A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Joseph, Lucas, Emma, Grace, and Chloe. Mason commented, "Joseph is a knight if and only if Mason is a knight". According to Joseph, "Emma is a knight and Joseph is a knight". Lucas stated, "Joseph is not a knave". In a statement by Emma: "Grace is not a knight". Grace expressed that Chloe is a knight. "Mason is a knight," Chloe claimed. So who is a knight and who is a knave?
Mason is a knave, Joseph is a knight, Lucas is a knight, Emma is a knight, Grace is a knave, and Chloe is a knave.
(1) Mason is a knave
(2) Joseph is a knight
(3) Lucas is a knight
(4) Emma is a knight
(5) Grace is a knave
(6) Chloe is a knave
Assume Mason is a knight. No contradiction is found in their claim that Joseph is a knight if and only if Mason is a knight. Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knight and Joseph is a knight. Assume Emma is a knight. No contradiction is found in their claim that Grace is not a knight. Grace cannot be a knight, because this would contradict the claim of Emma that Grace is not a knight. Assume Grace is a knave. No contradiction is found in their false claim that Chloe is a knight. Chloe cannot be a knight, because this would contradict the false claim of Grace that Chloe is a knight. Chloe cannot be a knave, because this would contradict the false claim of their own that Mason is a knight. We have exhausted all possibilities for Chloe and Grace, so let us go back and reconsider Emma. Emma cannot be a knave, because this would contradict the claim of Joseph that Emma is a knight and Joseph is a knight. We have exhausted all possibilities for Emma, so let us go back and reconsider Joseph. Joseph cannot be a knave, because this would contradict the claim of Mason that Joseph is a knight if and only if Mason is a knight. We have exhausted all possibilities for Joseph, so let us go back and reconsider Mason. Assume Mason is a knave. No contradiction is found in their false claim that Joseph is a knight if and only if Mason is a knight. Assume Joseph is a knight. No contradiction is found in their claim that Emma is a knight and Joseph is a knight. Assume Emma is a knight. No contradiction is found in their claim that Grace is not a knight. Grace cannot be a knight, because this would contradict the claim of Emma that Grace is not a knight. Assume Grace is a knave. No contradiction is found in their false claim that Chloe is a knight. Chloe cannot be a knight, because this would contradict the false claim of Grace that Chloe is a knight. Assume Chloe is a knave. No contradiction is found in their false claim that Mason is a knight. Assume Lucas is a knight. No contradiction is found in their claim that Joseph is not a knave.