A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Henry, Sofia, Emma, Liam, Elizabeth, and James. Henry expressed that Sofia is not a knight. Sofia said that Emma is a knight or Elizabeth is a knave. Emma said, "Liam is a knight and Sofia is a knight." "James is a knave," Liam claimed. According to Elizabeth, "Henry is a knave or Emma is a knight". James said that Sofia is not a knight. So who is a knight and who is a knave?
Henry is a knave, Sofia is a knight, Emma is a knight, Liam is a knight, Elizabeth is a knight, and James is a knave.
(1) Henry is a knave
(2) Sofia is a knight
(3) Emma is a knight
(4) Liam is a knight
(5) Elizabeth is a knight
(6) James is a knave
Assume Henry is a knight. No contradiction is found in their claim that Sofia is not a knight. Sofia cannot be a knight, because this would contradict the claim of Henry that Sofia is not a knight. Assume Sofia is a knave. No contradiction is found in their false claim that Emma is a knight or Elizabeth is a knave. Emma cannot be a knight, because this would contradict the false claim of Sofia that Emma is a knight or Elizabeth is a knave. Assume Emma is a knave. No contradiction is found in their false claim that Liam is a knight and Sofia is a knight. Assume Liam is a knight. No contradiction is found in their claim that James is a knave. James cannot be a knight, because this would contradict the claim of Liam that James is a knave. James cannot be a knave, because this would contradict the false claim of their own that Sofia is not a knight. We have exhausted all possibilities for James, so let us go back and reconsider Liam. Assume Liam is a knave. No contradiction is found in their false claim that James is a knave. Assume James is a knight. No contradiction is found in their claim that Sofia is not a knight. Elizabeth cannot be a knight, because this would contradict the claim of their own that Henry is a knave or Emma is a knight. Elizabeth cannot be a knave, because this would contradict the false claim of Sofia that Emma is a knight or Elizabeth is a knave. We have exhausted all possibilities for Elizabeth, so let us go back and reconsider James. James cannot be a knave, because this would contradict the false claim of Liam that James is a knave. We have exhausted all possibilities for James, Liam, Emma, and Sofia, so let us go back and reconsider Henry. Assume Henry is a knave. No contradiction is found in their false claim that Sofia is not a knight. Assume Sofia is a knight. No contradiction is found in their claim that Emma is a knight or Elizabeth is a knave. Assume Emma is a knight. No contradiction is found in their claim that Liam is a knight and Sofia is a knight. Assume Liam is a knight. No contradiction is found in their claim that James is a knave. James cannot be a knight, because this would contradict the claim of Liam that James is a knave. Assume James is a knave. No contradiction is found in their false claim that Sofia is not a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that Henry is a knave or Emma is a knight.