A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Luke, Elizabeth, Olivia, Scarlett, Owen, and Sebastian. Luke remarked, "Elizabeth is a knave or Olivia is a knight". Elizabeth said that If Owen is a knight then Scarlett is a knave. Olivia was heard saying, "Sebastian is a knave or Scarlett is a knight". Scarlett told you that Olivia is a knave. Owen told you that Scarlett is not a knight. In a statement by Sebastian: "Luke is a knave". So who is a knight and who is a knave?
Luke is a knight, Elizabeth is a knight, Olivia is a knight, Scarlett is a knave, Owen is a knight, and Sebastian is a knave.
(1) Luke is a knight
(2) Elizabeth is a knight
(3) Olivia is a knight
(4) Scarlett is a knave
(5) Owen is a knight
(6) Sebastian is a knave
Assume Luke is a knight. No contradiction is found in their claim that Elizabeth is a knave or Olivia is a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that If Owen is a knight then Scarlett is a knave. Assume Owen is a knight. No contradiction is found in their claim that Scarlett is not a knight. Scarlett cannot be a knight, because this would contradict the claim of Elizabeth that If Owen is a knight then Scarlett is a knave. Assume Scarlett is a knave. No contradiction is found in their false claim that Olivia is a knave. Assume Olivia is a knight. No contradiction is found in their claim that Sebastian is a knave or Scarlett is a knight. Sebastian cannot be a knight, because this would contradict the claim of Olivia that Sebastian is a knave or Scarlett is a knight. Assume Sebastian is a knave. No contradiction is found in their false claim that Luke is a knave.