Would the solution for #4 also work for #3? I’ve gone through it and it seems it would.

for question 4 i would ask either one “if i asked your counterpart which path is correct what would they saw?” either answer would end up being a lie so take the opposite

Referring to the chart above, simply asking, “If I asked you if this is the correct path, would you say yes?” has the result that a Yes answer means it’s the correct path and a No answer means it’s the incorrect path, so you get the information you are seeking. Ironically, you would never find out whether you were talking to a knight or a knave. In a sense, “If I asked you if this is the correct path, would you say yes?” is a trick question, because it provides us with an extra layer of information, allowing us to get the information we seek with only one question.

Sorry, no. The point is that you need to ask 2 questions to solve #4

But I don’t think you know which path is correct.

A knight and a knave can both give yes no answers… so it depends whether the path is correct or not, which you still do not know…?

Let’s have a look! A chart may be helpful in understanding #3 as well. Here again, the added layer of abstraction gives additional information, though here it is the knight’s answer that changes.

The new information comes from an added layer of abstraction with regard to the knave. To understand #4, suppose you are the knave, so you must always lie. A traveler approaches, who does not know whether you are a knight or a knave. If he points to a path, and simply asks, “Is this the correct path?” then you must lie, so if it is the correct path, you say No and if it is not the correct path, you say Yes. This does not help the traveler. But if the traveler instead asks, “If I asked you if this is the correct path, would you say yes?” then your answer must change! If it is the correct path and you were asked if it is the correct path, you would lie and say No, so in answer to the question of whether you would say Yes, you must lie and say Yes. Similarly, if it was the incorrect path, your answer to the question, “Is this the correct path?” would be Yes (a lie), but your answer to the question, “If I asked you if this is the correct path, would you say yes?” must be No (a lie). This forces the knave into a double lie, revealing the correct path. The knight, on the other hand, would be telling the truth in answer to either question, so no new information is needed in that case. Here’s a chart to illustrate the difference between the two questions: