A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Owen, Ethan, Daniel, Liam, Amelia, and Ava. Owen noted, "Ava is a knight if and only if Owen is a knight". Ethan asserted: "If Liam is a knight then Daniel is a knight". Daniel noted, "Ava is a knight". "If Ava is a knight then Amelia is a knave" - Liam. As Amelia put it, "Ava is a knave if and only if Owen is a knight". Ava asserted: "Ava is a knight if and only if Amelia is a knave". So who is a knight and who is a knave?
Owen is a knight, Ethan is a knight, Daniel is a knight, Liam is a knight, Amelia is a knave, and Ava is a knight.
(1) Owen is a knight
(2) Ethan is a knight
(3) Daniel is a knight
(4) Liam is a knight
(5) Amelia is a knave
(6) Ava is a knight
Assume Owen is a knight. No contradiction is found in their claim that Ava is a knight if and only if Owen is a knight. Assume Ava is a knight. No contradiction is found in their claim that Ava is a knight if and only if Amelia is a knave. Amelia cannot be a knight, because this would contradict the claim of their own that Ava is a knave if and only if Owen is a knight. Assume Amelia is a knave. No contradiction is found in their false claim that Ava is a knave if and only if Owen is a knight. Assume Ethan is a knight. No contradiction is found in their claim that If Liam is a knight then Daniel is a knight. Assume Liam is a knight. No contradiction is found in their claim that If Ava is a knight then Amelia is a knave. Assume Daniel is a knight. No contradiction is found in their claim that Ava is a knight.