A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Daniel, Matthew, Mason, Grace, Henry, and William. Daniel said that Matthew is a knight if and only if Daniel is a knight. Matthew commented, "William is a knight". According to Mason, "William is not a knight". According to Grace, "Daniel is a knight". Henry told you that If Mason is a knight then Matthew is a knave. William remarked, "Grace is not a knave". So who is a knight and who is a knave?
Daniel is a knight, Matthew is a knight, Mason is a knave, Grace is a knight, Henry is a knight, and William is a knight.
(1) Daniel is a knight
(2) Matthew is a knight
(3) Mason is a knave
(4) Grace is a knight
(5) Henry is a knight
(6) William is a knight
Assume Daniel is a knight. No contradiction is found in their claim that Matthew is a knight if and only if Daniel is a knight. Assume Matthew is a knight. No contradiction is found in their claim that William is a knight. Assume William is a knight. No contradiction is found in their claim that Grace is not a knave. Assume Grace is a knight. No contradiction is found in their claim that Daniel is a knight. Mason cannot be a knight, because this would contradict the claim of their own that William is not a knight. Assume Mason is a knave. No contradiction is found in their false claim that William is not a knight. Assume Henry is a knight. No contradiction is found in their claim that If Mason is a knight then Matthew is a knave.