You are in a popular tourist town in the land of Liars and Knights. You happen to overhear a conversation another tourist is having with three of the locals: Alex, Bert and Carl. Each of the three could be a knight, a knave or a liar. You know that for each question the tourist asks, Alex, Bert and Carl each give one response, but you don't know who said what. The conversation is as follows:
- What type are each of you?
- I am a knight.
- I am a knave.
- I am a liar.
- How many of you are the same type?
- We are all the same type.
- We are all different types.
- Exactly two of us are the same type.
- What type is Alex?
- A knave.
- A liar.
- Different from Bert.
Can you determine which type Alex, Bert and Carl are?
