A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Aria, Mia, Avery, William, and Aiden. Aria told you that Mia is a knave or Avery is a knave. "Aiden is not a knave," Mia claimed. Avery commented, "Aria is not a knave". "Mia is a knave and Avery is a knave," William declared. Aiden said, "If Aria is a knight then William is a knight." So who is a knight and who is a knave?

Aria is a knight, Mia is a knave, Avery is a knight, William is a knave, and Aiden is a knave.

(1) Aria is a knight
(2) Mia is a knave
(3) Avery is a knight
(4) William is a knave
(5) Aiden is a knave

Assume Aria is a knight. No contradiction is found in their claim that Mia is a knave or Avery is a knave.

Assume Mia is a knight. No contradiction is found in their claim that Aiden is not a knave.

Assume Aiden is a knight. No contradiction is found in their claim that If Aria is a knight then William is a knight.

William cannot be a knight, because this would contradict the claim of their own that Mia is a knave and Avery is a knave.

William cannot be a knave, because this would contradict the claim of Aiden that If Aria is a knight then William is a knight.

We have exhausted all possibilities for William, so let us go back and reconsider Aiden.

Aiden cannot be a knave, because this would contradict the claim of Mia that Aiden is not a knave.

We have exhausted all possibilities for Aiden, so let us go back and reconsider Mia.

Assume Mia is a knave. No contradiction is found in their false claim that Aiden is not a knave.

Aiden cannot be a knight, because this would contradict the false claim of Mia that Aiden is not a knave.

Assume Aiden is a knave. No contradiction is found in their false claim that If Aria is a knight then William is a knight.

William cannot be a knight, because this would contradict the false claim of Aiden that If Aria is a knight then William is a knight.

Assume William is a knave. No contradiction is found in their false claim that Mia is a knave and Avery is a knave.

Assume Avery is a knight. No contradiction is found in their claim that Aria is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Lily, Henry, Joseph, Amelia, and Sofia. "Amelia is not a knight," Lily declared. "Amelia is a knave if and only if Lily is a knave," Henry claimed. Joseph remarked, "Henry is not a knight". Amelia remarked, "If Henry is a knave then Sofia is a knight". As Sofia put it, "Joseph is a knave". So who is a knight and who is a knave?

Lily is a knight, Henry is a knave, Joseph is a knight, Amelia is a knave, and Sofia is a knave.

(1) Lily is a knight
(2) Henry is a knave
(3) Joseph is a knight
(4) Amelia is a knave
(5) Sofia is a knave

Let's think step by step, by considering whether each person is lying and if that leads to contradiction.

Assume Lily is a knight. No contradiction is found in their claim that Amelia is not a knight.

Amelia cannot be a knight, because this would contradict the claim of Lily that Amelia is not a knight.

Assume Amelia is a knave. No contradiction is found in their false claim that If Henry is a knave then Sofia is a knight.

Henry cannot be a knight, because this would contradict the claim of their own that Amelia is a knave if and only if Lily is a knave.

Assume Henry is a knave. No contradiction is found in their false claim that Amelia is a knave if and only if Lily is a knave.

Sofia cannot be a knight, because this would contradict the false claim of Amelia that If Henry is a knave then Sofia is a knight.

Assume Sofia is a knave. No contradiction is found in their false claim that Joseph is a knave.

Assume Joseph is a knight. No contradiction is found in their claim that Henry is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Jackson, Riley, Aiden, Sofia, and Samuel. "Sofia is a knave if and only if Samuel is a knave" - Jackson. Riley told you that Jackson is not a knight. Aiden said that If Sofia is a knave then Riley is a knave. Sofia expressed that Riley is not a knight. Samuel told you that If Jackson is a knight then Jackson is a knave. So who is a knight and who is a knave?

Jackson is a knave, Riley is a knight, Aiden is a knave, Sofia is a knave, and Samuel is a knight.

(1) Jackson is a knave
(2) Riley is a knight
(3) Aiden is a knave
(4) Sofia is a knave
(5) Samuel is a knight

Assume Jackson is a knight. No contradiction is found in their claim that Sofia is a knave if and only if Samuel is a knave.

Assume Sofia is a knight. No contradiction is found in their claim that Riley is not a knight.

Riley cannot be a knight, because this would contradict the claim of their own that Jackson is not a knight.

Assume Riley is a knave. No contradiction is found in their false claim that Jackson is not a knight.

Samuel cannot be a knight, because this would contradict the claim of their own that If Jackson is a knight then Jackson is a knave.

Samuel cannot be a knave, because this would contradict the claim of Jackson that Sofia is a knave if and only if Samuel is a knave.

We have exhausted all possibilities for Samuel and Riley, so let us go back and reconsider Sofia.

Assume Sofia is a knave. No contradiction is found in their false claim that Riley is not a knight.

Riley cannot be a knave, because this would contradict the false claim of Sofia that Riley is not a knight.

We have exhausted all possibilities for Riley and Sofia, so let us go back and reconsider Jackson.

Assume Jackson is a knave. No contradiction is found in their false claim that Sofia is a knave if and only if Samuel is a knave.

Riley cannot be a knight, because this would contradict the claim of Sofia that Riley is not a knight.

Riley cannot be a knave, because this would contradict the false claim of their own that Jackson is not a knight.

We have exhausted all possibilities for Riley, so let us go back and reconsider Sofia.

Assume Riley is a knight. No contradiction is found in their claim that Jackson is not a knight.

Assume Samuel is a knight. No contradiction is found in their claim that If Jackson is a knight then Jackson is a knave.

Aiden cannot be a knight, because this would contradict the claim of their own that If Sofia is a knave then Riley is a knave.

Assume Aiden is a knave. No contradiction is found in their false claim that If Sofia is a knave then Riley is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Harper, Oliver, Emma, Zoey, and Luke. Harper expressed that Zoey is a knight and Luke is a knight. Oliver stated, "Zoey is a knight or Luke is a knight". Emma told you that Luke is a knight and Emma is a knight. As Zoey put it, "Harper is not a knight". Luke said that Harper is a knight and Emma is a knave. So who is a knight and who is a knave?

Harper is a knave, Oliver is a knight, Emma is a knave, Zoey is a knight, and Luke is a knave.

(1) Harper is a knave
(2) Oliver is a knight
(3) Emma is a knave
(4) Zoey is a knight
(5) Luke is a knave

Assume Harper is a knight. No contradiction is found in their claim that Zoey is a knight and Luke is a knight.

Zoey cannot be a knight, because this would contradict the claim of their own that Harper is not a knight.

Zoey cannot be a knave, because this would contradict the claim of Harper that Zoey is a knight and Luke is a knight.

