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