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.
Sam has got three daughters. The eldest daughter is the most honest girl in the universe and she always speaks truth. The middle daughter is a modest woman. She speaks truth and lies according to the situations. The youngest one never speaks truth. Not a single word she spoke was true and would never be true.
Sam brought a marriage proposal for one of his girls. It was John. John wanted to marry either the eldest or the youngest daughter of Sam as he can easily identify whether the girl speaks truth or lie!
John told his desire to Sam. However, Sam laid a condition. He told John that he will not say who the eldest, middle or youngest one is. Also, he allowed John to ask only one question to identify the eldest or youngest so he can marry one.
John asked one question and found the right girl. What was the question and whom should he pick?
The question he asked is, 'Is she older than her?'
He asks this question to one of the daughters.
If he asked this question to older daughter pointing at other two, he probably would know the youngest one! NO matter, she always speaks truth.
If he asked the question to middle one, probably he can choose either.
If he asked the youngest one, she always lies and he can find eldest one. No matter, he has to choose the youngest one based on the answer.
I am pronounced as a one letter alphabet.
I am written with three letters.
I am complete with just two letters.
I am double.
I am blue I am black I am brown I am gray I am yellow and I am green.
I can read from both ends.
I appear the same every way!
What am I?