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, Alexander, Daniel, Sebastian, Amelia, and Owen. "Owen is a knight and Zoey is a knight," Zoey claimed. Alexander remarked, "If Daniel is a knight then Alexander is a knight". Daniel remarked, "Amelia is a knight if and only if Alexander is a knight". Sebastian commented, "Alexander is a knight". Amelia said that Daniel is a knight if and only if Owen is a knave. Owen remarked, "Sebastian is a knight or Zoey is a knight". So who is a knight and who is a knave?
Zoey is a knight, Alexander is a knave, Daniel is a knight, Sebastian is a knave, Amelia is a knave, and Owen is a knight.
(1) Zoey is a knight
(2) Alexander is a knave
(3) Daniel is a knight
(4) Sebastian is a knave
(5) Amelia is a knave
(6) Owen is a knight
Assume Zoey is a knight. No contradiction is found in their claim that Owen is a knight and Zoey is a knight. Assume Owen is a knight. No contradiction is found in their claim that Sebastian is a knight or Zoey is a knight. Assume Sebastian is a knight. No contradiction is found in their claim that Alexander is a knight. Assume Alexander is a knight. No contradiction is found in their claim that If Daniel is a knight then Alexander is a knight. Assume Daniel is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Alexander is a knight. Amelia cannot be a knight, because this would contradict the claim of their own that Daniel is a knight if and only if Owen is a knave. Amelia cannot be a knave, because this would contradict the claim of Daniel that Amelia is a knight if and only if Alexander is a knight. We have exhausted all possibilities for Amelia, so let us go back and reconsider Daniel. Assume Daniel is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Alexander is a knight. Amelia cannot be a knight, because this would contradict the false claim of Daniel that Amelia is a knight if and only if Alexander is a knight. Amelia cannot be a knave, because this would contradict the false claim of their own that Daniel is a knight if and only if Owen is a knave. We have exhausted all possibilities for Amelia and Daniel, so let us go back and reconsider Alexander. Alexander cannot be a knave, because this would contradict the claim of Sebastian that Alexander is a knight. We have exhausted all possibilities for Alexander, so let us go back and reconsider Sebastian. Assume Sebastian is a knave. No contradiction is found in their false claim that Alexander is a knight. Alexander cannot be a knight, because this would contradict the false claim of Sebastian that Alexander is a knight. Assume Alexander is a knave. No contradiction is found in their false claim that If Daniel is a knight then Alexander is a knight. Assume Daniel is a knight. No contradiction is found in their claim that Amelia is a knight if and only if Alexander is a knight. Amelia cannot be a knight, because this would contradict the claim of Daniel that Amelia is a knight if and only if Alexander is a knight. Assume Amelia is a knave. No contradiction is found in their false claim that Daniel is a knight if and only if Owen is a knave.