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Three gods - Truth-teller/Liar/Random
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Three gods,on a distant planet - one always tells the truth; one always lies and the other one lies and tells the truth at random.
Your task is to identify which god is which.
You are allowed to ask 3 questions which must be answerable with either a yes or a no - if you ask a question that causes one of them to answer with anything but a yes or a no (such as a maybe) - you will be incinerated on the spot.
The first question is asked to all 3 gods and they all answer in turn, with a yes or a no.
The 2nd question is asked to one (and only one) of the gods and he answers with a yes or a no.
The 3rd question must be directed to the same god that you asked the 2nd question to.
To make things awkward, the gods speak a language that you have never heard before and as such, you do not know what the words "yes" and "no" translate to in their language. After asking the first question, the gods may have all answered with the same answer (yes OR no), in which case you will only know one of their yes and no words; or they may have given different answers (yes AND no), so after the first question you may be lucky enough to know what both the words are (even though you won't know which word means yes and which word means no).
However, as you are a newcomer on this planet, use of their language is punishable by instant death, so you are not allowed to speak these words, or communicate them in any written form or whatever.
What questions do you ask in order to determine which god is which and to also enable you (without asking) what words mean yes and no.
Your task is to identify which god is which.
You are allowed to ask 3 questions which must be answerable with either a yes or a no - if you ask a question that causes one of them to answer with anything but a yes or a no (such as a maybe) - you will be incinerated on the spot.
The first question is asked to all 3 gods and they all answer in turn, with a yes or a no.
The 2nd question is asked to one (and only one) of the gods and he answers with a yes or a no.
The 3rd question must be directed to the same god that you asked the 2nd question to.
To make things awkward, the gods speak a language that you have never heard before and as such, you do not know what the words "yes" and "no" translate to in their language. After asking the first question, the gods may have all answered with the same answer (yes OR no), in which case you will only know one of their yes and no words; or they may have given different answers (yes AND no), so after the first question you may be lucky enough to know what both the words are (even though you won't know which word means yes and which word means no).
However, as you are a newcomer on this planet, use of their language is punishable by instant death, so you are not allowed to speak these words, or communicate them in any written form or whatever.
What questions do you ask in order to determine which god is which and to also enable you (without asking) what words mean yes and no.
Answers
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Q1: Do you always tell the truth?
The truthteller will give the local eqivalent of 'Yes'
The liar wil give the same answer.
The one who may be truthful, or a liar, at random may give the eqivalent of either yes, or no.
If you get two answers the same and one different, you know that the answer given by 2 persons is the local equivalent of yes, and the other answer means no. If all three answer the same, then the answer they use means yes.
So after 1 question (to all three) you know what the local word is for 'Yes'.
If one person gave a different answer then he must be the person who occasionally lies. (don't ask him anything more, it won't help!.)
In this example (where you have identified the ocasional liar) ask one of the others whether the occasional liar always tells the truth. The truth-teller will give the local equivalent of 'No', the liar will give the local equivalent of yes.
You can thus identify all three Gods after asking one question to each, and one additional question (if they do not all give the same answer to question 1)
That's half the question solve!
The truthteller will give the local eqivalent of 'Yes'
The liar wil give the same answer.
The one who may be truthful, or a liar, at random may give the eqivalent of either yes, or no.
If you get two answers the same and one different, you know that the answer given by 2 persons is the local equivalent of yes, and the other answer means no. If all three answer the same, then the answer they use means yes.
So after 1 question (to all three) you know what the local word is for 'Yes'.
If one person gave a different answer then he must be the person who occasionally lies. (don't ask him anything more, it won't help!.)
In this example (where you have identified the ocasional liar) ask one of the others whether the occasional liar always tells the truth. The truth-teller will give the local equivalent of 'No', the liar will give the local equivalent of yes.
You can thus identify all three Gods after asking one question to each, and one additional question (if they do not all give the same answer to question 1)
That's half the question solve!
Consider it done:
Firstly ask the question to each of them, "are you the random one?" this will always get either 2 yes's and a no, or 2 no's and a yes 'cos the liar will always reply yes and the truth-teller will always reply no, with the random one saying either yes or no.
We don't know which word means what but whichever answer is only given once, we know that he can't be the random one - we just don't know yet whether he is the liar or the truth-teller, so we now ask this one a question that he must answer no to - the question is, "are you the liar?". The truth-teller will reply no to this and the liar will reply no to this. So whatever word he replies with - this translates as "no". Now look at the answer that he gave to the first question. If he replied with the same word, then he said no to the first question so he must be the truth-teller. If he replied with a different word, then that word must mean yes and he must be the liar. So we now know the translation of the words and we have the identity of either the liar or the truth-teller (depending on what answers were given). Lastly, ask the truth-teller/liar, whilst pointing to one of the other 2 men, "is that the random one?" You can deduce the final identities, as you know the identity of the one you're asking the question to.
Firstly ask the question to each of them, "are you the random one?" this will always get either 2 yes's and a no, or 2 no's and a yes 'cos the liar will always reply yes and the truth-teller will always reply no, with the random one saying either yes or no.
We don't know which word means what but whichever answer is only given once, we know that he can't be the random one - we just don't know yet whether he is the liar or the truth-teller, so we now ask this one a question that he must answer no to - the question is, "are you the liar?". The truth-teller will reply no to this and the liar will reply no to this. So whatever word he replies with - this translates as "no". Now look at the answer that he gave to the first question. If he replied with the same word, then he said no to the first question so he must be the truth-teller. If he replied with a different word, then that word must mean yes and he must be the liar. So we now know the translation of the words and we have the identity of either the liar or the truth-teller (depending on what answers were given). Lastly, ask the truth-teller/liar, whilst pointing to one of the other 2 men, "is that the random one?" You can deduce the final identities, as you know the identity of the one you're asking the question to.
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