A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Ella, Olivia, Penelope, Oliver, Benjamin, and Scarlett. Ella was heard saying, "Oliver is a knight". Olivia remarked, "Scarlett is a knave if and only if Penelope is a knight". "Oliver is a knave" - Penelope. In a statement by Oliver: "Olivia is a knight if and only if Penelope is a knight". "If Scarlett is a knave then Benjamin is a knight," Benjamin claimed. Scarlett noted, "Olivia is a knave". So who is a knight and who is a knave?
Ella is a knave, Olivia is a knave, Penelope is a knight, Oliver is a knave, Benjamin is a knight, and Scarlett is a knight.
(1) Ella is a knave
(2) Olivia is a knave
(3) Penelope is a knight
(4) Oliver is a knave
(5) Benjamin is a knight
(6) Scarlett is a knight
Assume Ella is a knight. No contradiction is found in their claim that Oliver is a knight. Assume Oliver is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Penelope is a knight. Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Penelope is a knight. Scarlett cannot be a knight, because this would contradict the claim of their own that Olivia is a knave. Assume Scarlett is a knave. No contradiction is found in their false claim that Olivia is a knave. Penelope cannot be a knight, because this would contradict the claim of their own that Oliver is a knave. Penelope cannot be a knave, because this would contradict the claim of Olivia that Scarlett is a knave if and only if Penelope is a knight. We have exhausted all possibilities for Penelope and Scarlett, so let us go back and reconsider Olivia. Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Penelope is a knight. Assume Scarlett is a knight. No contradiction is found in their claim that Olivia is a knave. Penelope cannot be a knight, because this would contradict the claim of their own that Oliver is a knave. Penelope cannot be a knave, because this would contradict the false claim of Olivia that Scarlett is a knave if and only if Penelope is a knight. We have exhausted all possibilities for Penelope, so let us go back and reconsider Scarlett. Scarlett cannot be a knave, because this would contradict the false claim of their own that Olivia is a knave. We have exhausted all possibilities for Scarlett and Olivia, so let us go back and reconsider Oliver. Oliver cannot be a knave, because this would contradict the claim of Ella that Oliver is a knight. We have exhausted all possibilities for Oliver, so let us go back and reconsider Ella. Assume Ella is a knave. No contradiction is found in their false claim that Oliver is a knight. Oliver cannot be a knight, because this would contradict the false claim of Ella that Oliver is a knight. Assume Oliver is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Penelope is a knight. Assume Olivia is a knight. No contradiction is found in their claim that Scarlett is a knave if and only if Penelope is a knight. Scarlett cannot be a knight, because this would contradict the claim of their own that Olivia is a knave. Assume Scarlett is a knave. No contradiction is found in their false claim that Olivia is a knave. Penelope cannot be a knight, because this would contradict the false claim of Oliver that Olivia is a knight if and only if Penelope is a knight. Penelope cannot be a knave, because this would contradict the claim of Olivia that Scarlett is a knave if and only if Penelope is a knight. We have exhausted all possibilities for Penelope and Scarlett, so let us go back and reconsider Olivia. Assume Olivia is a knave. No contradiction is found in their false claim that Scarlett is a knave if and only if Penelope is a knight. Assume Scarlett is a knight. No contradiction is found in their claim that Olivia is a knave. Assume Penelope is a knight. No contradiction is found in their claim that Oliver is a knave. Assume Benjamin is a knight. No contradiction is found in their claim that If Scarlett is a knave then Benjamin is a knight.