Welcome to the Island of Knights, Knaves, and Sir Mix-a-lot! There are a few things you should know about this island:

- Knights
*always*tell the truth - Knaves
*always*lie - There is exactly one Knight named “Sir Mix-a-lot”. Like every other knight, he cannot lie.
- This island is one of a chain of islands containing knights and knaves, each one having its own quirk.

Today we are on the basic island of Knights and Knaves. We are driving along, trying to find the way back to our hotel when we come to a fork in the road. There is a resident of the island standing alongside the road, so I get out out to ask him for directions. I ask one question before returning to the car, to which the resident nods “Yes.” Upon returning to the car, I say, “We have to go left at this fork in the road to get back to our hotel.” You ask, “Did he tell you that? Do you even know if he is a knight or a knave?” I respond, “I have no idea if he is a knight or a knave, but I do know we need to go left.” What did I ask him?

#### Solution:

If I had just asked, “Is the hotel to the left?” I would have no way of knowing if his answer was the truth or not. The resident could have been lying and I would have no way of knowing. Instead, I asked, “Are you the type of person who could claim that the hotel is to the left?” Assuming that the hotel is actually to the left, a knight would answer “Yes.” Surprisingly, a knave would also answer “Yes.” If asked directly if the hotel were to the left, he would lie and say “No,” but since he is a knave, he will also lie about lying.

Perhaps it would be easier to think about it another way. What would a knave say to, “Are you the type of person who could claim 2 + 2 = 4?” That question could be changed to “Are you the type of person who tells the truth?” Even more simply, you could ask, “Are you a knight?” A knave would certainly say yes to all of those questions.

Conversely, a “No” answer would have meant the hotel was to the right, no matter what.