We have exhausted all possibilities for Zoey, so let us go back and reconsider Harper.

Assume Harper is a knave. No contradiction is found in their false claim that Zoey is a knight and Luke is a knight.

Assume Zoey is a knight. No contradiction is found in their claim that Harper is not a knight.

Luke cannot be a knight, because this would contradict the false claim of Harper that Zoey is a knight and Luke is a knight.

Assume Luke is a knave. No contradiction is found in their false claim that Harper is a knight and Emma is a knave.

Emma cannot be a knight, because this would contradict the claim of their own that Luke is a knight and Emma is a knight.

Assume Emma is a knave. No contradiction is found in their false claim that Luke is a knight and Emma is a knight.

Assume Oliver is a knight. No contradiction is found in their claim that Zoey is a knight or Luke is a knight.

(('and', ('telling-truth', 3), ('telling-truth', 4)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('and', ('telling-truth', 4), ('telling-truth', 2)), ('not', ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 2)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: David, Isabella, Michael, Sebastian, and Charlotte. David asserted: "Michael is a knight". Isabella said, "David is a knave and Charlotte is a knave." According to Michael, "Sebastian is a knight if and only if Michael is a knight". Sebastian noted, "Michael is not a knave". Charlotte stated, "If Charlotte is a knight then Sebastian is a knight". So who is a knight and who is a knave?

David Isabella Michael Sebastian Charlotte

David is a knight, Isabella is a knave, Michael is a knight, Sebastian is a knight, and Charlotte is a knight.

(1) David is a knight
(2) Isabella is a knave
(3) Michael is a knight
(4) Sebastian is a knight
(5) Charlotte is a knight

Assume David is a knight. No contradiction is found in their claim that Michael is a knight.

Assume Michael is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Michael is a knight.

Assume Sebastian is a knight. No contradiction is found in their claim that Michael is not a knave.

Isabella cannot be a knight, because this would contradict the claim of their own that David is a knave and Charlotte is a knave.

Assume Isabella is a knave. No contradiction is found in their false claim that David is a knave and Charlotte is a knave.

Assume Charlotte is a knight. No contradiction is found in their claim that If Charlotte is a knight then Sebastian is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Jacob, Penelope, Ethan, Matthew, and Noah. Jacob commented, "Ethan is a knave". "Jacob is a knight and Ethan is a knave," Penelope claimed. Ethan was heard saying, "If Penelope is a knave then Matthew is a knave". Matthew was heard saying, "Jacob is a knight or Noah is a knight". In Noah's words: "Jacob is a knight and Ethan is a knight". So who is a knight and who is a knave?

Jacob is a knave, Penelope is a knave, Ethan is a knight, Matthew is a knave, and Noah is a knave.

(1) Jacob is a knave
(2) Penelope is a knave
(3) Ethan is a knight
(4) Matthew is a knave
(5) Noah is a knave

Assume Jacob is a knight. No contradiction is found in their claim that Ethan is a knave.

Ethan cannot be a knight, because this would contradict the claim of Jacob that Ethan is a knave.

Assume Ethan is a knave. No contradiction is found in their false claim that If Penelope is a knave then Matthew is a knave.

Penelope cannot be a knight, because this would contradict the false claim of Ethan that If Penelope is a knave then Matthew is a knave.

Penelope cannot be a knave, because this would contradict the false claim of their own that Jacob is a knight and Ethan is a knave.

We have exhausted all possibilities for Penelope and Ethan, so let us go back and reconsider Jacob.

Assume Jacob is a knave. No contradiction is found in their false claim that Ethan is a knave.

Assume Ethan is a knight. No contradiction is found in their claim that If Penelope is a knave then Matthew is a knave.

Penelope cannot be a knight, because this would contradict the claim of their own that Jacob is a knight and Ethan is a knave.

Assume Penelope is a knave. No contradiction is found in their false claim that Jacob is a knight and Ethan is a knave.

Matthew cannot be a knight, because this would contradict the claim of Ethan that If Penelope is a knave then Matthew is a knave.

Assume Matthew is a knave. No contradiction is found in their false claim that Jacob is a knight or Noah is a knight.

Noah cannot be a knight, because this would contradict the false claim of Matthew that Jacob is a knight or Noah is a knight.

Assume Noah is a knave. No contradiction is found in their false claim that Jacob is a knight and Ethan is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Ethan, Aurora, Sofia, Scarlett, and Jack. Ethan remarked, "Scarlett is not a knight". Aurora said that Ethan is a knight and Sofia is a knight. In a statement by Sofia: "Jack is a knight if and only if Aurora is a knave". "Scarlett is a knight or Jack is a knave," Scarlett declared. Jack remarked, "If Ethan is a knight then Scarlett is a knave". So who is a knight and who is a knave?

Ethan is a knave, Aurora is a knave, Sofia is a knight, Scarlett is a knight, and Jack is a knight.

(1) Ethan is a knave
(2) Aurora is a knave
(3) Sofia is a knight
(4) Scarlett is a knight
(5) Jack is a knight

Assume Ethan is a knight. No contradiction is found in their claim that Scarlett is not a knight.

Scarlett cannot be a knight, because this would contradict the claim of Ethan that Scarlett is not a knight.

Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight or Jack is a knave.

Assume Jack is a knight. No contradiction is found in their claim that If Ethan is a knight then Scarlett is a knave.

Assume Aurora is a knight. No contradiction is found in their claim that Ethan is a knight and Sofia is a knight.

Sofia cannot be a knight, because this would contradict the claim of their own that Jack is a knight if and only if Aurora is a knave.

Sofia cannot be a knave, because this would contradict the claim of Aurora that Ethan is a knight and Sofia is a knight.

We have exhausted all possibilities for Sofia, so let us go back and reconsider Aurora.

Assume Aurora is a knave. No contradiction is found in their false claim that Ethan is a knight and Sofia is a knight.

Sofia cannot be a knight, because this would contradict the false claim of Aurora that Ethan is a knight and Sofia is a knight.

Sofia cannot be a knave, because this would contradict the false claim of their own that Jack is a knight if and only if Aurora is a knave.

We have exhausted all possibilities for Sofia and Aurora, so let us go back and reconsider Jack.

Jack cannot be a knave, because this would contradict the false claim of Scarlett that Scarlett is a knight or Jack is a knave.

We have exhausted all possibilities for Jack and Scarlett, so let us go back and reconsider Ethan.

Assume Ethan is a knave. No contradiction is found in their false claim that Scarlett is not a knight.

Assume Scarlett is a knight. No contradiction is found in their claim that Scarlett is a knight or Jack is a knave.

Aurora cannot be a knight, because this would contradict the claim of their own that Ethan is a knight and Sofia is a knight.

