A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, David, Evelyn, Joseph, Ella, and Matthew. According to Emily, "If David is a knave then Joseph is a knave". David said that Emily is a knight. Evelyn remarked, "Joseph is a knave and Matthew is a knave". According to Joseph, "David is a knave". In Ella's words: "Evelyn is not a knight". Matthew asserted: "Ella is a knave and Evelyn is a knight". So who is a knight and who is a knave?
Emily is a knave, David is a knave, Evelyn is a knave, Joseph is a knight, Ella is a knight, and Matthew is a knave.
(1) Emily is a knave
(2) David is a knave
(3) Evelyn is a knave
(4) Joseph is a knight
(5) Ella is a knight
(6) Matthew is a knave
Assume Emily is a knight. No contradiction is found in their claim that If David is a knave then Joseph is a knave. Assume David is a knight. No contradiction is found in their claim that Emily is a knight. Joseph cannot be a knight, because this would contradict the claim of their own that David is a knave. Assume Joseph is a knave. No contradiction is found in their false claim that David is a knave. Assume Evelyn is a knight. No contradiction is found in their claim that Joseph is a knave and Matthew is a knave. Matthew cannot be a knight, because this would contradict the claim of Evelyn that Joseph is a knave and Matthew is a knave. Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knave and Evelyn is a knight. Ella cannot be a knight, because this would contradict the claim of their own that Evelyn is not a knight. Ella cannot be a knave, because this would contradict the false claim of Matthew that Ella is a knave and Evelyn is a knight. We have exhausted all possibilities for Ella and Matthew, so let us go back and reconsider Evelyn. Assume Evelyn is a knave. No contradiction is found in their false claim that Joseph is a knave and Matthew is a knave. Matthew cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Evelyn is a knight. Matthew cannot be a knave, because this would contradict the false claim of Evelyn that Joseph is a knave and Matthew is a knave. We have exhausted all possibilities for Matthew, Evelyn, and Joseph, so let us go back and reconsider David. David cannot be a knave, because this would contradict the false claim of their own that Emily is a knight. We have exhausted all possibilities for David, so let us go back and reconsider Emily. Assume Emily is a knave. No contradiction is found in their false claim that If David is a knave then Joseph is a knave. David cannot be a knight, because this would contradict the false claim of Emily that If David is a knave then Joseph is a knave. Assume David is a knave. No contradiction is found in their false claim that Emily is a knight. Assume Joseph is a knight. No contradiction is found in their claim that David is a knave. Evelyn cannot be a knight, because this would contradict the claim of their own that Joseph is a knave and Matthew is a knave. Assume Evelyn is a knave. No contradiction is found in their false claim that Joseph is a knave and Matthew is a knave. Matthew cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Evelyn is a knight. Assume Matthew is a knave. No contradiction is found in their false claim that Ella is a knave and Evelyn is a knight. Assume Ella is a knight. No contradiction is found in their claim that Evelyn is not a knight.