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