Assume Sofia is a knight. No contradiction is found in their claim that Jack is a knight if and only if Aurora is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: William, Emma, Isabella, Ethan, and Amelia. "If Emma is a knight then Ethan is a knave," William claimed. "If Amelia is a knight then William is a knight," Emma declared. Isabella stated, "William is a knave and Amelia is a knight". Ethan asserted: "Ethan is a knight". "Ethan is a knight if and only if Emma is a knight," Amelia claimed. So who is a knight and who is a knave?

William is a knight, Emma is a knight, Isabella is a knave, Ethan is a knave, and Amelia is a knave.

(1) William is a knight
(2) Emma is a knight
(3) Isabella is a knave
(4) Ethan is a knave
(5) Amelia is a knave

Assume William is a knight. No contradiction is found in their claim that If Emma is a knight then Ethan is a knave.

Assume Emma is a knight. No contradiction is found in their claim that If Amelia is a knight then William is a knight.

Assume Amelia is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Emma is a knight.

Ethan cannot be a knight, because this would contradict the claim of William that If Emma is a knight then Ethan is a knave.

Ethan cannot be a knave, because this would contradict the claim of Amelia that Ethan is a knight if and only if Emma is a knight.

We have exhausted all possibilities for Ethan, so let us go back and reconsider Amelia.

Assume Amelia is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Emma is a knight.

Assume Ethan is a knave. No contradiction is found in their false claim that Ethan is a knight.

Isabella cannot be a knight, because this would contradict the claim of their own that William is a knave and Amelia is a knight.

Assume Isabella is a knave. No contradiction is found in their false claim that William is a knave and Amelia is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Chloe, Sofia, Oliver, Avery, and Charlotte. "Charlotte is a knave or Avery is a knight," Chloe declared. Sofia stated, "Avery is a knave and Oliver is a knave". Oliver stated, "Chloe is a knight or Sofia is a knight". Avery noted, "Oliver is not a knave". "Oliver is a knight" - Charlotte. So who is a knight and who is a knave?

Chloe is a knight, Sofia is a knave, Oliver is a knight, Avery is a knight, and Charlotte is a knight.

(1) Chloe is a knight
(2) Sofia is a knave
(3) Oliver is a knight
(4) Avery is a knight
(5) Charlotte is a knight

Assume Chloe is a knight. No contradiction is found in their claim that Charlotte is a knave or Avery is a knight.

Assume Charlotte 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 Chloe is a knight or Sofia is a knight.

Sofia cannot be a knight, because this would contradict the claim of their own that Avery is a knave and Oliver is a knave.

Assume Sofia is a knave. No contradiction is found in their false claim that Avery is a knave and Oliver is a knave.

Assume Avery is a knight. No contradiction is found in their claim that Oliver is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Benjamin, Mia, Elizabeth, Sebastian, and David. Benjamin noted, "Elizabeth is a knave or Elizabeth is a knight". Mia said, "Benjamin is a knight and Benjamin is a knave." "Sebastian is a knave or David is a knight," Elizabeth declared. Sebastian asserted: "Mia is a knave or Sebastian is a knight". David stated, "Mia is a knave". So who is a knight and who is a knave?

Benjamin is a knight, Mia is a knave, Elizabeth is a knight, Sebastian is a knight, and David is a knight.

(1) Benjamin is a knight
(2) Mia is a knave
(3) Elizabeth is a knight
(4) Sebastian is a knight
(5) David is a knight

Assume Benjamin is a knight. No contradiction is found in their claim that Elizabeth is a knave or Elizabeth is a knight.

Assume Elizabeth is a knight. No contradiction is found in their claim that Sebastian is a knave or David is a knight.

Assume Sebastian is a knight. No contradiction is found in their claim that Mia is a knave or Sebastian is a knight.

Mia cannot be a knight, because this would contradict the claim of their own that Benjamin is a knight and Benjamin is a knave.

Assume Mia is a knave. No contradiction is found in their false claim that Benjamin is a knight and Benjamin is a knave.

Assume David is a knight. No contradiction is found in their claim that Mia is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: James, Benjamin, Sophia, Matthew, and Jack. "Jack is a knight or Matthew is a knight," James claimed. "Matthew is a knave or Jack is a knave" - Benjamin. Sophia told you that Jack is a knave. As Matthew put it, "Sophia is a knave if and only if Sophia is a knight". In a statement by Jack: "Matthew is not a knight". So who is a knight and who is a knave?

James is a knight, Benjamin is a knight, Sophia is a knave, Matthew is a knave, and Jack is a knight.

(1) James is a knight
(2) Benjamin is a knight
(3) Sophia is a knave
(4) Matthew is a knave
(5) Jack is a knight

Assume James is a knight. No contradiction is found in their claim that Jack is a knight or Matthew is a knight.

Assume Jack is a knight. No contradiction is found in their claim that Matthew is not a knight.

Matthew cannot be a knight, because this would contradict the claim of their own that Sophia is a knave if and only if Sophia is a knight.

Assume Matthew is a knave. No contradiction is found in their false claim that Sophia is a knave if and only if Sophia is a knight.

Sophia cannot be a knight, because this would contradict the claim of their own that Jack is a knave.

Assume Sophia is a knave. No contradiction is found in their false claim that Jack is a knave.

Assume Benjamin is a knight. No contradiction is found in their claim that Matthew is a knave or Jack is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Amelia, Scarlett, Mia, Aiden, and Michael. Amelia told you that If Mia is a knave then Scarlett is a knave. As Scarlett put it, "Mia is a knight and Scarlett is a knight". In Mia's words: "Aiden is not a knight". In a statement by Aiden: "If Scarlett is a knight then Mia is a knight". Michael stated, "If Scarlett is a knave then Aiden is a knave". So who is a knight and who is a knave?

Amelia is a knight, Scarlett is a knave, Mia is a knave, Aiden is a knight, and Michael is a knave.

(1) Amelia is a knight
(2) Scarlett is a knave
(3) Mia is a knave
(4) Aiden is a knight
(5) Michael is a knave

Assume Amelia is a knight. No contradiction is found in their claim that If Mia is a knave then Scarlett is a knave.

Assume Mia is a knight. No contradiction is found in their claim that Aiden is not a knight.

Aiden cannot be a knight, because this would contradict the claim of Mia that Aiden is not a knight.

Aiden cannot be a knave, because this would contradict the false claim of their own that If Scarlett is a knight then Mia is a knight.

We have exhausted all possibilities for Aiden, so let us go back and reconsider Mia.

Assume Mia is a knave. No contradiction is found in their false claim that Aiden is not a knight.

Assume Aiden is a knight. No contradiction is found in their claim that If Scarlett is a knight then Mia is a knight.

