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, Samuel, Harper, Michael, Sofia, and Evelyn. Abigail commented, "Sofia is a knave and Samuel is a knight". Samuel commented, "Abigail is a knave and Evelyn is a knave". In a statement by Harper: "If Evelyn is a knave then Samuel is a knight". "Samuel is a knave if and only if Evelyn is a knight," Michael declared. In Sofia's words: "Michael is a knight and Evelyn is a knight". Evelyn was heard saying, "If Harper is a knave then Harper is a knight". So who is a knight and who is a knave?
Abigail is a knave, Samuel is a knave, Harper is a knight, Michael is a knight, Sofia is a knight, and Evelyn is a knight.
(1) Abigail is a knave
(2) Samuel is a knave
(3) Harper is a knight
(4) Michael is a knight
(5) Sofia is a knight
(6) Evelyn is a knight
Assume Abigail is a knight. No contradiction is found in their claim that Sofia is a knave and Samuel is a knight. Sofia cannot be a knight, because this would contradict the claim of Abigail that Sofia is a knave and Samuel is a knight. Assume Sofia is a knave. No contradiction is found in their false claim that Michael is a knight and Evelyn is a knight. Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Evelyn is a knight. Samuel cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Evelyn is a knave. Samuel cannot be a knave, because this would contradict the claim of Abigail that Sofia is a knave and Samuel is a knight. We have exhausted all possibilities for Samuel, so let us go back and reconsider Michael. Assume Michael is a knave. No contradiction is found in their false claim that Samuel is a knave if and only if Evelyn is a knight. Samuel cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Evelyn is a knave. Samuel cannot be a knave, because this would contradict the claim of Abigail that Sofia is a knave and Samuel is a knight. We have exhausted all possibilities for Samuel, Michael, and Sofia, so let us go back and reconsider Abigail. Assume Abigail is a knave. No contradiction is found in their false claim that Sofia is a knave and Samuel is a knight. Assume Sofia is a knight. No contradiction is found in their claim that Michael is a knight and Evelyn is a knight. Assume Michael is a knight. No contradiction is found in their claim that Samuel is a knave if and only if Evelyn is a knight. Assume Samuel is a knight. No contradiction is found in their claim that Abigail is a knave and Evelyn is a knave. Evelyn cannot be a knight, because this would contradict the claim of Samuel that Abigail is a knave and Evelyn is a knave. Evelyn cannot be a knave, because this would contradict the claim of Sofia that Michael is a knight and Evelyn is a knight. We have exhausted all possibilities for Evelyn, so let us go back and reconsider Samuel. Assume Samuel is a knave. No contradiction is found in their false claim that Abigail is a knave and Evelyn is a knave. Assume Evelyn is a knight. No contradiction is found in their claim that If Harper is a knave then Harper is a knight. Assume Harper is a knight. No contradiction is found in their claim that If Evelyn is a knave then Samuel is a knight.