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