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, Lily, Ella, David, Oliver, and Sebastian. Michael expressed that David is a knave. As Lily put it, "Ella is not a knight". According to Ella, "Lily is a knight if and only if Sebastian is a knave". As David put it, "If Ella is a knight then Oliver is a knave". "If Michael is a knave then Lily is a knight" - Oliver. Sebastian was heard saying, "Ella is a knave if and only if Michael is a knight". So who is a knight and who is a knave?
Michael is a knave, Lily is a knave, Ella is a knight, David is a knight, Oliver is a knave, and Sebastian is a knight.
(1) Michael is a knave
(2) Lily is a knave
(3) Ella is a knight
(4) David is a knight
(5) Oliver is a knave
(6) Sebastian is a knight
Assume Michael is a knight. No contradiction is found in their claim that David is a knave. David cannot be a knight, because this would contradict the claim of Michael that David is a knave. Assume David is a knave. No contradiction is found in their false claim that If Ella is a knight then Oliver is a knave. Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave. Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight. Assume Lily is a knave. No contradiction is found in their false claim that Ella is not a knight. Sebastian cannot be a knight, because this would contradict the claim of their own that Ella is a knave if and only if Michael is a knight. Sebastian cannot be a knave, because this would contradict the claim of Ella that Lily is a knight if and only if Sebastian is a knave. We have exhausted all possibilities for Sebastian and Lily, so let us go back and reconsider Ella. Ella cannot be a knave, because this would contradict the false claim of David that If Ella is a knight then Oliver is a knave. We have exhausted all possibilities for Ella and David, so let us go back and reconsider Michael. Assume Michael is a knave. No contradiction is found in their false claim that David is a knave. Assume David is a knight. No contradiction is found in their claim that If Ella is a knight then Oliver is a knave. Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight if and only if Sebastian is a knave. Lily cannot be a knight, because this would contradict the claim of their own that Ella is not a knight. Assume Lily is a knave. No contradiction is found in their false claim that Ella is not a knight. Assume Sebastian is a knight. No contradiction is found in their claim that Ella is a knave if and only if Michael is a knight. Oliver cannot be a knight, because this would contradict the claim of David that If Ella is a knight then Oliver is a knave. Assume Oliver is a knave. No contradiction is found in their false claim that If Michael is a knave then Lily is a knight.