Question: There is a prison with 100 prisoners, each in separate cells with no form of contact. There is an area in the prison with a single light bulb in it. Each day, the warden picks one of the prisoners at random, even if they have been picked before, and takes them out to the lobby. The prisoner will have the choice to flip the switch if they want. The light bulb starts off.
When a prisoner is taken into the area with the light bulb, he can also say "Every prisoner has been brought to the light bulb." If this is true all prisoners will go free. However, if a prisoner chooses to say this and it's wrong, all the prisoners will be executed. So a prisoner should only say this if he knows it is true for sure.
Before the first day of this process begins, all the prisoners are allowed to get together to discuss a strategy to eventually save themselves.
What strategy could they use to ensure they will go free?
Answer: Only allow one prisoner to turn the light bulb off and all of the others turn it on if they have never turned it on before. If they have turned it on before they do nothing. The prisoner that can turn it off then knows they have all been there and saves them all when he has turned it off 99 times.
Question: You have a glass of water that looks about half full. How can you tell, only using the glass of water itself, if the glass is half full or not?
The glass is a right cylinder.
Answer: Tip the glass of water until the water reaches the rim of the glass and if the water lines up perfectly with the bottom rim of the glass, it is half full.
Question: There were 2 doors. Behind the 1 door, is hell and behind the other door, is heaven but you don't know which door will take you to heaven. In front of them, there were 2 brothers, which is guarding the door. One of the brother always lie and the other one always tell the truth. Of course you don't know who is lying and who is not. You only get 1 question to ask one of them to figure out which door leads to heaven. What question you might ask? Remember you only get to ask 1 question. it means that you can't ask one question each of them. that will be 2 questions. You only ask 1 question to any of them and no more. How do you do that?
Answer: Go up to one of the guy and ask this question, " Hello, which door that your brother will point if I ask him which way is the heaven." Then take the other door. Don't enter the door that he was pointing. This question will work for both of them because if you ask this question to the truth guy, he will point the hell because he knows that his brother will point hell and if you asked to the liar, he'll still point hell because he knows that his brother will point to heaven door, so he lied. That's why you take the other door.