A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mason, Alexander, Emily, Noah, Lucas, and Oliver. Mason told you that Oliver is not a knave. "Lucas is not a knave" - Alexander. As Emily put it, "If Lucas is a knave then Emily is a knight". Noah asserted: "Emily is a knight". Lucas stated, "Mason is not a knight". In Oliver's words: "Noah is a knave if and only if Emily is a knight". So who is a knight and who is a knave?
Mason is a knave, Alexander is a knight, Emily is a knight, Noah is a knight, Lucas is a knight, and Oliver is a knave.
(1) Mason is a knave
(2) Alexander is a knight
(3) Emily is a knight
(4) Noah is a knight
(5) Lucas is a knight
(6) Oliver is a knave
Assume Mason is a knight. No contradiction is found in their claim that Oliver is not a knave. Assume Oliver is a knight. No contradiction is found in their claim that Noah is a knave if and only if Emily is a knight. Assume Noah is a knight. No contradiction is found in their claim that Emily is a knight. Emily cannot be a knight, because this would contradict the claim of Oliver that Noah is a knave if and only if Emily is a knight. Emily cannot be a knave, because this would contradict the claim of Noah that Emily is a knight. We have exhausted all possibilities for Emily, so let us go back and reconsider Noah. Assume Noah is a knave. No contradiction is found in their false claim that Emily is a knight. Emily cannot be a knight, because this would contradict the false claim of Noah that Emily is a knight. Emily cannot be a knave, because this would contradict the claim of Oliver that Noah is a knave if and only if Emily is a knight. We have exhausted all possibilities for Emily and Noah, so let us go back and reconsider Oliver. Oliver cannot be a knave, because this would contradict the claim of Mason that Oliver is not a knave. We have exhausted all possibilities for Oliver, so let us go back and reconsider Mason. Assume Mason is a knave. No contradiction is found in their false claim that Oliver is not a knave. Oliver cannot be a knight, because this would contradict the false claim of Mason that Oliver is not a knave. Assume Oliver is a knave. No contradiction is found in their false claim that Noah is a knave if and only if Emily is a knight. Assume Noah is a knight. No contradiction is found in their claim that Emily is a knight. Assume Emily is a knight. No contradiction is found in their claim that If Lucas is a knave then Emily is a knight. Assume Lucas is a knight. No contradiction is found in their claim that Mason is not a knight. Assume Alexander is a knight. No contradiction is found in their claim that Lucas is not a knave.