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, Lucas, Daniel, Ethan, and Logan. Oliver was heard saying, "Ethan is a knight if and only if Oliver is a knight". In Henry's words: "Lucas is a knave and Oliver is a knave". "Henry is a knight or Logan is a knight," Lucas claimed. Daniel told you that Logan is a knave if and only if Henry is a knight. Ethan remarked, "Daniel is not a knave". Logan asserted: "Oliver is a knight or Lucas is a knave". So who is a knight and who is a knave?
Oliver is a knight, Henry is a knave, Lucas is a knight, Daniel is a knight, Ethan is a knight, and Logan is a knight.
(1) Oliver is a knight
(2) Henry is a knave
(3) Lucas is a knight
(4) Daniel is a knight
(5) Ethan is a knight
(6) Logan is a knight
Assume Oliver is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Oliver is a knight. Assume Ethan is a knight. No contradiction is found in their claim that Daniel is not a knave. Assume Daniel is a knight. No contradiction is found in their claim that Logan is a knave if and only if Henry is a knight. Assume Logan is a knight. No contradiction is found in their claim that Oliver is a knight or Lucas is a knave. Assume Lucas is a knight. No contradiction is found in their claim that Henry is a knight or Logan is a knight. Henry cannot be a knight, because this would contradict the claim of their own that Lucas is a knave and Oliver is a knave. Assume Henry is a knave. No contradiction is found in their false claim that Lucas is a knave and Oliver is a knave.