Scarlett cannot be a knight, because this would contradict the claim of Amelia that If Mia is a knave then Scarlett is a knave.

Assume Scarlett is a knave. No contradiction is found in their false claim that Mia is a knight and Scarlett is a knight.

Michael cannot be a knight, because this would contradict the claim of their own that If Scarlett is a knave then Aiden is a knave.

Assume Michael is a knave. No contradiction is found in their false claim that If Scarlett is a knave then Aiden is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Ella, Sofia, Jack, Matthew, and Liam. Ella asserted: "Jack is not a knight". "Jack is a knight," Sofia mentioned. "Sofia is a knight or Matthew is a knave" - Jack. "Ella is a knave," Matthew declared. Liam said that Sofia is a knave and Jack is a knave. So who is a knight and who is a knave?

Ella is a knave, Sofia is a knight, Jack is a knight, Matthew is a knight, and Liam is a knave.

(1) Ella is a knave
(2) Sofia is a knight
(3) Jack is a knight
(4) Matthew is a knight
(5) Liam is a knave

Assume Ella is a knight. No contradiction is found in their claim that Jack is not a knight.

Jack cannot be a knight, because this would contradict the claim of Ella that Jack is not a knight.

Assume Jack is a knave. No contradiction is found in their false claim that Sofia is a knight or Matthew is a knave.

Sofia cannot be a knight, because this would contradict the claim of their own that Jack is a knight.

Assume Sofia is a knave. No contradiction is found in their false claim that Jack is a knight.

Matthew cannot be a knight, because this would contradict the claim of their own that Ella is a knave.

Matthew cannot be a knave, because this would contradict the false claim of Jack that Sofia is a knight or Matthew is a knave.

We have exhausted all possibilities for Matthew, Sofia, and Jack, so let us go back and reconsider Ella.

Assume Ella is a knave. No contradiction is found in their false claim that Jack is not a knight.

Assume Jack is a knight. No contradiction is found in their claim that Sofia is a knight or Matthew is a knave.

Assume Sofia is a knight. No contradiction is found in their claim that Jack is a knight.

Assume Matthew is a knight. No contradiction is found in their claim that Ella is a knave.

Liam cannot be a knight, because this would contradict the claim of their own that Sofia is a knave and Jack is a knave.

Assume Liam is a knave. No contradiction is found in their false claim that Sofia is a knave and Jack is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Joseph, Daniel, Owen, Jacob, and Ava. Joseph noted, "If Ava is a knight then Jacob is a knave". Daniel stated, "If Joseph is a knight then Owen is a knave". Owen commented, "Joseph is a knight or Daniel is a knight". Jacob was heard saying, "Daniel is a knight and Joseph is a knave". Ava was heard saying, "Jacob is a knight and Daniel is a knave". So who is a knight and who is a knave?

Joseph is a knight, Daniel is a knave, Owen is a knight, Jacob is a knave, and Ava is a knave.

(1) Joseph is a knight
(2) Daniel is a knave
(3) Owen is a knight
(4) Jacob is a knave
(5) Ava is a knave

Assume Joseph is a knight. No contradiction is found in their claim that If Ava is a knight then Jacob is a knave.

Assume Ava is a knight. No contradiction is found in their claim that Jacob is a knight and Daniel is a knave.

Jacob cannot be a knight, because this would contradict the claim of Joseph that If Ava is a knight then Jacob is a knave.

Jacob cannot be a knave, because this would contradict the claim of Ava that Jacob is a knight and Daniel is a knave.

We have exhausted all possibilities for Jacob, so let us go back and reconsider Ava.

Assume Ava is a knave. No contradiction is found in their false claim that Jacob is a knight and Daniel is a knave.

Jacob cannot be a knight, because this would contradict the claim of their own that Daniel is a knight and Joseph is a knave.

Assume Jacob is a knave. No contradiction is found in their false claim that Daniel is a knight and Joseph is a knave.

Assume Daniel is a knight. No contradiction is found in their claim that If Joseph is a knight then Owen is a knave.

Owen cannot be a knight, because this would contradict the claim of Daniel that If Joseph is a knight then Owen is a knave.

Owen cannot be a knave, because this would contradict the false claim of their own that Joseph is a knight or Daniel is a knight.

We have exhausted all possibilities for Owen, so let us go back and reconsider Daniel.

Assume Daniel is a knave. No contradiction is found in their false claim that If Joseph is a knight then Owen is a knave.

Assume Owen is a knight. No contradiction is found in their claim that Joseph is a knight or Daniel is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Jacob, Grace, James, Oliver, and Elizabeth. According to Jacob, "Oliver is a knight if and only if James is a knight". In a statement by Grace: "If Jacob is a knight then Oliver is a knave". James noted, "Oliver is a knave or Elizabeth is a knave". Oliver was heard saying, "Grace is not a knave". "James is a knave or Oliver is a knight," Elizabeth claimed. So who is a knight and who is a knave?

Jacob is a knave, Grace is a knight, James is a knave, Oliver is a knight, and Elizabeth is a knight.

(1) Jacob is a knave
(2) Grace is a knight
(3) James is a knave
(4) Oliver is a knight
(5) Elizabeth is a knight

Assume Jacob is a knight. No contradiction is found in their claim that Oliver is a knight if and only if James is a knight.

Assume Oliver is a knight. No contradiction is found in their claim that Grace is not a knave.

Grace cannot be a knight, because this would contradict the claim of their own that If Jacob is a knight then Oliver is a knave.

Grace cannot be a knave, because this would contradict the claim of Oliver that Grace is not a knave.

We have exhausted all possibilities for Grace, so let us go back and reconsider Oliver.

Assume Oliver is a knave. No contradiction is found in their false claim that Grace is not a knave.

Grace cannot be a knight, because this would contradict the false claim of Oliver that Grace is not a knave.

Grace cannot be a knave, because this would contradict the false claim of their own that If Jacob is a knight then Oliver is a knave.

We have exhausted all possibilities for Grace and Oliver, so let us go back and reconsider Jacob.

Assume Jacob is a knave. No contradiction is found in their false claim that Oliver is a knight if and only if James is a knight.

Assume Grace is a knight. No contradiction is found in their claim that If Jacob is a knight then Oliver is a knave.

James cannot be a knight, because this would contradict the false claim of Jacob that Oliver is a knight if and only if James is a knight.

Assume James is a knave. No contradiction is found in their false claim that Oliver is a knave or Elizabeth is a knave.

