A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 6 inhabitants: Chloe, Ava, Amelia, William, Abigail, and Mason. Chloe expressed that Amelia is a knave if and only if Mason is a knave. "William is a knight if and only if Mason is a knight," Ava declared. Amelia commented, "Abigail is a knave and Ava is a knave". "Abigail is a knave" - William. Abigail was heard saying, "Chloe is a knight or Amelia is a knight". Mason was heard saying, "William is a knave if and only if Abigail is a knight". So who is a knight and who is a knave?
Chloe is a knave, Ava is a knight, Amelia is a knave, William is a knight, Abigail is a knave, and Mason is a knight.
(1) Chloe is a knave
(2) Ava is a knight
(3) Amelia is a knave
(4) William is a knight
(5) Abigail is a knave
(6) Mason is a knight
Assume Chloe is a knight. No contradiction is found in their claim that Amelia is a knave if and only if Mason is a knave. Assume Amelia is a knight. No contradiction is found in their claim that Abigail is a knave and Ava is a knave. Abigail cannot be a knight, because this would contradict the claim of Amelia that Abigail is a knave and Ava is a knave. Abigail cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Amelia is a knight. We have exhausted all possibilities for Abigail, so let us go back and reconsider Amelia. Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knave and Ava is a knave. Assume Abigail is a knight. No contradiction is found in their claim that Chloe is a knight or Amelia is a knight. Assume Ava is a knight. No contradiction is found in their claim that William is a knight if and only if Mason is a knight. William cannot be a knight, because this would contradict the claim of their own that Abigail is a knave. Assume William is a knave. No contradiction is found in their false claim that Abigail is a knave. Mason cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knave if and only if Mason is a knave. Mason cannot be a knave, because this would contradict the false claim of their own that William is a knave if and only if Abigail is a knight. We have exhausted all possibilities for Mason and William, so let us go back and reconsider Ava. Assume Ava is a knave. No contradiction is found in their false claim that William is a knight if and only if Mason is a knight. William cannot be a knight, because this would contradict the claim of their own that Abigail is a knave. Assume William is a knave. No contradiction is found in their false claim that Abigail is a knave. Mason cannot be a knight, because this would contradict the claim of Chloe that Amelia is a knave if and only if Mason is a knave. Mason cannot be a knave, because this would contradict the false claim of Ava that William is a knight if and only if Mason is a knight. We have exhausted all possibilities for Mason, William, and Ava, so let us go back and reconsider Abigail. Abigail cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Amelia is a knight. We have exhausted all possibilities for Abigail and Amelia, so let us go back and reconsider Chloe. Assume Chloe is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Mason is a knave. Assume Amelia is a knight. No contradiction is found in their claim that Abigail is a knave and Ava is a knave. Abigail cannot be a knight, because this would contradict the claim of Amelia that Abigail is a knave and Ava is a knave. Abigail cannot be a knave, because this would contradict the false claim of their own that Chloe is a knight or Amelia is a knight. We have exhausted all possibilities for Abigail, so let us go back and reconsider Amelia. Assume Amelia is a knave. No contradiction is found in their false claim that Abigail is a knave and Ava is a knave. Abigail cannot be a knight, because this would contradict the claim of their own that Chloe is a knight or Amelia is a knight. Assume Abigail is a knave. No contradiction is found in their false claim that Chloe is a knight or Amelia is a knight. Assume Ava is a knight. No contradiction is found in their claim that William is a knight if and only if Mason is a knight. Assume William is a knight. No contradiction is found in their claim that Abigail is a knave. Assume Mason is a knight. No contradiction is found in their claim that William is a knave if and only if Abigail is a knight.