A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Michael, Benjamin, Olivia, Mason, Zoey, and Grace. Michael commented, "Benjamin is a knave if and only if Grace is a knave". "Mason is a knight or Olivia is a knave," Benjamin mentioned. Olivia said, "Benjamin is a knave." "Olivia is a knight or Michael is a knave," Mason declared. Zoey commented, "Benjamin is not a knight". According to Grace, "If Olivia is a knave then Zoey is a knave". So who is a knight and who is a knave?
Michael is a knight, Benjamin is a knight, Olivia is a knave, Mason is a knave, Zoey is a knave, and Grace is a knight.
(1) Michael is a knight
(2) Benjamin is a knight
(3) Olivia is a knave
(4) Mason is a knave
(5) Zoey is a knave
(6) Grace is a knight
Assume Michael is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if Grace is a knave. Assume Benjamin is a knight. No contradiction is found in their claim that Mason is a knight or Olivia is a knave. Assume Mason is a knight. No contradiction is found in their claim that Olivia is a knight or Michael is a knave. Olivia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knave. Olivia cannot be a knave, because this would contradict the claim of Mason that Olivia is a knight or Michael is a knave. We have exhausted all possibilities for Olivia, so let us go back and reconsider Mason. Assume Mason is a knave. No contradiction is found in their false claim that Olivia is a knight or Michael is a knave. Olivia cannot be a knight, because this would contradict the claim of Benjamin that Mason is a knight or Olivia is a knave. Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is a knave. Assume Grace is a knight. No contradiction is found in their claim that If Olivia is a knave then Zoey is a knave. Zoey cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight. Assume Zoey is a knave. No contradiction is found in their false claim that Benjamin is not a knight.