So: You find yourself in a room that has only 2 exit point doors, that are closed. You can safely exit through one of the 2 doors. If you choose the wrong door, the entire room will explode and kill you instantly.
In the center of the room, is a computer on a table. It is programmed to either ONLY lie or ONLY tell the truth as an ANSWER to ONE QUESTION only, that you can ask it.. You don't know which one it is programmed to do, but you know this variable exists.
What's the question you will ask it to make it choose without doubt, to point you to the correct door?
To make the computer point you to the correct door, you can ask it the following question: "If I were to ask the other door, 'Which door leads to safety?' what would it say?"
To understand why this question works, you need to consider the possibilities:
1. If the computer is programmed to only tell the truth:
- The computer would truthfully answer the question from the perspective of the other door, which would be the wrong door.
- So, when you ask the computer this question, it would say that the other door would point you to the wrong door.
- Therefore, you should choose the opposite door that the computer indicates.
2. If the computer is programmed to only lie:
- The computer would lie about what the other door would say, which means it would indicate the wrong door.
- So, when you ask the computer this question, it would again say that the other door would point you to the wrong door.
- Therefore, you should choose the opposite door that the computer indicates.
In both cases, the computer, regardless of its programming, would provide the same answer that points you to the same wrong door. By choosing the opposite door that the computer indicates, you will be directed to the correct one, ensuring your safe exit from the room.