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, Aiden, Emma, Matthew, Logan, and Ava. In a statement by Emily: "Matthew is a knave if and only if Ava is a knave". Aiden asserted: "Logan is a knave if and only if Ava is a knight". Emma told you that Emily is a knight and Logan is a knight. As Matthew put it, "Ava is a knave if and only if Matthew is a knight". Logan asserted: "Logan is a knight and Matthew is a knave". "Logan is a knave or Emma is a knave," Ava declared. So who is a knight and who is a knave?
Emily is a knight, Aiden is a knight, Emma is a knight, Matthew is a knave, Logan is a knight, and Ava is a knave.
(1) Emily is a knight
(2) Aiden is a knight
(3) Emma is a knight
(4) Matthew is a knave
(5) Logan is a knight
(6) Ava is a knave
Assume Emily is a knight. No contradiction is found in their claim that Matthew is a knave if and only if Ava is a knave. Assume Matthew is a knight. No contradiction is found in their claim that Ava is a knave if and only if Matthew is a knight. Ava cannot be a knight, because this would contradict the claim of Matthew that Ava is a knave if and only if Matthew is a knight. Ava cannot be a knave, because this would contradict the claim of Emily that Matthew is a knave if and only if Ava is a knave. We have exhausted all possibilities for Ava, so let us go back and reconsider Matthew. Assume Matthew is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Matthew is a knight. Ava cannot be a knight, because this would contradict the claim of Emily that Matthew is a knave if and only if Ava is a knave. Assume Ava is a knave. No contradiction is found in their false claim that Logan is a knave or Emma is a knave. Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight and Matthew is a knave. Assume Emma is a knight. No contradiction is found in their claim that Emily is a knight and Logan is a knight. Assume Aiden is a knight. No contradiction is found in their claim that Logan is a knave if and only if Ava is a knight.