A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Isabella, Daniel, Logan, James, Sofia, and Ethan. Isabella said, "Sofia is a knight." Daniel said, "Isabella is a knight." "Logan is a knight if and only if Daniel is a knave," Logan claimed. James said, "Sofia is not a knave." Sofia told you that Logan is a knave. Ethan noted, "If Isabella is a knight then Ethan is a knight". So who is a knight and who is a knave?
Isabella is a knave, Daniel is a knave, Logan is a knight, James is a knave, Sofia is a knave, and Ethan is a knight.
(1) Isabella is a knave
(2) Daniel is a knave
(3) Logan is a knight
(4) James is a knave
(5) Sofia is a knave
(6) Ethan is a knight
Assume Isabella is a knight. No contradiction is found in their claim that Sofia is a knight. Assume Sofia is a knight. No contradiction is found in their claim that Logan is a knave. Logan cannot be a knight, because this would contradict the claim of Sofia that Logan is a knave. Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Daniel is a knave. Daniel cannot be a knight, because this would contradict the false claim of Logan that Logan is a knight if and only if Daniel is a knave. Daniel cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight. We have exhausted all possibilities for Daniel and Logan, so let us go back and reconsider Sofia. Sofia cannot be a knave, because this would contradict the claim of Isabella that Sofia is a knight. We have exhausted all possibilities for Sofia, so let us go back and reconsider Isabella. Assume Isabella is a knave. No contradiction is found in their false claim that Sofia is a knight. Sofia cannot be a knight, because this would contradict the false claim of Isabella that Sofia is a knight. Assume Sofia is a knave. No contradiction is found in their false claim that Logan is a knave. Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Daniel is a knave. Daniel cannot be a knight, because this would contradict the claim of their own that Isabella is a knight. Assume Daniel is a knave. No contradiction is found in their false claim that Isabella is a knight. James cannot be a knight, because this would contradict the claim of their own that Sofia is not a knave. Assume James is a knave. No contradiction is found in their false claim that Sofia is not a knave. Assume Ethan is a knight. No contradiction is found in their claim that If Isabella is a knight then Ethan is a knight.