A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Jacob, David, Ethan, Scarlett, Olivia, and William. Jacob told you that Scarlett is a knight. "Ethan is a knave or Scarlett is a knight," David declared. In Ethan's words: "Scarlett is a knave". As Scarlett put it, "David is a knave and David is a knight". Olivia asserted: "David is not a knight". "Jacob is a knight and Scarlett is a knight" - William. So who is a knight and who is a knave?
Jacob is a knave, David is a knave, Ethan is a knight, Scarlett is a knave, Olivia is a knight, and William is a knave.
(1) Jacob is a knave
(2) David is a knave
(3) Ethan is a knight
(4) Scarlett is a knave
(5) Olivia is a knight
(6) William is a knave
Assume Jacob is a knight. No contradiction is found in their claim that Scarlett is a knight. Scarlett cannot be a knight, because this would contradict the claim of their own that David is a knave and David is a knight. Scarlett cannot be a knave, because this would contradict the claim of Jacob that Scarlett is a knight. We have exhausted all possibilities for Scarlett, so let us go back and reconsider Jacob. Assume Jacob is a knave. No contradiction is found in their false claim that Scarlett is a knight. Scarlett cannot be a knight, because this would contradict the false claim of Jacob that Scarlett is a knight. Assume Scarlett is a knave. No contradiction is found in their false claim that David is a knave and David is a knight. Assume David is a knight. No contradiction is found in their claim that Ethan is a knave or Scarlett is a knight. Ethan cannot be a knight, because this would contradict the claim of David that Ethan is a knave or Scarlett is a knight. Ethan cannot be a knave, because this would contradict the false claim of their own that Scarlett is a knave. We have exhausted all possibilities for Ethan, so let us go back and reconsider David. Assume David is a knave. No contradiction is found in their false claim that Ethan is a knave or Scarlett is a knight. Assume Ethan is a knight. No contradiction is found in their claim that Scarlett is a knave. Assume Olivia is a knight. No contradiction is found in their claim that David is not a knight. William cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Scarlett is a knight. Assume William is a knave. No contradiction is found in their false claim that Jacob is a knight and Scarlett is a knight.