You awake in a locked dungeon containing three chests, numbered 1, 2, and 3. The guard tells you that he has placed the key to the dungeon on one of the three chests, but in the other two, there are thousands of poisonous scorpions, all very hungry for prisoners. The guard says he will allow you one yes/no question, which he will answer truthfully. What should you ask him in order to locate the chest containing the key?
Help
Hint
The guard will either answer yes, no, or not at all (if he does not know the right answer). That's three possible responses to your question.
Solution
There are many possible solutions. One of them is this: ask the guard, "If I were to think of either the number 1 or 2, would the number on the chest containing the key be greater than the number I am thinking of?" Now if the key is in chest 1, then the guard will say "no," since 1 is not greater than either 1 or 2. If the key is in chest 2, then the guard will not answer, since it is impossible for him to know whether you were thinking of the number 1 or 2. If the key is in chest 3, then the guard will answer "yes," since 3 is greater than both 1 and 2. In any case, you know which chest contains the key.