A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Avery, Zoey, Lily, Evelyn, Aria, and Aiden. Avery commented, "Zoey is a knight if and only if Aiden is a knave". Zoey commented, "Aria is not a knave". As Lily put it, "Zoey is a knight and Aiden is a knight". Evelyn said that Aria is a knave or Lily is a knight. Aria asserted: "Evelyn is a knight or Avery is a knave". "Avery is a knave," Aiden declared. So who is a knight and who is a knave?
Avery is a knave, Zoey is a knight, Lily is a knight, Evelyn is a knight, Aria is a knight, and Aiden is a knight.
(1) Avery is a knave
(2) Zoey is a knight
(3) Lily is a knight
(4) Evelyn is a knight
(5) Aria is a knight
(6) Aiden is a knight
Assume Avery is a knight. No contradiction is found in their claim that Zoey is a knight if and only if Aiden is a knave. Assume Zoey is a knight. No contradiction is found in their claim that Aria is not a knave. Assume Aria is a knight. No contradiction is found in their claim that Evelyn is a knight or Avery is a knave. Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knave or Lily is a knight. Assume Lily is a knight. No contradiction is found in their claim that Zoey is a knight and Aiden is a knight. Aiden cannot be a knight, because this would contradict the claim of Avery that Zoey is a knight if and only if Aiden is a knave. Aiden cannot be a knave, because this would contradict the claim of Lily that Zoey is a knight and Aiden is a knight. We have exhausted all possibilities for Aiden, so let us go back and reconsider Lily. Lily cannot be a knave, because this would contradict the claim of Evelyn that Aria is a knave or Lily is a knight. We have exhausted all possibilities for Lily, so let us go back and reconsider Evelyn. Evelyn cannot be a knave, because this would contradict the claim of Aria that Evelyn is a knight or Avery is a knave. We have exhausted all possibilities for Evelyn, so let us go back and reconsider Aria. Aria cannot be a knave, because this would contradict the claim of Zoey that Aria is not a knave. We have exhausted all possibilities for Aria, so let us go back and reconsider Zoey. Assume Zoey is a knave. No contradiction is found in their false claim that Aria is not a knave. Aria cannot be a knight, because this would contradict the false claim of Zoey that Aria is not a knave. Assume Aria is a knave. No contradiction is found in their false claim that Evelyn is a knight or Avery is a knave. Evelyn cannot be a knight, because this would contradict the false claim of Aria that Evelyn is a knight or Avery is a knave. Evelyn cannot be a knave, because this would contradict the false claim of their own that Aria is a knave or Lily is a knight. We have exhausted all possibilities for Evelyn, Aria, and Zoey, so let us go back and reconsider Avery. Assume Avery is a knave. No contradiction is found in their false claim that Zoey is a knight if and only if Aiden is a knave. Assume Zoey is a knight. No contradiction is found in their claim that Aria is not a knave. Assume Aria is a knight. No contradiction is found in their claim that Evelyn is a knight or Avery is a knave. Assume Evelyn is a knight. No contradiction is found in their claim that Aria is a knave or Lily is a knight. Assume Lily is a knight. No contradiction is found in their claim that Zoey is a knight and Aiden is a knight. Assume Aiden is a knight. No contradiction is found in their claim that Avery is a knave.