Question

The Island of Knights and Knaves has two types of inhabitants: Knights, who always tell the truth, and Knaves, who always lie. As you are exploring the Island of Knights and Knaves you encounter two people named A and B. B tells you “I am a Knave, but A isn’t”. A says nothing. Determine the nature of A and B, if you can.

Answer 1

Solution :

There are only total two possible cases for A and B

Case(1): Suppose A = Knaves | B = Knight

• So as per the question Knights always tell the truth. that means B will always say the truth. But B is saying "I am a knave but A isn't" which is contradicting the Case (1).
• Because If B is a knight then how can he be a knave at same time.
• So above use case is wrong.

Case (2):   Suppose A = Knight | B = Knaves

• So as per the question Knaves always tell the lie. that means B will always say lie and B is saying "I am a knave but A isn't" which means B is a Knight and A is a Knave.
• Again its contradicting Case (2).
• Because If B is a knave then how can he be a knight at same time.
• So above use case is also wrong.

Hence we can't determine the Nature of A and B using above statement.