Assume Elizabeth is a knight. No contradiction is found in their claim that James is a knave or Oliver is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Emily, Penelope, William, Scarlett, and Ava. Emily expressed that William is not a knight. Penelope expressed that William is a knight or Scarlett is a knave. "Penelope is a knave if and only if William is a knight," William claimed. As Scarlett put it, "Ava is a knave". Ava noted, "Scarlett is a knight if and only if Scarlett is a knave". So who is a knight and who is a knave?

Emily is a knight, Penelope is a knave, William is a knave, Scarlett is a knight, and Ava is a knave.

(1) Emily is a knight
(2) Penelope is a knave
(3) William is a knave
(4) Scarlett is a knight
(5) Ava is a knave

Assume Emily is a knight. No contradiction is found in their claim that William is not a knight.

William cannot be a knight, because this would contradict the claim of Emily that William is not a knight.

Assume William is a knave. No contradiction is found in their false claim that Penelope is a knave if and only if William is a knight.

Penelope cannot be a knight, because this would contradict the false claim of William that Penelope is a knave if and only if William is a knight.

Assume Penelope is a knave. No contradiction is found in their false claim that William is a knight or Scarlett is a knave.

Assume Scarlett is a knight. No contradiction is found in their claim that Ava is a knave.

Ava cannot be a knight, because this would contradict the claim of Scarlett that Ava is a knave.

Assume Ava is a knave. No contradiction is found in their false claim that Scarlett is a knight if and only if Scarlett is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Charlotte, Alexander, Ella, Chloe, and Lily. "Ella is a knave if and only if Chloe is a knave," Charlotte declared. "Chloe is not a knight," Alexander claimed. Ella asserted: "Lily is a knight or Charlotte is a knight". As Chloe put it, "If Alexander is a knave then Charlotte is a knave". Lily commented, "Chloe is not a knight". So who is a knight and who is a knave?

Charlotte is a knave, Alexander is a knave, Ella is a knave, Chloe is a knight, and Lily is a knave.

(1) Charlotte is a knave
(2) Alexander is a knave
(3) Ella is a knave
(4) Chloe is a knight
(5) Lily is a knave

Assume Charlotte is a knight. No contradiction is found in their claim that Ella is a knave if and only if Chloe is a knave.

Assume Ella is a knight. No contradiction is found in their claim that Lily is a knight or Charlotte is a knight.

Assume Lily is a knight. No contradiction is found in their claim that Chloe is not a knight.

Chloe cannot be a knight, because this would contradict the claim of Lily that Chloe is not a knight.

Chloe cannot be a knave, because this would contradict the claim of Charlotte that Ella is a knave if and only if Chloe is a knave.

We have exhausted all possibilities for Chloe, so let us go back and reconsider Lily.

Assume Lily is a knave. No contradiction is found in their false claim that Chloe is not a knight.

Assume Chloe is a knight. No contradiction is found in their claim that If Alexander is a knave then Charlotte is a knave.

Alexander cannot be a knight, because this would contradict the claim of their own that Chloe is not a knight.

Alexander cannot be a knave, because this would contradict the claim of Chloe that If Alexander is a knave then Charlotte is a knave.

We have exhausted all possibilities for Alexander, so let us go back and reconsider Chloe.

We have exhausted all possibilities for Chloe and Lily, so let us go back and reconsider Ella.

Ella cannot be a knave, because this would contradict the false claim of their own that Lily is a knight or Charlotte is a knight.

We have exhausted all possibilities for Ella, so let us go back and reconsider Charlotte.

Assume Charlotte is a knave. No contradiction is found in their false claim that Ella is a knave if and only if Chloe is a knave.

Chloe cannot be a knight, because this would contradict the false claim of Charlotte that Ella is a knave if and only if Chloe is a knave.

Chloe cannot be a knave, because this would contradict the false claim of their own that If Alexander is a knave then Charlotte is a knave.

Lily cannot be a knave, because this would contradict the claim of Ella that Lily is a knight or Charlotte is a knight.

We have exhausted all possibilities for Lily, so let us go back and reconsider Ella.

Assume Ella is a knave. No contradiction is found in their false claim that Lily is a knight or Charlotte is a knight.

Lily cannot be a knight, because this would contradict the false claim of Ella that Lily is a knight or Charlotte is a knight.

Assume Alexander is a knave. No contradiction is found in their false claim that Chloe is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Henry, Avery, Chloe, Oliver, and Evelyn. Henry was heard saying, "Chloe is a knight". Avery said that Evelyn is a knave if and only if Evelyn is a knight. Chloe said that Avery is a knave. Oliver told you that Chloe is a knave or Avery is a knight. "Chloe is a knight," Evelyn claimed. So who is a knight and who is a knave?

Henry is a knight, Avery is a knave, Chloe is a knight, Oliver is a knave, and Evelyn is a knight.

(1) Henry is a knight
(2) Avery is a knave
(3) Chloe is a knight
(4) Oliver is a knave
(5) Evelyn is a knight

Assume Henry is a knight. No contradiction is found in their claim that Chloe is a knight.

Assume Chloe is a knight. No contradiction is found in their claim that Avery is a knave.

Avery cannot be a knight, because this would contradict the claim of their own that Evelyn is a knave if and only if Evelyn is a knight.

Assume Avery is a knave. No contradiction is found in their false claim that Evelyn is a knave if and only if Evelyn is a knight.

Assume Evelyn is a knight. No contradiction is found in their claim that Chloe is a knight.

Oliver cannot be a knight, because this would contradict the claim of their own that Chloe is a knave or Avery is a knight.

Assume Oliver is a knave. No contradiction is found in their false claim that Chloe is a knave or Avery is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: William, Amelia, Jacob, Aiden, and Samuel. William told you that If Samuel is a knave then Jacob is a knave. Amelia noted, "Samuel is a knave or William is a knave". Jacob asserted: "Samuel is a knight or Samuel is a knave". In Aiden's words: "If Amelia is a knave then Aiden is a knight". "Aiden is a knight" - Samuel. So who is a knight and who is a knave?

William is a knight, Amelia is a knave, Jacob is a knight, Aiden is a knight, and Samuel is a knight.

(1) William is a knight
(2) Amelia is a knave
(3) Jacob is a knight
(4) Aiden is a knight
(5) Samuel is a knight

Assume William is a knight. No contradiction is found in their claim that If Samuel is a knave then Jacob is a knave.

Assume Samuel is a knight. No contradiction is found in their claim that Aiden is a knight.

Assume Aiden is a knight. No contradiction is found in their claim that If Amelia is a knave then Aiden is a knight.

Amelia cannot be a knight, because this would contradict the claim of their own that Samuel is a knave or William is a knave.

Assume Amelia is a knave. No contradiction is found in their false claim that Samuel is a knave or William is a knave.

