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.