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