A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Abigail, Elizabeth, Aurora, Grace, Harper, and Oliver. "Elizabeth is a knight," Abigail mentioned. Elizabeth told you that Oliver is a knight or Harper is a knave. As Aurora put it, "Abigail is a knight or Elizabeth is a knave". Grace was heard saying, "Elizabeth is a knight and Abigail is a knave". Harper stated, "Grace is a knave if and only if Aurora is a knight". "If Harper is a knave then Abigail is a knight," Oliver claimed. So who is a knight and who is a knave?
Abigail is a knight, Elizabeth is a knight, Aurora is a knight, Grace is a knave, Harper is a knight, and Oliver is a knight.
(1) Abigail is a knight
(2) Elizabeth is a knight
(3) Aurora is a knight
(4) Grace is a knave
(5) Harper is a knight
(6) Oliver is a knight
Assume Abigail is a knight. No contradiction is found in their claim that Elizabeth is a knight. Assume Elizabeth is a knight. No contradiction is found in their claim that Oliver is a knight or Harper is a knave. Assume Oliver is a knight. No contradiction is found in their claim that If Harper is a knave then Abigail is a knight. Assume Harper is a knight. No contradiction is found in their claim that Grace is a knave if and only if Aurora is a knight. Grace cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and Abigail is a knave. Assume Grace is a knave. No contradiction is found in their false claim that Elizabeth is a knight and Abigail is a knave. Assume Aurora is a knight. No contradiction is found in their claim that Abigail is a knight or Elizabeth is a knave.