Assume Jacob is a knight. No contradiction is found in their claim that Samuel is a knight or Samuel is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Liam, Olivia, Emily, Isabella, and Evelyn. According to Liam, "Olivia is a knave". Olivia expressed that Emily is a knight. Emily told you that Olivia is a knight and Evelyn is a knight. Isabella said, "Olivia is a knave and Emily is a knave." "Emily is a knight if and only if Emily is a knave," Evelyn claimed. So who is a knight and who is a knave?

Liam is a knight, Olivia is a knave, Emily is a knave, Isabella is a knight, and Evelyn is a knave.

(1) Liam is a knight
(2) Olivia is a knave
(3) Emily is a knave
(4) Isabella is a knight
(5) Evelyn is a knave

Assume Liam is a knight. No contradiction is found in their claim that Olivia is a knave.

Olivia cannot be a knight, because this would contradict the claim of Liam that Olivia is a knave.

Assume Olivia is a knave. No contradiction is found in their false claim that Emily is a knight.

Emily cannot be a knight, because this would contradict the false claim of Olivia that Emily is a knight.

Assume Emily is a knave. No contradiction is found in their false claim that Olivia is a knight and Evelyn is a knight.

Evelyn cannot be a knight, because this would contradict the claim of their own that Emily is a knight if and only if Emily is a knave.

Assume Evelyn is a knave. No contradiction is found in their false claim that Emily is a knight if and only if Emily is a knave.

Assume Isabella is a knight. No contradiction is found in their claim that Olivia is a knave and Emily is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Henry, Riley, Emily, Mason, and Samuel. Henry said that Mason is a knight or Samuel is a knave. In a statement by Riley: "Henry is a knave or Emily is a knave". Emily asserted: "Henry is not a knave". Mason said, "Emily is a knight if and only if Samuel is a knave." "Riley is not a knave" - Samuel. So who is a knight and who is a knave?

Henry is a knight, Riley is a knave, Emily is a knight, Mason is a knight, and Samuel is a knave.

(1) Henry is a knight
(2) Riley is a knave
(3) Emily is a knight
(4) Mason is a knight
(5) Samuel is a knave

Assume Henry is a knight. No contradiction is found in their claim that Mason is a knight or Samuel is a knave.

Assume Mason is a knight. No contradiction is found in their claim that Emily is a knight if and only if Samuel is a knave.

Assume Emily is a knight. No contradiction is found in their claim that Henry is not a knave.

Samuel cannot be a knight, because this would contradict the claim of Mason that Emily is a knight if and only if Samuel is a knave.

Assume Samuel is a knave. No contradiction is found in their false claim that Riley is not a knave.

Riley cannot be a knight, because this would contradict the claim of their own that Henry is a knave or Emily is a knave.

Assume Riley is a knave. No contradiction is found in their false claim that Henry is a knave or Emily is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Oliver, Penelope, Olivia, Ava, and Samuel. According to Oliver, "Penelope is not a knight". Penelope told you that Olivia is not a knight. Olivia asserted: "Ava is a knave". Ava commented, "Oliver is a knave and Olivia is a knight". Samuel asserted: "Penelope is a knave or Penelope is a knight". So who is a knight and who is a knave?

Oliver is a knight, Penelope is a knave, Olivia is a knight, Ava is a knave, and Samuel is a knight.

(1) Oliver is a knight
(2) Penelope is a knave
(3) Olivia is a knight
(4) Ava is a knave
(5) Samuel is a knight

Assume Oliver is a knight. No contradiction is found in their claim that Penelope is not a knight.

Penelope cannot be a knight, because this would contradict the claim of Oliver that Penelope is not a knight.

Assume Penelope is a knave. No contradiction is found in their false claim that Olivia is not a knight.

Assume Olivia is a knight. No contradiction is found in their claim that Ava is a knave.

Ava cannot be a knight, because this would contradict the claim of Olivia that Ava is a knave.

Assume Ava is a knave. No contradiction is found in their false claim that Oliver is a knave and Olivia is a knight.

Assume Samuel is a knight. No contradiction is found in their claim that Penelope is a knave or Penelope is a knight.

(('not', ('telling-truth', 1)), ('not', ('telling-truth', 2)), ('lying', 3), ('and', ('lying', 0), ('telling-truth', 2)), ('or', ('lying', 1), ('telling-truth', 1)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Aurora, Oliver, Abigail, Luke, and Mason. Aurora stated, "Oliver is not a knight". Oliver commented, "If Luke is a knave then Mason is a knave". According to Abigail, "Aurora is not a knight". Luke said, "If Oliver is a knight then Abigail is a knave." "Aurora is a knight," Mason claimed. So who is a knight and who is a knave?

Aurora is a knave, Oliver is a knight, Abigail is a knight, Luke is a knave, and Mason is a knave.

(1) Aurora is a knave
(2) Oliver is a knight
(3) Abigail is a knight
(4) Luke is a knave
(5) Mason is a knave

Assume Aurora is a knight. No contradiction is found in their claim that Oliver is not a knight.

Oliver cannot be a knight, because this would contradict the claim of Aurora that Oliver is not a knight.

Assume Oliver is a knave. No contradiction is found in their false claim that If Luke is a knave then Mason is a knave.

Luke cannot be a knight, because this would contradict the false claim of Oliver that If Luke is a knave then Mason is a knave.

Luke cannot be a knave, because this would contradict the false claim of their own that If Oliver is a knight then Abigail is a knave.

We have exhausted all possibilities for Luke and Oliver, so let us go back and reconsider Aurora.

Assume Aurora is a knave. No contradiction is found in their false claim that Oliver is not a knight.

Assume Oliver is a knight. No contradiction is found in their claim that If Luke is a knave then Mason is a knave.

Assume Luke is a knight. No contradiction is found in their claim that If Oliver is a knight then Abigail is a knave.

Abigail cannot be a knight, because this would contradict the claim of Luke that If Oliver is a knight then Abigail is a knave.

Abigail cannot be a knave, because this would contradict the false claim of their own that Aurora is not a knight.

We have exhausted all possibilities for Abigail, so let us go back and reconsider Luke.

Assume Luke is a knave. No contradiction is found in their false claim that If Oliver is a knight then Abigail is a knave.

Assume Abigail is a knight. No contradiction is found in their claim that Aurora is not a knight.

Mason cannot be a knight, because this would contradict the claim of Oliver that If Luke is a knave then Mason is a knave.

Assume Mason is a knave. No contradiction is found in their false claim that Aurora is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Avery, Sebastian, Logan, Ethan, and Penelope. As Avery put it, "Sebastian is a knight if and only if Ethan is a knight". Sebastian expressed that Ethan is a knight. "Logan is a knight and Sebastian is a knight," Logan claimed. Ethan said that Logan is a knave if and only if Logan is a knight. Penelope remarked, "If Logan is a knight then Logan is a knave". So who is a knight and who is a knave?

