A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Lily, Henry, Charlotte, Scarlett, and Lucas. Ella commented, "Lily is a knave". Lily said that Scarlett is a knave if and only if Charlotte is a knave. Henry stated, "Lily is a knight if and only if Scarlett is a knight". In a statement by Charlotte: "Lucas is not a knave". Scarlett was heard saying, "Lucas is a knave or Henry is a knight". Lucas was heard saying, "Lily is a knight if and only if Ella is a knave". So who is a knight and who is a knave?
Ella is a knave, Lily is a knight, Henry is a knight, Charlotte is a knight, Scarlett is a knight, and Lucas is a knight.
(1) Ella is a knave
(2) Lily is a knight
(3) Henry is a knight
(4) Charlotte is a knight
(5) Scarlett is a knight
(6) Lucas is a knight
Assume Ella is a knight. No contradiction is found in their claim that Lily is a knave. Lily cannot be a knight, because this would contradict the claim of Ella that Lily is a knave. Assume Lily is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Charlotte is a knave. Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave or Henry is a knight. Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knave. Henry cannot be a knight, because this would contradict the claim of their own that Lily is a knight if and only if Scarlett is a knight. Henry cannot be a knave, because this would contradict the claim of Scarlett that Lucas is a knave or Henry is a knight. We have exhausted all possibilities for Henry, so let us go back and reconsider Lucas. Lucas cannot be a knave, because this would contradict the false claim of their own that Lily is a knight if and only if Ella is a knave. We have exhausted all possibilities for Lucas, so let us go back and reconsider Scarlett. Assume Scarlett is a knave. No contradiction is found in their false claim that Lucas is a knave or Henry is a knight. Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knave. Henry cannot be a knight, because this would contradict the false claim of Scarlett that Lucas is a knave or Henry is a knight. Henry cannot be a knave, because this would contradict the false claim of their own that Lily is a knight if and only if Scarlett is a knight. We have exhausted all possibilities for Henry, so let us go back and reconsider Lucas. Lucas cannot be a knave, because this would contradict the false claim of Scarlett that Lucas is a knave or Henry is a knight. We have exhausted all possibilities for Lucas, Scarlett, and Lily, so let us go back and reconsider Ella. Assume Ella is a knave. No contradiction is found in their false claim that Lily is a knave. Assume Lily is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Charlotte is a knave. Assume Scarlett is a knight. No contradiction is found in their claim that Lucas is a knave or Henry is a knight. Assume Lucas is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knave. Assume Henry is a knight. No contradiction is found in their claim that Lily is a knight if and only if Scarlett is a knight. Assume Charlotte is a knight. No contradiction is found in their claim that Lucas is not a knave.