A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sofia, Lily, Emma, Ella, Aiden, and Jackson. In Sofia's words: "Aiden is a knight if and only if Jackson is a knave". "If Aiden is a knave then Ella is a knave," Lily mentioned. Emma told you that Jackson is a knight or Ella is a knight. "Lily is a knight," Ella claimed. "Lily is a knight if and only if Ella is a knight," Aiden declared. Jackson noted, "If Emma is a knave then Emma is a knight". So who is a knight and who is a knave?
Sofia is a knave, Lily is a knight, Emma is a knight, Ella is a knight, Aiden is a knight, and Jackson is a knight.
(1) Sofia is a knave
(2) Lily is a knight
(3) Emma is a knight
(4) Ella is a knight
(5) Aiden is a knight
(6) Jackson is a knight
Assume Sofia is a knight. No contradiction is found in their claim that Aiden is a knight if and only if Jackson is a knave. Assume Aiden is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knight. Assume Lily is a knight. No contradiction is found in their claim that If Aiden is a knave then Ella is a knave. Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight. Jackson cannot be a knight, because this would contradict the claim of Sofia that Aiden is a knight if and only if Jackson is a knave. Assume Jackson is a knave. No contradiction is found in their false claim that If Emma is a knave then Emma is a knight. Emma cannot be a knight, because this would contradict the false claim of Jackson that If Emma is a knave then Emma is a knight. Emma cannot be a knave, because this would contradict the false claim of their own that Jackson is a knight or Ella is a knight. We have exhausted all possibilities for Emma and Jackson, so let us go back and reconsider Ella. Ella cannot be a knave, because this would contradict the false claim of their own that Lily is a knight. We have exhausted all possibilities for Ella, so let us go back and reconsider Lily. Lily cannot be a knave, because this would contradict the false claim of their own that If Aiden is a knave then Ella is a knave. We have exhausted all possibilities for Lily, so let us go back and reconsider Aiden. Assume Aiden is a knave. No contradiction is found in their false claim that Lily is a knight if and only if Ella is a knight. Assume Lily is a knight. No contradiction is found in their claim that If Aiden is a knave then Ella is a knave. Ella cannot be a knight, because this would contradict the claim of Lily that If Aiden is a knave then Ella is a knave. Ella cannot be a knave, because this would contradict the false claim of their own that Lily is a knight. We have exhausted all possibilities for Ella, so let us go back and reconsider Lily. Assume Lily is a knave. No contradiction is found in their false claim that If Aiden is a knave then Ella is a knave. Ella cannot be a knight, because this would contradict the claim of their own that Lily is a knight. Ella cannot be a knave, because this would contradict the false claim of Lily that If Aiden is a knave then Ella is a knave. We have exhausted all possibilities for Ella, Lily, and Aiden, so let us go back and reconsider Sofia. Assume Sofia is a knave. No contradiction is found in their false claim that Aiden is a knight if and only if Jackson is a knave. Assume Aiden is a knight. No contradiction is found in their claim that Lily is a knight if and only if Ella is a knight. Assume Lily is a knight. No contradiction is found in their claim that If Aiden is a knave then Ella is a knave. Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight. Assume Jackson is a knight. No contradiction is found in their claim that If Emma is a knave then Emma is a knight. Assume Emma is a knight. No contradiction is found in their claim that Jackson is a knight or Ella is a knight.