In the land of Brainopia, there are three races of people: Mikkos, who tell the truth all the time, Kikkos, who always tell lies, and Zikkos, who tell alternate false and true statements, in which the order is not known (i.e. true, false, true or false, true, false). When interviewing three Brainopians, a foreigner received the following statements:
I am a Mikko.
I am a Kikko.
a. They are both lying.
b. I am a Zikko.
Can you help the very confused foreigner determine who is who, assuming each person represents a different race?
Person 1 is a Miko.
Person 2 is a Ziko.
Person 3 is a Kikko.
You're walking down a path and come to two doors. One of the doors leads to a life of prosperity and happiness, and the other door leads to a life of misery and sorrow. You don't know which door is which.
In front of the door is ONE man. You know that this man either always lies, or always tells the truth, but you don't know which. The man knows which door is which.
You are allowed to ask the man ONE yes-or-no question to figure out which door to go through. To make things more difficult, the man is very self-centered, so you are only allowed to ask him a question about what he thinks or knows; your question cannot involve what any other person or object (real or hypothetical) might say.
What question should you ask to ensure you go through the good door?
You should ask: "If I asked you if the good door is on the left, would you say yes?"
Notice that this is subtly different than asking "Is the good door on the left?", in that you are asking him IF he would say yes to that question, not what his answer to the question would be. Thus you are asking a question about a question, and if it ends up being the liar you are talking to, this will cause him to lie about a lie and thus tell the truth. The four possible cases are:
The man is a truth-teller and the good door is on the left. He will say "yes".
The man is a truth-teller and the good door is on the right. He will say "no".
The man is a liar and the good door is on the left. He will say "yes" because if you asked him "Is the good door on the left?", he would lie and say "no", and so when you ask him if he would say "yes", he will lie and say "yes".
The man is a liar and the good door is on the right. Similar to the previous example, he'll say "no".
So regardless of whether the man is a truth-teller or a liar, this question will get a "yes" if the door on the left is the good door, and a "no" if it's not.
You are walking down a path when you come to two doors. Opening one of the doors will lead you to a life of prosperity and happiness, while opening the other door will lead to a life of misery and sorrow. You don't know which door leads to which life.
In front of the doors are two twin brothers who know which door leads where. One of the brothers always lies, and the other always tells the truth. You don't know which brother is the liar and which is the truth-teller.
You are allowed to ask one single question to one of the brothers (not both) to figure out which door to open.
What question should you ask?
Ask "If I asked your brother what the good door is, what would he say?"
If you ask the truth-telling brother, he will point to the bad door, because this is what the lying brother would point to.
Alternatively, if you ask the lying brother, he will also point to the bad door, because this is NOT what the truth-telling brother would point to.
So whichever door is pointed to, you should go through the other one.
Once upon a time there existed a temple in India which housed three identical idols which spoke to the devotees.
The idols were of – God of Truth, which always spoke the truth; God of Falsehood, which always lied; and God of Diplomacy which sometimes spoke the truth and at other times lied.
The pilgrims come from all parts of the world to get their questions answered by the Gods. But there was a problem. As the idols were indistinguishable, devotees were not sure from which idol to ask their questions and in turn they did not know which God has answered and whether to believe it or not.
Once a wise man visited the temple. He asked the question: "Which God is seated at the centre?" to all the three idols. The idol on the left, centre and right replied God of Truth, God of Diplomacy and God of Falsehood respectively. The wise man at once proclaimed that he had solved the mystery of the temple.
The idols from left to right are: God of Diplomacy, God of Falsehood, God of Truth.
The God of Truth is not seated on the left because he always speaks the truth whereas the idol on the left replied that the God of Truth is seated at the centre.
The God of Truth is also not seated in the centre as he always speaks the truth but the idol at the centre replied that the God of Diplomacy is seated at the centre.
Therefore, the God of Truth is seated on the right. As God of Truth is seated on the right, and he always speaks the truth, then the The God of Falsehood is seated at the centre. The God of Diplomacy is seated on the left and he has lied.