Avery is a knight, Sebastian is a knave, Logan is a knave, Ethan is a knave, and Penelope is a knight.

(1) Avery is a knight
(2) Sebastian is a knave
(3) Logan is a knave
(4) Ethan is a knave
(5) Penelope is a knight

Assume Avery is a knight. No contradiction is found in their claim that Sebastian is a knight if and only if Ethan is a knight.

Assume Sebastian is a knight. No contradiction is found in their claim that Ethan is a knight.

Ethan cannot be a knight, because this would contradict the claim of their own that Logan is a knave if and only if Logan is a knight.

Ethan cannot be a knave, because this would contradict the claim of Avery that Sebastian is a knight if and only if Ethan is a knight.

We have exhausted all possibilities for Ethan, so let us go back and reconsider Sebastian.

Assume Sebastian is a knave. No contradiction is found in their false claim that Ethan is a knight.

Ethan cannot be a knight, because this would contradict the claim of Avery that Sebastian is a knight if and only if Ethan is a knight.

Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knave if and only if Logan is a knight.

Logan cannot be a knight, because this would contradict the claim of their own that Logan is a knight and Sebastian is a knight.

Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight and Sebastian is a knight.

Assume Penelope is a knight. No contradiction is found in their claim that If Logan is a knight then Logan is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Mia, Ava, Scarlett, Emily, and Lily. Mia noted, "If Emily is a knight then Ava is a knave". Ava asserted: "Mia is a knave if and only if Emily is a knave". Scarlett was heard saying, "Lily is not a knave". As Emily put it, "Lily is not a knave". In a statement by Lily: "Ava is not a knave". So who is a knight and who is a knave?

Mia is a knight, Ava is a knave, Scarlett is a knave, Emily is a knave, and Lily is a knave.

(1) Mia is a knight
(2) Ava is a knave
(3) Scarlett is a knave
(4) Emily is a knave
(5) Lily is a knave

Assume Mia is a knight. No contradiction is found in their claim that If Emily is a knight then Ava is a knave.

Assume Emily is a knight. No contradiction is found in their claim that Lily is not a knave.

Assume Lily is a knight. No contradiction is found in their claim that Ava is not a knave.

Ava cannot be a knight, because this would contradict the claim of Mia that If Emily is a knight then Ava is a knave.

Ava cannot be a knave, because this would contradict the false claim of their own that Mia is a knave if and only if Emily is a knave.

We have exhausted all possibilities for Ava, so let us go back and reconsider Lily.

Lily cannot be a knave, because this would contradict the claim of Emily that Lily is not a knave.

We have exhausted all possibilities for Lily, so let us go back and reconsider Emily.

Assume Emily is a knave. No contradiction is found in their false claim that Lily is not a knave.

Lily cannot be a knight, because this would contradict the false claim of Emily that Lily is not a knave.

Assume Lily is a knave. No contradiction is found in their false claim that Ava is not a knave.

Ava cannot be a knight, because this would contradict the claim of their own that Mia is a knave if and only if Emily is a knave.

Assume Ava is a knave. No contradiction is found in their false claim that Mia is a knave if and only if Emily is a knave.

Scarlett cannot be a knight, because this would contradict the claim of their own that Lily is not a knave.

Assume Scarlett is a knave. No contradiction is found in their false claim that Lily is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Jacob, Chloe, Penelope, Avery, and Scarlett. Jacob commented, "Penelope is a knave". Chloe remarked, "Scarlett is a knight or Avery is a knave". Penelope asserted: "Avery is a knight if and only if Chloe is a knight". Avery was heard saying, "If Jacob is a knave then Penelope is a knave". As Scarlett put it, "Chloe is not a knave". So who is a knight and who is a knave?

Jacob is a knight, Chloe is a knave, Penelope is a knave, Avery is a knight, and Scarlett is a knave.

(1) Jacob is a knight
(2) Chloe is a knave
(3) Penelope is a knave
(4) Avery is a knight
(5) Scarlett is a knave

Assume Jacob is a knight. No contradiction is found in their claim that Penelope is a knave.

Penelope cannot be a knight, because this would contradict the claim of Jacob that Penelope is a knave.

Assume Penelope is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Chloe is a knight.

Assume Avery is a knight. No contradiction is found in their claim that If Jacob is a knave then Penelope is a knave.

Chloe cannot be a knight, because this would contradict the false claim of Penelope that Avery is a knight if and only if Chloe is a knight.

Assume Chloe is a knave. No contradiction is found in their false claim that Scarlett is a knight or Avery is a knave.

Scarlett cannot be a knight, because this would contradict the false claim of Chloe that Scarlett is a knight or Avery is a knave.

Assume Scarlett is a knave. No contradiction is found in their false claim that Chloe is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Luke, Jackson, Lucas, Charlotte, and Logan. Luke noted, "Charlotte is a knight or Luke is a knight". "Logan is a knave or Logan is a knight," Jackson mentioned. "Logan is a knight if and only if Charlotte is a knave," Lucas mentioned. Charlotte was heard saying, "Jackson is a knight and Luke is a knave". "Charlotte is a knight," Logan mentioned. So who is a knight and who is a knave?

Luke is a knight, Jackson is a knight, Lucas is a knave, Charlotte is a knave, and Logan is a knave.

(1) Luke is a knight
(2) Jackson is a knight
(3) Lucas is a knave
(4) Charlotte is a knave
(5) Logan is a knave

Assume Luke is a knight. No contradiction is found in their claim that Charlotte is a knight or Luke is a knight.

Charlotte cannot be a knight, because this would contradict the claim of their own that Jackson is a knight and Luke is a knave.

Assume Charlotte is a knave. No contradiction is found in their false claim that Jackson is a knight and Luke is a knave.

Assume Jackson is a knight. No contradiction is found in their claim that Logan is a knave or Logan is a knight.

Logan cannot be a knight, because this would contradict the claim of their own that Charlotte is a knight.

Assume Logan is a knave. No contradiction is found in their false claim that Charlotte is a knight.

Lucas cannot be a knight, because this would contradict the claim of their own that Logan is a knight if and only if Charlotte is a knave.

Assume Lucas is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Charlotte is a knave.

(('or', ('telling-truth', 3), ('telling-truth', 0)), ('or', ('lying', 4), ('telling-truth', 4)), ('<=>', ('telling-truth', 4), ('lying', 3)), ('and', ('telling-truth', 1), ('lying', 0)), ('telling-truth', 3))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Lucas, Aurora, Noah, Penelope, and Benjamin. "Aurora is a knight if and only if Penelope is a knight," Lucas mentioned. In a statement by Aurora: "Aurora is a knight and Penelope is a knight". Noah said that Lucas is a knight or Penelope is a knight. In a statement by Penelope: "Lucas is a knave if and only if Lucas is a knight". Benjamin was heard saying, "Lucas is a knight and Noah is a knave". So who is a knight and who is a knave?

