A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Benjamin, Jackson, Henry, Scarlett, Olivia, and David. Benjamin commented, "Scarlett is a knave and Henry is a knight". "Olivia is a knight if and only if Benjamin is a knave," Jackson declared. According to Henry, "Olivia is not a knight". Scarlett asserted: "Jackson is a knight if and only if Henry is a knave". Olivia commented, "Scarlett is a knave if and only if Henry is a knave". David stated, "Henry is a knave if and only if Jackson is a knave". So who is a knight and who is a knave?
Benjamin is a knight, Jackson is a knight, Henry is a knight, Scarlett is a knave, Olivia is a knave, and David is a knight.
(1) Benjamin is a knight
(2) Jackson is a knight
(3) Henry is a knight
(4) Scarlett is a knave
(5) Olivia is a knave
(6) David is a knight
Assume Benjamin is a knight. No contradiction is found in their claim that Scarlett is a knave and Henry is a knight. Scarlett cannot be a knight, because this would contradict the claim of Benjamin that Scarlett is a knave and Henry is a knight. Assume Scarlett is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Henry is a knave. Assume Jackson is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Benjamin is a knave. Olivia cannot be a knight, because this would contradict the claim of Jackson that Olivia is a knight if and only if Benjamin is a knave. Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Henry is a knave. Assume Henry is a knight. No contradiction is found in their claim that Olivia is not a knight. Assume David is a knight. No contradiction is found in their claim that Henry is a knave if and only if Jackson is a knave.