Welcome to the realm of knights and knaves. Knights are noble individuals and only tell the truth, but knaves are wicked and always lie.
The issue? Knights and knaves look the same. You can only distinguish them with the power of thought!
On this particular encounter, the knights and knaves do not speak English but can understand the language perfectly well.
The knights and knaves only respond to questions with either “ya” or “na”, which means “no” and “yes”. However, you don’t know which is which.
You approach a pair of strange doors and have it on good authority that it leads to either eternal riches or certain death.
There is a knight or knave guarding the door.
You may ask ONE question, to which the individual replies with either “ya” or “na”.
How do you determine the path to eternal riches?
To discover the correct door, you have to ask the question: “If I were to ask you if this path leads to eternal riches, would you say ya?”
If the person says “ya,” it is the path to eternal riches. If he says “na,” it’s the path to certain death. It’s as simple as that. Here’s why:
Let’s first assume the person is a knight to find out why this is the case. In that case, there are four additional possibilities:
- “Ya” means “yes” and the path leads to riches. Knight’s response: “ya.”
- “Ya” means “yes” and the path leads to death. Knight’s response: “na.”
- “Ya” means “no” and the path leads to riches. Knight’s response: “ya.”
- “Ya” means “no” and the path leads to death. Knight’s response: “na.”
It works out the same if the individual is the knave.
Read the question again slowly: “if I were to ask you.” This essentially tricks the knave into providing the same responses as the knight. So, for example, if the path led to riches, and you asked a knave if it leads to riches, he would say “no.”
But if you instead ask, “if I were to ask you if this path leads to riches, would you say yes?” then he would say “yes” (this would be a lie, because the knave wouldn’t say “yes” if you were to ask him).
So, you can discover which path is the path to riches without knowing if the person is a knight or a knave, and also without determining the meanings of the responses “na” and “ya.”
