A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Oliver, Michael, Chloe, Ethan, and David. "Ethan is a knave if and only if Michael is a knight," Ella declared. "Ethan is not a knight," Oliver mentioned. "David is a knave" - Michael. Chloe remarked, "If Michael is a knight then Oliver is a knave". Ethan told you that Ella is not a knave. David expressed that If Michael is a knave then Ella is a knave. So who is a knight and who is a knave?
Ella is a knave, Oliver is a knight, Michael is a knave, Chloe is a knight, Ethan is a knave, and David is a knight.
(1) Ella is a knave
(2) Oliver is a knight
(3) Michael is a knave
(4) Chloe is a knight
(5) Ethan is a knave
(6) David is a knight
Assume Ella is a knight. No contradiction is found in their claim that Ethan is a knave if and only if Michael is a knight. Assume Ethan is a knight. No contradiction is found in their claim that Ella is not a knave. Michael cannot be a knight, because this would contradict the claim of Ella that Ethan is a knave if and only if Michael is a knight. Assume Michael is a knave. No contradiction is found in their false claim that David is a knave. David cannot be a knight, because this would contradict the claim of their own that If Michael is a knave then Ella is a knave. David cannot be a knave, because this would contradict the false claim of Michael that David is a knave. We have exhausted all possibilities for David and Michael, so let us go back and reconsider Ethan. Ethan cannot be a knave, because this would contradict the false claim of their own that Ella is not a knave. We have exhausted all possibilities for Ethan, so let us go back and reconsider Ella. Assume Ella is a knave. No contradiction is found in their false claim that Ethan is a knave if and only if Michael is a knight. Ethan cannot be a knight, because this would contradict the claim of their own that Ella is not a knave. Assume Ethan is a knave. No contradiction is found in their false claim that Ella is not a knave. Michael cannot be a knight, because this would contradict the false claim of Ella that Ethan is a knave if and only if Michael is a knight. Assume Michael is a knave. No contradiction is found in their false claim that David is a knave. Assume David is a knight. No contradiction is found in their claim that If Michael is a knave then Ella is a knave. Assume Oliver is a knight. No contradiction is found in their claim that Ethan is not a knight. Assume Chloe is a knight. No contradiction is found in their claim that If Michael is a knight then Oliver is a knave.