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 Very Difficult Logic Problems Three gods A, B, and C are called, in some order, True, Fal Goto page 1, 2  Next
 Thu Oct 11, 2007 4:23 pm  by Bazza Three gods A, B, and C are called, in some order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which. " It could be that some god gets asked more than one question (and hence that some god is not asked any question at all). What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.) Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely. Random will answer 'da' or 'ja' when asked any yes-no question.[2]
 Mon Dec 22, 2008 10:30 pm  by alexonfyre how would the truth telling god answer if one were to ask him "Would he tell me that he is the False God?" referring to the Random God?
 Sat Dec 18, 2010 2:30 pm  by bugbustter The Truth God would keep silent, because he would not be able to give a truthfull answer.
 Tue May 17, 2011 4:08 pm  by randompattern I imagine that the false good also would remain silent if you asked what the random god would say bec the false god must be sure that his answer is false. With that in mind, I would start with A and ask: "What would B say if I asked him if the sky were blue?" (or any definite truth) If A will remains quiet: I know B is Random. I then ask A what C would say if I asked him if the sky were blue. Whatever the reply, that is the word for "no", because if A is True, then C is False, so A will truthfully tell me that C will lie and if A is False and C is true, then A will lie about C's truthful response. Now that I know which word means "no", I simply ask either A or C if the sky is blue. Let's Say I ask C: If the Answer is the word for "no", C is False and A is True. If it is "yes", C is True and A is False. If after my first question, A gives me an answer: I know that B is not Random. I ask B what C would say if I asked if the sky were blue. If B gives an answer, then I know A must be Random, and the Answer that B gave means "No". I then ask B or C if the sky is Blue to determine which one is True and which one is False. If A answers, but B remains silent: I know that C is Random, and that what A answered must have meant "No". I then ask A or B if the sky is blue to determine which one is True and which one is False.
 Wed Jun 22, 2011 3:27 am  by icemaster How do you know the true or false gods answer if they say da or ja because you have no idea if it means yes or no, other than that i like your answer :D
 Wed Jun 22, 2011 12:50 pm  by randompattern If I ask either the false or the true god what the other would say if I asked the other whether something I know to be true is in fact true, whatever they answer, whether da or ja must mean no. Here is why: If god A is true and god B is false, and I ask what god A what god B would answer the question: : "Is the sky blue?", then god A must say the word for No because that is truthfully what g-d B would say. If god A is false and god B is true, and I ask god A the same question, well god be would have answered the word for Yes, so god B will lie and see the word for No.
 Fri Dec 13, 2013 3:53 pm  by simon155 heh I like this one. I'm not entirely convinced by the "silence" tactic however: Just as Truth may decide not to answer because he can't be "sure" of giving an honest answer, Lies may not answer because he want's be be sure of giving a dishonest answer. Random on the other hand, will decide if he wishes to be honest or not... and then say nothing because he too can't be sure of achieving that. Thus you have 3 silences and no solutions :) Weekend time. Laters ;) I don't have time for now, but at a glance try more complex logic like "is the answer to ... and .... the same?" ;)
 Thu May 08, 2014 2:15 am  by EJsta to solve this, all u gotta do is ask the same question for all three. for instance, i ask A, if the sky is blue, then i'd go to B and ask the same question, and to C as well. 2 of them will answer the same answer. With those 2 i'll ask the same question again, until 1 changes his answer. That is the random god. to find the the honest or the lying god, i'll ask the remainder who is the lying god or who is the honest god, doesnt really matter which, as long as it's the same question: Are you the lying god? both will answer no, therefore i get the answer for what is da and ja. vise versa if you ask are you the honest god, both will say yes. i then ask an answer i know that is absolutely true. And there you have it the solution.
 Sun Jun 01, 2014 10:54 am  by yuk To every yes-or-no question Q, construct the following yes-or-no question: "If I ask you Q, would you answer ja?", and call it Q*. It turns out that the answer to Q* is ja if the answer to Q is yes, and da if the answer to Q is no, no matter if the god being asked is True or False, and no matter the meaning of ja and da. Here's the table for all cases, if you follow each case you can confirm it works out. God | answer to Q | meaning of ja | answer to Q* ------------------------------------------------------------ T | y | y | ja T | y | n | ja T | n | y | da T | n | n | da F | y | y | ja F | y | n | ja F | n | y | da F | n | n | da So with Q* it's possible to get the truth of any question Q from the false god, but the random god is still a problem. Now the solution depends on the definition of the randomness of the random god. If we use the definition in the original problem (that he flips a coin to decide whether he's true of false) the solution can be as follows: The first question for god A will be the Q* version of the following question: "If I ask you whether you're the random god what will you answer?" The true and false god will both answer no, the random god will answer yes (to see why check out the two cases, the one when he decides to lie and the one when he decides to tell the truth). So if the answer is yes, you know which is the random god, and with one more question you can find out who's the true god (remember that with Q* kind of questions, both gods are essentially truth telling now, so you can just ask the * version of a question like: "Are you the false god?"). It the answer is no, ask god B the same question. If the answer is yes, one more question will tell you which is true from A and C. If god B answers no, then C is random, and one more question will tell you which is true and false between A and B. It is also possible to solve this problem with 3 questions even if the random god is purely random, meaning he might answer yes or no to any question. In that case the questions should be: Ask god A: "Is god B random?" (the Q* version of this). If he says Yes, it means that either B is random or A is random. But C is not! If he says no, then either A or C is random, but B is not. So after one question we know about one god which isn't random. Ask that god whether A is random - if yes, one more question will differentiate between B and C, if no we know which one is random, and one more question will differentiate between the two remaining gods.
