This island holds 3 tribes: truth tellers, liars, and randomizers. They will answer any question "yes", "no", or "I don't know".
A randomizer will randomly select one answer, equiprobable. A liar will select one of the 2 false answers at random, 50-50 (his best game theoretic strategy).
You meet 3 natives; Tom True, Lou Liar, Rick Random. You do not know which is which.
i) What sequence of questions will determine their identities?
ii) What is the minimum number of questions necessary?
[ (ii) can be derived from information theory, as a schoolboy problem. ]
Nobody seems to want to try this one! It seems to me that however many questions you ask, there is a possibility that the randomizer might give the same answers as the truth teller would have given, in which case it would be impossible to distinguish the randomizer from the truth teller. But maybe it is a trick question, so how about a hint?
Sometimes the subtleties of these puzzles get lost in transcription.
For example, if I ask a person, not being Rick Random (and arguably even then), "Will Rick Random answer yes to my next question", then the true answer can only be "I don't know". But if it turns out that I've asked that question of Lou Liar, he can't say that, because it's true. And he can't answer either "yes" or "no", because they may turn out to be true. So he can't say anything.
So either it's incorrect to state that they will answer any question "yes", "no" or "I don't know", or there is an unstated restriction on what "any question" can be.
No. In this one the liar won't answer 'I don't know'.
[quote] "A liar will select one of the 2 false answers at random,
50-50 (his best game theoretic strategy)."[\quote]
so Tom(Rick) =3D I don't know Lou(Rick) =3D Yes or No Rick(Rick) =3D Yes or No
So you ask the first person "If I asked Rick if you were Tom would he says 'Yes'" If the answer is I don't know, he's Tom. If there is an answer the first person is either Rick or Lou. If there is an answer, you repeat the question to the second person. After the second question you know who is Tom. Once you know who Tom is you just get him to identify one of the other two.
Three questions max.
Another variation is the three princesses. You have to marry one of the king's daughters. The oldest always tells the truth, the youngest always lies and the middle answers randomly. You can't tell by looking the age of the daughters. You want to marry either the youngest or the oldest because you will always get an interpretable answer. You can ask one Yes or No question to one daughter before deciding who to marry. What is the question?
Derek Holt wrote: ) On 22 Sep, 20:02, PT wrote: )> A variation of the island of knights & knaves... )>
)> This island holds 3 tribes: truth tellers, liars, and randomizers. )> They will answer any question "yes", "no", or "I don't know". )>
)> A randomizer will randomly select one answer, equiprobable. )> A liar will select one of the 2 false answers )> at random, 50-50 (his best game theoretic strategy). )>
)> You meet 3 natives; Tom True, Lou Liar, Rick Random. )> You do not know which is which. )>
)> i) ?What sequence of questions will determine their identities? )>
)> ii) What is the minimum number of questions necessary? )>
)> [ ?(ii) can be derived from information theory, as a schoolboy )> problem. ] ) ) Nobody seems to want to try this one! It seems to me that however many ) questions you ask, there is a possibility that the randomizer might ) give the same answers as the truth teller would have given, in which ) case it would be impossible to distinguish the randomizer from the ) truth teller. But maybe it is a trick question, so how about a hint?
Hint: The three natives know each other.
SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT
According to that line of reasoning Lou Liar cannot answer any question to which he doesn't know the answer, like "will it rain tomorrow?", because he may inadvertently give the correct answer. You could reason that since "I don't know" is the correct answer, he is entitled to answer yes or no.
But since Rick Random ignores all questions and just gives answers at random, I am still unconvinced that you can be certain of distinguishing him from Tom True in any fixed number of questions. Of course with probability 1 he will eventually reveal his true identity!
There are versions of the puzzle(like the three princess puzzle) which have the truth teller and the liar answer true or false when they can and answer randomly when they can't.
The idea is the functions of other functions of statements are:
Think of them as program functions that return True or False. Knight and Knave actually call Random and get an answer and then perform their function on it. They ask random the question and get his answer before replying. The next time you ask Random the same question you may get a different answer.
In the OP's question the liar best strategy to equivocate is to answer randomly when he doesn't know the answer.
"Ask Sister A if Sister B is older (or tells the truth more often) than Sister C. If the answer is yes choose C, if the answer is no choose B. After the wedding you will still have to figure out if you have the oldest or youngest sister.
I figured this out on a long car trip back form Stowe with my wife. Sadly, I cannot think of a way to figure out which sister is the middle one. The marriage to her would be the most interesting.
Line them up left-to-right. Ask the person on the left: "Is the middle person more truthful than the right person?" (Where we define "more truthful than" by: truthtellers are more truthful than randomizers, which are more truthful than liars)
If he answers "yes", then there are 4 possibilities:
T R L In this case, the truthful answer is "yes", and the left person is a truthteller, so he answers "yes"
L R T In this case, the truthful answer is "no", and the left person is a liar, and so answers "yes".
R T L In this case, the truthful answer is "yes", and the left person is a randomizer, and happens to answer "yes".
R L T In this case, the truthful answer is "no", and the left person is a randomizer, and happens to answer "yes".
Note that in all 4 cases, we know that the randomizer is NOT the person on the right. So ask the person on the right "Are you the randomizer?" If he answers yes, then he is a liar, and if he answers no, then he is the truthteller.
For the final question, again ask the person on the right: "Is the person on the left a randomizer?" If that person is a liar, and answers "yes", then you know that the order is
T R L
If the rightmost person is a liar, and answers "no", you know the order is
R T L
If the rightmost person is a truthteller, and answers "yes", then the order is
R L T
If the rightmost person is a truthteller, and answers "no", then the order is
L R T
Now, going back to the original question: "Is the person in the middle more truthful than the person on the right?" If the answer was "no", then we have the following possibilities:
T L R
L T R
R L T
R T L
In this case, we know that the middle person is not the randomizer. So we find out if he is a liar, and then ask him whether the person on the left is the randomizer.
So, it seems to me that it requires three questions.
Oh, somehow I missed that that was a possible answer. Can we assume that the people do know who is who (so "I don't know" is always a lie)? So answering "I don't know" means that the person answering is either a liar or a randomizer?
ElectronDepot website is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.