You are to meet with two brothers. You know that one of them, named Bob, has a very important package for you. Unfortunately, you never saw Bob or his brother, and don’t know who is who.
To make the matter worse, one of the brothers is a pathological liar who never tells the truth, while the other never lies. You do not know whether Bob is the liar or not.
Upon meeting the brothers, you can ask one short question of either of the brothers (but not both) to establish with certainty which of the two is Bob.
What question do you ask?
Ask “Is Bob a liar?” Only Bob will answer “No”.
Proof
There are four possibilities:
- You speak to Bob and he tells the truth: “No”.
- You speak to Bob and he lies: “No”.
- You speak to his brother and he tells the truth: “Yes”.
- You speak to his brother and he lies: “Yes”.
So it can be seen that Bob will always answer “No” and his brother will always answer “Yes”.