A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Sophia, Chloe, Alexander, Scarlett, Evelyn, and Charlotte. Sophia expressed that Chloe is not a knight. "Evelyn is not a knave," Chloe claimed. Alexander noted, "Evelyn is a knight or Alexander is a knight". In a statement by Scarlett: "Charlotte is a knight or Chloe is a knight". "If Alexander is a knave then Alexander is a knight," Evelyn mentioned. As Charlotte put it, "If Charlotte is a knight then Evelyn is a knight". So who is a knight and who is a knave?
Sophia is a knave, Chloe is a knight, Alexander is a knight, Scarlett is a knight, Evelyn is a knight, and Charlotte is a knight.
(1) Sophia is a knave
(2) Chloe is a knight
(3) Alexander is a knight
(4) Scarlett is a knight
(5) Evelyn is a knight
(6) Charlotte is a knight
Assume Sophia is a knight. No contradiction is found in their claim that Chloe is not a knight. Chloe cannot be a knight, because this would contradict the claim of Sophia that Chloe is not a knight. Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is not a knave. Evelyn cannot be a knight, because this would contradict the false claim of Chloe that Evelyn is not a knave. Assume Evelyn is a knave. No contradiction is found in their false claim that If Alexander is a knave then Alexander is a knight. Alexander cannot be a knight, because this would contradict the false claim of Evelyn that If Alexander is a knave then Alexander is a knight. Assume Alexander is a knave. No contradiction is found in their false claim that Evelyn is a knight or Alexander is a knight. Assume Scarlett is a knight. No contradiction is found in their claim that Charlotte is a knight or Chloe is a knight. Charlotte cannot be a knight, because this would contradict the claim of their own that If Charlotte is a knight then Evelyn is a knight. Charlotte cannot be a knave, because this would contradict the claim of Scarlett that Charlotte is a knight or Chloe is a knight. We have exhausted all possibilities for Charlotte, so let us go back and reconsider Scarlett. Assume Scarlett is a knave. No contradiction is found in their false claim that Charlotte is a knight or Chloe is a knight. Charlotte cannot be a knight, because this would contradict the false claim of Scarlett that Charlotte is a knight or Chloe is a knight. Charlotte cannot be a knave, because this would contradict the false claim of their own that If Charlotte is a knight then Evelyn is a knight. We have exhausted all possibilities for Charlotte, Scarlett, Alexander, Evelyn, and Chloe, so let us go back and reconsider Sophia. Assume Sophia is a knave. No contradiction is found in their false claim that Chloe is not a knight. Assume Chloe is a knight. No contradiction is found in their claim that Evelyn is not a knave. Assume Evelyn is a knight. No contradiction is found in their claim that If Alexander is a knave then Alexander is a knight. Assume Alexander is a knight. No contradiction is found in their claim that Evelyn is a knight or Alexander is a knight. Assume Scarlett is a knight. No contradiction is found in their claim that Charlotte is a knight or Chloe is a knight. Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Evelyn is a knight.