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