A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Abigail, Ethan, Evelyn, Mason, and Alexander. Michael told you that Evelyn is a knave. In a statement by Abigail: "Evelyn is a knave or Alexander is a knave". Ethan stated, "Michael is a knight or Alexander is a knave". "Michael is a knight or Mason is a knave," Evelyn declared. Mason commented, "Abigail is a knave if and only if Ethan is a knight". "Michael is a knave or Michael is a knight" - Alexander. So who is a knight and who is a knave?
Michael is a knave, Abigail is a knave, Ethan is a knave, Evelyn is a knight, Mason is a knave, and Alexander is a knight.
(1) Michael is a knave
(2) Abigail is a knave
(3) Ethan is a knave
(4) Evelyn is a knight
(5) Mason is a knave
(6) Alexander is a knight
Assume Michael is a knight. No contradiction is found in their claim that Evelyn is a knave. Evelyn cannot be a knight, because this would contradict the claim of Michael that Evelyn is a knave. Evelyn cannot be a knave, because this would contradict the false claim of their own that Michael is a knight or Mason is a knave. We have exhausted all possibilities for Evelyn, so let us go back and reconsider Michael. Assume Michael is a knave. No contradiction is found in their false claim that Evelyn is a knave. Assume Evelyn is a knight. No contradiction is found in their claim that Michael is a knight or Mason is a knave. Mason cannot be a knight, because this would contradict the claim of Evelyn that Michael is a knight or Mason is a knave. Assume Mason is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Ethan is a knight. Assume Abigail is a knight. No contradiction is found in their claim that Evelyn is a knave or Alexander is a knave. Alexander cannot be a knight, because this would contradict the claim of Abigail that Evelyn is a knave or Alexander is a knave. Alexander cannot be a knave, because this would contradict the false claim of their own that Michael is a knave or Michael is a knight. We have exhausted all possibilities for Alexander, so let us go back and reconsider Abigail. Assume Abigail is a knave. No contradiction is found in their false claim that Evelyn is a knave or Alexander is a knave. Assume Alexander is a knight. No contradiction is found in their claim that Michael is a knave or Michael is a knight. Ethan cannot be a knight, because this would contradict the claim of their own that Michael is a knight or Alexander is a knave. Assume Ethan is a knave. No contradiction is found in their false claim that Michael is a knight or Alexander is a knave.