A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Zoey, Oliver, Lily, Daniel, Luke, and Joseph. According to Zoey, "Joseph is a knave". Oliver noted, "Daniel is not a knave". "Daniel is a knave and Luke is a knight" - Lily. According to Daniel, "If Luke is a knight then Zoey is a knave". "If Joseph is a knave then Zoey is a knave," Luke mentioned. In a statement by Joseph: "Oliver is a knight if and only if Lily is a knight". So who is a knight and who is a knave?
Zoey is a knight, Oliver is a knight, Lily is a knave, Daniel is a knight, Luke is a knave, and Joseph is a knave.
(1) Zoey is a knight
(2) Oliver is a knight
(3) Lily is a knave
(4) Daniel is a knight
(5) Luke is a knave
(6) Joseph is a knave
Assume Zoey is a knight. No contradiction is found in their claim that Joseph is a knave. Joseph cannot be a knight, because this would contradict the claim of Zoey that Joseph is a knave. Assume Joseph is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if Lily is a knight. Assume Oliver 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 If Luke is a knight then Zoey is a knave. Luke cannot be a knight, because this would contradict the claim of Daniel that If Luke is a knight then Zoey is a knave. Assume Luke is a knave. No contradiction is found in their false claim that If Joseph is a knave then Zoey is a knave. Lily cannot be a knight, because this would contradict the claim of their own that Daniel is a knave and Luke is a knight. Assume Lily is a knave. No contradiction is found in their false claim that Daniel is a knave and Luke is a knight.