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