A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Mia, Michael, Chloe, Daniel, Lucas, and Samuel. Mia said, "Michael is a knight or Chloe is a knave." Michael told you that Chloe is a knight if and only if Samuel is a knight. As Chloe put it, "Lucas is not a knave". Daniel asserted: "If Lucas is a knight then Samuel is a knave". In a statement by Lucas: "Samuel is a knave if and only if Michael is a knave". Samuel remarked, "Daniel is a knight". So who is a knight and who is a knave?
Mia is a knight, Michael is a knave, Chloe is a knave, Daniel is a knight, Lucas is a knave, and Samuel is a knight.
(1) Mia is a knight
(2) Michael is a knave
(3) Chloe is a knave
(4) Daniel is a knight
(5) Lucas is a knave
(6) Samuel is a knight
Assume Mia is a knight. No contradiction is found in their claim that Michael is a knight or Chloe is a knave. Assume Michael is a knight. No contradiction is found in their claim that Chloe is a knight if and only if Samuel is a knight. Assume Chloe is a knight. No contradiction is found in their claim that Lucas is not a knave. Assume Lucas is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Michael is a knave. Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knight. Daniel cannot be a knight, because this would contradict the claim of their own that If Lucas is a knight then Samuel is a knave. Daniel cannot be a knave, because this would contradict the claim of Samuel that Daniel is a knight. We have exhausted all possibilities for Daniel, so let us go back and reconsider Samuel. Samuel cannot be a knave, because this would contradict the claim of Michael that Chloe is a knight if and only if Samuel is a knight. We have exhausted all possibilities for Samuel, so let us go back and reconsider Lucas. Lucas cannot be a knave, because this would contradict the claim of Chloe that Lucas is not a knave. We have exhausted all possibilities for Lucas, so let us go back and reconsider Chloe. Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is not a knave. Lucas cannot be a knight, because this would contradict the false claim of Chloe that Lucas is not a knave. Assume Lucas is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Michael is a knave. Samuel cannot be a knight, because this would contradict the claim of Michael that Chloe is a knight if and only if Samuel is a knight. Assume Samuel is a knave. No contradiction is found in their false claim that Daniel is a knight. Daniel cannot be a knight, because this would contradict the false claim of Samuel that Daniel is a knight. Daniel cannot be a knave, because this would contradict the false claim of their own that If Lucas is a knight then Samuel is a knave. We have exhausted all possibilities for Daniel, Samuel, Lucas, and Chloe, so let us go back and reconsider Michael. Assume Michael is a knave. No contradiction is found in their false claim that Chloe is a knight if and only if Samuel is a knight. Chloe cannot be a knight, because this would contradict the claim of Mia that Michael is a knight or Chloe is a knave. Assume Chloe is a knave. No contradiction is found in their false claim that Lucas is not a knave. Lucas cannot be a knight, because this would contradict the false claim of Chloe that Lucas is not a knave. Assume Lucas is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Michael is a knave. Assume Samuel is a knight. No contradiction is found in their claim that Daniel is a knight. Assume Daniel is a knight. No contradiction is found in their claim that If Lucas is a knight then Samuel is a knave.