A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Logan, Zoey, Noah, Luke, Sophia, and Amelia. Logan was heard saying, "Sophia is a knave if and only if Noah is a knave". According to Zoey, "Logan is a knave and Luke is a knight". In a statement by Noah: "Logan is a knave". Luke commented, "If Sophia is a knight then Sophia is a knave". In Sophia's words: "Zoey is a knave or Amelia is a knave". Amelia said, "Amelia is a knight or Sophia is a knight." So who is a knight and who is a knave?
Logan is a knave, Zoey is a knight, Noah is a knight, Luke is a knight, Sophia is a knave, and Amelia is a knight.
(1) Logan is a knave
(2) Zoey is a knight
(3) Noah is a knight
(4) Luke is a knight
(5) Sophia is a knave
(6) Amelia is a knight
Assume Logan is a knight. No contradiction is found in their claim that Sophia is a knave if and only if Noah is a knave. Assume Sophia is a knight. No contradiction is found in their claim that Zoey is a knave or Amelia is a knave. Zoey cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Luke is a knight. Assume Zoey is a knave. No contradiction is found in their false claim that Logan is a knave and Luke is a knight. Luke cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Sophia is a knave. Assume Luke is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave. Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knight. Noah cannot be a knight, because this would contradict the claim of their own that Logan is a knave. Noah cannot be a knave, because this would contradict the claim of Logan that Sophia is a knave if and only if Noah is a knave. We have exhausted all possibilities for Noah, so let us go back and reconsider Amelia. Amelia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Sophia is a knight. We have exhausted all possibilities for Amelia, Luke, and Zoey, so let us go back and reconsider Sophia. Assume Sophia is a knave. No contradiction is found in their false claim that Zoey is a knave or Amelia is a knave. Zoey cannot be a knight, because this would contradict the claim of their own that Logan is a knave and Luke is a knight. Zoey cannot be a knave, because this would contradict the false claim of Sophia that Zoey is a knave or Amelia is a knave. We have exhausted all possibilities for Zoey and Sophia, so let us go back and reconsider Logan. Assume Logan is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Noah is a knave. Assume Sophia is a knight. No contradiction is found in their claim that Zoey is a knave or Amelia is a knave. Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knave and Luke is a knight. Luke cannot be a knight, because this would contradict the claim of their own that If Sophia is a knight then Sophia is a knave. Luke cannot be a knave, because this would contradict the claim of Zoey that Logan is a knave and Luke is a knight. We have exhausted all possibilities for Luke, so let us go back and reconsider Zoey. Assume Zoey is a knave. No contradiction is found in their false claim that Logan is a knave and Luke is a knight. Luke cannot be a knight, because this would contradict the false claim of Zoey that Logan is a knave and Luke is a knight. Assume Luke is a knave. No contradiction is found in their false claim that If Sophia is a knight then Sophia is a knave. Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knight. Noah cannot be a knight, because this would contradict the false claim of Logan that Sophia is a knave if and only if Noah is a knave. Noah cannot be a knave, because this would contradict the false claim of their own that Logan is a knave. We have exhausted all possibilities for Noah, so let us go back and reconsider Amelia. Amelia cannot be a knave, because this would contradict the false claim of their own that Amelia is a knight or Sophia is a knight. We have exhausted all possibilities for Amelia, Luke, and Zoey, so let us go back and reconsider Sophia. Assume Sophia is a knave. No contradiction is found in their false claim that Zoey is a knave or Amelia is a knave. Assume Zoey is a knight. No contradiction is found in their claim that Logan is a knave and Luke is a knight. Assume Luke is a knight. No contradiction is found in their claim that If Sophia is a knight then Sophia is a knave. Assume Amelia is a knight. No contradiction is found in their claim that Amelia is a knight or Sophia is a knight. Assume Noah is a knight. No contradiction is found in their claim that Logan is a knave.