A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Emma, David, Abigail, Lily, Penelope, and Jackson. Emma remarked, "If Jackson is a knave then David is a knight". David said, "Penelope is not a knight." Abigail told you that Lily is not a knight. "David is a knave or Abigail is a knave," Lily declared. Penelope commented, "If Penelope is a knight then David is a knave". Jackson stated, "Lily is a knave". So who is a knight and who is a knave?
Emma is a knave, David is a knave, Abigail is a knave, Lily is a knight, Penelope is a knight, and Jackson is a knave.
(1) Emma is a knave
(2) David is a knave
(3) Abigail is a knave
(4) Lily is a knight
(5) Penelope is a knight
(6) Jackson is a knave
Assume Emma is a knight. No contradiction is found in their claim that If Jackson is a knave then David is a knight. Assume Jackson is a knight. No contradiction is found in their claim that Lily is a knave. Lily cannot be a knight, because this would contradict the claim of Jackson that Lily is a knave. Assume Lily is a knave. No contradiction is found in their false claim that David is a knave or Abigail is a knave. Assume David is a knight. No contradiction is found in their claim that Penelope is not a knight. Penelope cannot be a knight, because this would contradict the claim of David that Penelope is not a knight. Penelope cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knight then David is a knave. We have exhausted all possibilities for Penelope, so let us go back and reconsider David. David cannot be a knave, because this would contradict the false claim of Lily that David is a knave or Abigail is a knave. We have exhausted all possibilities for David and Lily, so let us go back and reconsider Jackson. Assume Jackson is a knave. No contradiction is found in their false claim that Lily is a knave. Assume Lily is a knight. No contradiction is found in their claim that David is a knave or Abigail is a knave. Assume David is a knight. No contradiction is found in their claim that Penelope is not a knight. Penelope cannot be a knight, because this would contradict the claim of David that Penelope is not a knight. Penelope cannot be a knave, because this would contradict the false claim of their own that If Penelope is a knight then David is a knave. We have exhausted all possibilities for Penelope, so let us go back and reconsider David. David cannot be a knave, because this would contradict the claim of Emma that If Jackson is a knave then David is a knight. We have exhausted all possibilities for David, so let us go back and reconsider Lily. Lily cannot be a knave, because this would contradict the false claim of Jackson that Lily is a knave. We have exhausted all possibilities for Lily and Jackson, so let us go back and reconsider Emma. Assume Emma is a knave. No contradiction is found in their false claim that If Jackson is a knave then David is a knight. Jackson cannot be a knight, because this would contradict the false claim of Emma that If Jackson is a knave then David is a knight. Assume Jackson is a knave. No contradiction is found in their false claim that Lily is a knave. Assume Lily is a knight. No contradiction is found in their claim that David is a knave or Abigail is a knave. David cannot be a knight, because this would contradict the false claim of Emma that If Jackson is a knave then David is a knight. Assume David is a knave. No contradiction is found in their false claim that Penelope is not a knight. Assume Penelope is a knight. No contradiction is found in their claim that If Penelope is a knight then David is a knave. Abigail cannot be a knight, because this would contradict the claim of their own that Lily is not a knight. Assume Abigail is a knave. No contradiction is found in their false claim that Lily is not a knight.