A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emily, Avery, Mia, Victoria, James, and Lily. Emily said that If Mia is a knave then Avery is a knight. Avery noted, "Lily is a knight and Mia is a knave". Mia was heard saying, "Victoria is a knight". Victoria said that If Avery is a knight then Avery is a knave. "If Mia is a knave then Emily is a knight," James claimed. Lily asserted: "Avery is a knave and James is a knave". So who is a knight and who is a knave?
Emily is a knight, Avery is a knave, Mia is a knight, Victoria is a knight, James is a knight, and Lily is a knave.
(1) Emily is a knight
(2) Avery is a knave
(3) Mia is a knight
(4) Victoria is a knight
(5) James is a knight
(6) Lily is a knave
Assume Emily is a knight. No contradiction is found in their claim that If Mia is a knave then Avery is a knight. Assume Mia is a knight. No contradiction is found in their claim that Victoria is a knight. Assume Victoria is a knight. No contradiction is found in their claim that If Avery is a knight then Avery is a knave. Avery cannot be a knight, because this would contradict the claim of their own that Lily is a knight and Mia is a knave. Assume Avery is a knave. No contradiction is found in their false claim that Lily is a knight and Mia is a knave. Assume Lily is a knight. No contradiction is found in their claim that Avery is a knave and James is a knave. James cannot be a knight, because this would contradict the claim of Lily that Avery is a knave and James is a knave. James cannot be a knave, because this would contradict the false claim of their own that If Mia is a knave then Emily is a knight. We have exhausted all possibilities for James, so let us go back and reconsider Lily. Assume Lily is a knave. No contradiction is found in their false claim that Avery is a knave and James is a knave. Assume James is a knight. No contradiction is found in their claim that If Mia is a knave then Emily is a knight.