A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Joseph, Liam, Alexander, Ella, and Aiden. Benjamin noted, "If Aiden is a knight then Liam is a knave". "Alexander is a knight and Liam is a knave" - Joseph. Liam said that Ella is a knight. Alexander stated, "Joseph is a knight and Joseph is a knave". Ella noted, "Alexander is a knave and Aiden is a knave". Aiden said that Joseph is not a knave. So who is a knight and who is a knave?
Benjamin is a knight, Joseph is a knave, Liam is a knight, Alexander is a knave, Ella is a knight, and Aiden is a knave.
(1) Benjamin is a knight
(2) Joseph is a knave
(3) Liam is a knight
(4) Alexander is a knave
(5) Ella is a knight
(6) Aiden is a knave
Assume Benjamin is a knight. No contradiction is found in their claim that If Aiden is a knight then Liam is a knave. Assume Aiden is a knight. No contradiction is found in their claim that Joseph is not a knave. Assume Joseph is a knight. No contradiction is found in their claim that Alexander is a knight and Liam is a knave. Alexander cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave. Alexander cannot be a knave, because this would contradict the claim of Joseph that Alexander is a knight and Liam is a knave. We have exhausted all possibilities for Alexander, so let us go back and reconsider Joseph. Joseph cannot be a knave, because this would contradict the claim of Aiden that Joseph is not a knave. We have exhausted all possibilities for Joseph, so let us go back and reconsider Aiden. Assume Aiden is a knave. No contradiction is found in their false claim that Joseph is not a knave. Joseph cannot be a knight, because this would contradict the false claim of Aiden that Joseph is not a knave. Assume Joseph is a knave. No contradiction is found in their false claim that Alexander is a knight and Liam is a knave. Alexander cannot be a knight, because this would contradict the claim of their own that Joseph is a knight and Joseph is a knave. Assume Alexander is a knave. No contradiction is found in their false claim that Joseph is a knight and Joseph is a knave. Assume Liam is a knight. No contradiction is found in their claim that Ella is a knight. Assume Ella is a knight. No contradiction is found in their claim that Alexander is a knave and Aiden is a knave.