Question

You are in a land where there are only knights and knaves. Knights always tell the truth and knaves always lie. You come across three inhabitants of this land who are out on a boat off shore. It’s dark and you can’t tell who is who so you shout out to them, "Which one of you is a knight and which one is a knave?" The first one says something, but the wind comes up and you can’t hear what they said. The second one then says, "She said she’s an knight, and so am I." The third one says, "They’re both lying; I’m an knight and they’re both knaves." Who is a knight and who is a knave? For full credit, you must explain/prove your answer.

Answer 1

Based on logical analysis, the third person is a knave and the first person is a knight.

Step-by-step explanation:

The first person's statement is indeterminate due to the wind. However, we can analyze the statements made by the second and third persons. The second person says that the first person claimed to be a knight, making them a knight as well. If we assume the second person is telling the truth, then the third person's statement contradicts this by claiming they are a knight and the others are knaves. This would mean that the third person is a knight and the first two are knaves. However, if we assume the second person is lying, then the first person did not claim to be a knight. This still makes the third person's statement false, as they claim both the first and second person are knaves. Therefore, based on logical analysis, the third person must be a knave and the first person is a knight.

Answer 2

The first two are Knights

Step-by-step explanation:

Assume A is a knave. In that case, she is lying. B’s statement is then a contradiction because a knight could never say “If she is lying (she is), then I am a knave,” because that would be a lie. Similarly, if B was a knave, B would never say, “If she is lying (she is), then I am a knave,” because that would be the truth. So if A is a knave, B cannot be a knight or a knave, which is a contradiction. Therefore, A cannot be a knave. Because A cannot be a knave, A must be a knight. In that case, she is not lying. B’s statement is then vacuously true. Therefore, B must be a knight, since a knave cannot make a true statement.