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#1
12-30-2008, 04:47 AM
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The Liar, The Truth Teller and The Random Answerer
There is a truth teller (always tells the truth), a liar (always lies), and one that sometimes answers truthfully and sometimes lies. Each man knows who is who. You may ask three yes or no question to determine who is who. Each time you ask a question, it must only be directed to one of the men (of your choice). You may ask the same question more than once, but of course it will count towards your total. What are your questions and to whom will you ask them? |
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12-31-2008, 04:44 AM
#2
Let me frame a scenario... There are two ways... One leads to Hell and the other leads to Heaven...
And only these three people know which one leads where... Since there are 3 people we can form them into 3 groups each consisting of 2 people... These three groups are: TL, LR and RT where L-> Liar, T ->Truth and R -> Random answerer Since we dont know who is in which group... we need to ask the same question to each groups... The question could be as follows: If i would ask the other person (who is not in this group) which way leads to hell what would he answer? Case 1: TL group The Truth person would know that the other person is a Random Answerer and since he says the truth he should point to both the locations... The Liar would give some arbitrary answer since he is not sure what the Random Answerer would tell... That implies the other person is a Random Answerer and the one which points to both the locations is the Truth teller and the left out is the Liar... Case 2: LR group The Liar would point to Heaven since... he knows that the Truth teller tells the truth(point to Hell) and the Liar would lie(point to Heaven) The Random teller would point to some arbitrary location... Case 3: RT group The Truth teller would point to Heaven since... he knows that the Liar would tell a lie(point to Heaven) and the Truth teller would say the truth(point to Heaven) The Random teller would point to some arbitrary location... From the last two cases we cannot predict who is who... So... the worst case would be if you have asked the same question 3 times to 3 groups... and... the best possible case is the question asked only once... Hope you understood what i meant... |
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12-31-2008, 06:57 AM
#3
There are 6 possible states for the order of the men: TRL, TLR, LTR, LRT, RTL, RLT
There are 8 possible combinations of anwers for questions: TTT, TTL, TLT, TLL, LTT, LTL, LLT, LLL.
So: Ask #1 if L is standing on R's right arm (our left if they are facing us). The answer gives you a split in the order they are standing: If YES, then it has to be T telling the truth, L telling a lie, or one of R's worthless answers, so: TLR, LTR, or RTL, RLT. If NO, then it has to be T telling the truth, L telling a lie, or R and his worthless answers, so: TRL, LRT, or RTL, RLT. Now we know, based on the answer to #1 where to avoid R's worthless answers. We now ask T or L "Is T in the lineup?" If answer 1 was Yes, we ask person 2, if it was no we ask person 3. The answer now will give us some more info. If it's Yes, it's T answering the truth, if it's no, it's L answering a lie. So based on who we asked, we now know: Yes, Yes: Has to be LTR, or RTL Yes, No: TLR, RLT No, Yes: LRT, RLT No, No: TRL, RTL Now any question separating the two possiblities works - just make sure you are avoiding R's worthless answers. For example: Yes, Yes - ask #2 if #1 is L. (We know #2 is T and will tell the truth) - Yes = LTR, No = RTL Yes, No, - ask #2 if #1 is T. ( We know #2 is L and will tell a lie) - Yes = RLT, No = TLR No, Yes - ask # 3 if #1 is L. (We know #3 is T and will tell the truth) - Yes = LRT, No = RLT No, No, - ask #3 if #1 is T. (We know #3 is L and will tell a lie) - Yes = RTL, No = TRL So we have the order and know who is who.:whistle: |
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