 Wed Jul 23, 2014 6:04 am  by nicejojo12 After wasting my entire day staring at this problem, I realized that you can solve this with 2 questions! Because if you think about it, you can easily solve this with 2 questions if you change the question so that the gods answer in english. Q1 - Directed to A Would you and B give the same answer to the question of whether the sky is the ocean (sorry, but I like the sky and ocean, but you can use any definite false statement)? If A cannot answer, then B must be random. If A says yes or no, then either A is random, or A and B is True or false in some order. Either way, B cannot be random. Q2 - Directed to the god identified as not random from the previous question. Would you and C give the same answer to the question of whether the sky is the ocean (again, any definite false)? If he doesn't answer, then C is random, and A and B are true and false in some order, we can tell which one is which by the first question, if for the first question A answered yes, then he is false and B is true, if A answered no, then A is true, and B is false. If he answers no, then we know that C is not random (and B is random, from our previous question). And the god you asked the question to is false, and C is true. If he answers yes, then we know that C is not random (and B is random, from our previous question). And the god you asked the question to is true, and C is false. That's how you solve it with 2 questions if the gods answer in english. The rest was easy to figure out. Just change the questions to: Q1 - Directed to A Would you answer ‘ja’ to the question of whether you would say yes in your languge to the question of whether you and B would give the same answer to the question whether the sky is the ocean? If A cannot answer, then B must be random. If A says da or ja, then either A is random, or A and B is True or false in some order. Either way, B cannot be random. Q2 - Directed to the god identified as not random from the previous question. Would you answer ‘ja’ to the question of whether you would say yes in your language to the question of whether you and C would give the same answer to the question whether the sky is the ocean? If he doesn't answer, then C is random, and A and B are true and false in some order, we can tell which one is which by the first question, if for the first question A answered ja, then he is false and B is true, if A answered da, then A is true, and B is false. If he answers da, then we know that C is not random (and B is random, from our previous question). And the god you asked the question to is false, and C is true. If he answers ja, then we know that C is not random (and B is random, from our previous question). And the god you asked the question to is true, and C is false. Notice how the questions are changed in a way so that I can replace yes with ja and no with da. If you were to say that true or false can somehow predict what random's going to say, then I believe it's impossible to solve with 2 questions
 Thu Oct 09, 2014 6:31 am  by elcanrebat EJsta - you only get to ask 3 questions. yuk - wrong answer given by false god quote "If I ask you whether you're the random god what will you answer?" [color=red]The true and false god will both answer no[/color], the random god will answer yes (to see why check out the two cases, the one when he decides to lie and the one when he decides to tell the truth). truth god will answer no, false god will answer yes. rest of the logic falls apart. nicejob12 - wrong assumption of ya = yes and da = no. quote from original question, " The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which. " can we please think through the question before replying?
 Fri Oct 10, 2014 5:57 am  by nicejojo12 elcanrebat: Actually, no. Well sort of but no. Most people can see that you can solve this with 2 questions if the gods answered "yes" or "no" instead of "da" or "ja" right? Having the basis structure for this kind of problem can easily be modified to fit with "da" and "ja". Q1 - Directed to A Would you answer ‘ja’ to the question of whether you would say yes in your language to the question of whether you and B would give the same answer to the question whether the sky is the ocean? The question above is an example of it. If A cannot answer, then B is definitely random. Otherwise, A is random, or A and B is true or false in an unknown order. Under every circumstance, we know of at least 1 god who is not random. Q2 (1) - Directed to the god identified as not random from the previous question. Would you answer ‘ja’ to the question of whether you would say yes in your language to the question of whether you and C would give the same answer to the question whether the sky is the ocean? This question proves another god. We should agree that if this god does not answer, then C is definitely random and if during the first question A answered "ja" then he is True, if A answered "da" then he is False. Read the rest in my post above. Q2 (2 only ask if A responded to the first question) - Directed B. Would you answer ‘ja’ to the question of whether you would say yes in your language to the question of whether you and C would give the same answer to the question whether the sky is the ocean? Heres a list: A is True and B is false and C is Random if: Q1:"ja" Q2:"da" A is False and B is True and C is Random if: Q1:"da" Q2:"ja" A is True and B is Random and C is False if: Q1: unanswered Q2:"ja" A is False and B is Random and C is True if: Q1: unanswered Q2:"da" A is Random and B is False and C is True if: Q1:"da" Q2:"da" A is Random and B is True and C is False if: Q1:"ja" Q2:"ja" TEST #1: A is True B is False C is Random Q1: A will return "ja" Q2: B will return "da" So here's your proof, and I'm sorry I wasn't as clear last time, I think I even forgot about including the second part to Q2. So here it is!
