while I take cover. Quote Link to comment Share on other sites More sharing options...
Benpercent Posted June 24, 2008 Report Share Posted June 24, 2008 He would answer "NO, its ZaathhruUus, not ZaAathhruus" which to the interregator would sound exactly the same, thus diffusing the logical trap! (Babylon 5 reference) Then there's an easy fix to the problem: "Is your name Billy?" Quote Link to comment Share on other sites More sharing options...
JMeganSnow Posted June 24, 2008 Report Share Posted June 24, 2008 Applying your second answer to the first problem, surely you only need to ask Zathras one question rather than two ("if my next question is 'will the stock go up?' then what will you tell me?'). It specified two questions. Actually, if you ask him only one question you KNOW he's going to lie (since he lies once and only once in any given interview). Quote Link to comment Share on other sites More sharing options...
D'kian Posted June 24, 2008 Author Report Share Posted June 24, 2008 2. Ask one of the guards (it doesn't matter which one) "Which door would the other guard tell me to go through?" then take the opposite of the answer. I'm a bit confused. Does it matter where the guards want you to go? If the liar wants you to go free, he'd tell you to go through the dungeon door, right? If he doesn't, he'd tell you to use the freedom door. If you do the opposite, you wind up in jail. Since the answer from either guard must be a lie, aren't you better off seeking factual information rather than the guard's desire? I'll go away now... Quote Link to comment Share on other sites More sharing options...
DragonMaci Posted June 25, 2008 Report Share Posted June 25, 2008 Since the answer from either guard must be a lie How is that the case? The original post said, "One guard always lies, the other always tells the truth" Sounds to be like only what one says is a lie and what the other says is the truth. Quote Link to comment Share on other sites More sharing options...
D'kian Posted June 25, 2008 Author Report Share Posted June 25, 2008 How is that the case? The original post said, "One guard always lies, the other always tells the truth" Sounds to be like only what one says is a lie and what the other says is the truth. Let's call the guards A and B. Let's say A always tell the truth and B always lies. So you ask A "What would B say if I asked him what color is the sky?" Since A always tells the truth, he can answer the question truthfully by telling you what B would say. He knows B would lie, therefore his answer would be, let us say, "yellow." Now suppose you ask B what would A answer to the same question. He knows A would tell the truth. But B always lies. So he will lie about what A would answer. He'd tell you "Yellow." See, the answer to that form of a question will always be a lie. Quote Link to comment Share on other sites More sharing options...
JMeganSnow Posted June 25, 2008 Report Share Posted June 25, 2008 Christ on a crutch. The wording can vary but the question you have to ask is basically "which choice would the *other* guard tell me to make?" Why? Because if you ask the truth-telling guard, he will truthfully tell you what the other guard would say, which is a falsehood. If you ask the lying guard, he will untruthfully tell you what the other guard would say, which is ALSO a falsehood. Or, alternately, you can do this. Quote Link to comment Share on other sites More sharing options...
D'kian Posted June 25, 2008 Author Report Share Posted June 25, 2008 Or, alternately, you can do this. I did disassemble many a Rubik's Cube Quote Link to comment Share on other sites More sharing options...
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