 Mon Nov 09, 2015 7:03 am  by branch You would ask one god what the random god would say if I asked whether the sky was blue. If they answered they would be the random god, and if not they would either be the false or true god. If it was the random god then you would pick one of the other two, and if it was not the random god then you would pick that god to ask the next question to. It would be “Not including the random god, what would the god here that is not you answer to the question is the sky blue?” This would be no, so you could assume that the other would (da or ja) would be no you can then ask the same god whether the sky is blue, to discover if they are the true or false god. If you have already discover the random god then you have finished, if not then you will need to ask one of the other gods question one to discover their identities.
 Wed Jul 20, 2016 9:56 am  by bathfilms This is the best puzzle I've ever read! While I admire the "non-reply" solutions, I don't believe they are valid. The question provides only 2 answers: da and ja. Not answering does not comply. If we also try limiting the question to only being able to ask all 3 people exactly once, then there are 6 arrangements of the people: (T = True person, F = False person, R = Random person) TFR TRF FRT FTR RTF RFT If I use 0 and 1 to represent the possible answers, there are also 7: 001 010 011 100 101 110 111 This might indicate that that the solution can be found without recourse to a non-response. However, this list of answers does not differentiate a random 1 or 0 from a genuine 1 or 0. Therefore, more information must be gleaned via the questions themselves. As we don't originally know if 1 or 0 is true or false, then whatever the outcome to the first question, then the second question can be independent of the reply to the first one. This leaves the final question being fully dependent on the outcomes of the first 2. The only information externally visible is if the first answers are equal or unequal. Internally, however, conditional questioning brings more evidence. To be continued... (I have a plan!)Last edited by bathfilms on Thu Jul 21, 2016 10:17 am; edited 2 times in total
 Thu Jul 21, 2016 8:15 am  by Dzallen Here is one solution: First of all, one cannot assume that a god would stay silent and not answer when faced with an impossible question, because that is not given in the question. For example, if faced with an impossible question a god may just give a random answer, so it is best to avoid asking questions with no definitive answer. Important notes: a) You can make the false god speak the truth by adding "if I were to ask you..." in front of the main question, as the layered question cancels out his lies. b) By using "...would you say da?" as the end of a question, you can infer whether the god means yes or no in his answer, regardless of what da and ja mean: if he answers da, then he must mean yes, because even if da means no, two negatives make a positive. Similarly, if he answers ja, the he must mean no. From a)&b), it is possible to phrase any question to the true or false gods such that they tell the truth and you understand the answer. The problem lies only with the random god, so the first two questions are aimed at identifying him. Questions: 1. (to god A) If I were to ask you whether god B is the random god, would you say da? 2.1. A answers da. This means that the random god is god A, or god B, hence next question is directed to C: If I were to ask you whether god B is the random god, would you say da? 3.1. C answers da. C is not random, so he must be telling the truth, therefore god B is random. Next question to C again: If I were to ask you whether god A is the false god, would you say da? Answers da: A is false, B is random, C is true Answers ja: A is true, B is random, C is false 3.2. C answers ja. A must be random. Next question to C again: If I were to ask you whether god B is the false god, would you say da? Answers da: A is random, B is false, C is true Answers ja: A is random, B is true, C is false 2.2. A answers ja. This means the random god is god A, or god C, so next question is to god B: If I were to ask you whether god C is the random god, would you say da? 3.3. B answers da. C must be random. Next question to B again: If I were to ask you whether god A is the false god, would you say da? Answers da: A is false, B is true, C is random Answers ja: A is true, B is false, C is random 3.4. B answers ja. A must be random. Next question to B again: If I were to ask you whether god C is the false god, would you say da? Answers da: A is random, B is true, C is false Answers ja: A is random, B is false, C is true In Summary: 1st question determines who is not random, and hence who to ask next. 2nd question determines who is random. 3rd question determines who is true and who is false. Answers: da da da...................A-False B-Random C-True da da ja....................A-True B-Random C-False da ja da....................A-Random B-False C-True da ja ja.....................A-Random B-True C-False ja da da....................A-False B-True C-Random ja da ja.....................A-True B-False C-Random ja ja da.....................A-Random B-True C-False ja ja ja......................A-Random B-False C-True This provides the answer without even knowing what da and ja mean! It is possible, though, to find the answer as well as what da and ja mean, using a much more complicated strategy.
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