Lucas is a knight, Aurora is a knave, Noah is a knight, Penelope is a knave, and Benjamin is a knave.

(1) Lucas is a knight
(2) Aurora is a knave
(3) Noah is a knight
(4) Penelope is a knave
(5) Benjamin is a knave

Assume Lucas is a knight. No contradiction is found in their claim that Aurora is a knight if and only if Penelope is a knight.

Assume Aurora is a knight. No contradiction is found in their claim that Aurora is a knight and Penelope is a knight.

Penelope cannot be a knight, because this would contradict the claim of their own that Lucas is a knave if and only if Lucas is a knight.

Penelope cannot be a knave, because this would contradict the claim of Lucas that Aurora is a knight if and only if Penelope is a knight.

We have exhausted all possibilities for Penelope, so let us go back and reconsider Aurora.

Assume Aurora is a knave. No contradiction is found in their false claim that Aurora is a knight and Penelope is a knight.

Penelope cannot be a knight, because this would contradict the claim of Lucas that Aurora is a knight if and only if Penelope is a knight.

Assume Penelope is a knave. No contradiction is found in their false claim that Lucas is a knave if and only if Lucas is a knight.

Assume Noah is a knight. No contradiction is found in their claim that Lucas is a knight or Penelope is a knight.

Benjamin cannot be a knight, because this would contradict the claim of their own that Lucas is a knight and Noah is a knave.

Assume Benjamin is a knave. No contradiction is found in their false claim that Lucas is a knight and Noah is a knave.

(('<=>', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 3)), ('<=>', ('lying', 0), ('telling-truth', 0)), ('and', ('telling-truth', 0), ('lying', 2)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Chloe, Riley, Logan, Avery, and Evelyn. As Chloe put it, "Evelyn is a knight if and only if Riley is a knight". As Riley put it, "Logan is a knight or Evelyn is a knave". In Logan's words: "Logan is a knight if and only if Avery is a knave". Avery commented, "Riley is a knight and Logan is a knight". Evelyn said, "If Logan is a knight then Avery is a knight." So who is a knight and who is a knave?

Chloe is a knave, Riley is a knave, Logan is a knave, Avery is a knave, and Evelyn is a knight.

(1) Chloe is a knave
(2) Riley is a knave
(3) Logan is a knave
(4) Avery is a knave
(5) Evelyn is a knight

Assume Chloe is a knight. No contradiction is found in their claim that Evelyn is a knight if and only if Riley is a knight.

Assume Evelyn is a knight. No contradiction is found in their claim that If Logan is a knight then Avery is a knight.

Assume Logan is a knight. No contradiction is found in their claim that Logan is a knight if and only if Avery is a knave.

Avery cannot be a knight, because this would contradict the claim of Logan that Logan is a knight if and only if Avery is a knave.

Avery cannot be a knave, because this would contradict the claim of Evelyn that If Logan is a knight then Avery is a knight.

We have exhausted all possibilities for Avery, so let us go back and reconsider Logan.

Assume Logan is a knave. No contradiction is found in their false claim that Logan is a knight if and only if Avery is a knave.

Avery cannot be a knight, because this would contradict the false claim of Logan that Logan is a knight if and only if Avery is a knave.

Assume Avery is a knave. No contradiction is found in their false claim that Riley is a knight and Logan is a knight.

Riley cannot be a knight, because this would contradict the claim of their own that Logan is a knight or Evelyn is a knave.

Riley cannot be a knave, because this would contradict the claim of Chloe that Evelyn is a knight if and only if Riley is a knight.

We have exhausted all possibilities for Riley, Avery, and Logan, so let us go back and reconsider Evelyn.

Assume Evelyn is a knave. No contradiction is found in their false claim that If Logan is a knight then Avery is a knight.

Riley cannot be a knight, because this would contradict the claim of Chloe that Evelyn is a knight if and only if Riley is a knight.

Riley cannot be a knave, because this would contradict the false claim of their own that Logan is a knight or Evelyn is a knave.

We have exhausted all possibilities for Riley and Avery, so let us go back and reconsider Logan.

Logan cannot be a knave, because this would contradict the false claim of Evelyn that If Logan is a knight then Avery is a knight.

We have exhausted all possibilities for Logan and Evelyn, so let us go back and reconsider Chloe.

Assume Chloe is a knave. No contradiction is found in their false claim that Evelyn is a knight if and only if Riley is a knight.

Riley cannot be a knight, because this would contradict the false claim of Chloe that Evelyn is a knight if and only if Riley is a knight.

Assume Riley is a knave. No contradiction is found in their false claim that Logan is a knight or Evelyn is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Elizabeth, Emma, William, Sebastian, and Harper. "Emma is a knave and Harper is a knave," Elizabeth claimed. "Elizabeth is a knight and William is a knave," Emma mentioned. William expressed that Elizabeth is a knight. Sebastian remarked, "Emma is not a knight". Harper said, "If Elizabeth is a knave then Sebastian is a knight." So who is a knight and who is a knave?

Elizabeth is a knave, Emma is a knave, William is a knave, Sebastian is a knight, and Harper is a knight.

(1) Elizabeth is a knave
(2) Emma is a knave
(3) William is a knave
(4) Sebastian is a knight
(5) Harper is a knight

Assume Elizabeth is a knight. No contradiction is found in their claim that Emma is a knave and Harper is a knave.

Emma cannot be a knight, because this would contradict the claim of Elizabeth that Emma is a knave and Harper is a knave.

Assume Emma is a knave. No contradiction is found in their false claim that Elizabeth is a knight and William is a knave.

Assume William is a knight. No contradiction is found in their claim that Elizabeth is a knight.

Harper cannot be a knight, because this would contradict the claim of Elizabeth that Emma is a knave and Harper is a knave.

Harper cannot be a knave, because this would contradict the false claim of their own that If Elizabeth is a knave then Sebastian is a knight.

We have exhausted all possibilities for Harper, so let us go back and reconsider William.

William cannot be a knave, because this would contradict the false claim of Emma that Elizabeth is a knight and William is a knave.

We have exhausted all possibilities for William and Emma, so let us go back and reconsider Elizabeth.

Assume Elizabeth is a knave. No contradiction is found in their false claim that Emma is a knave and Harper is a knave.

Emma cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight and William is a knave.

William cannot be a knight, because this would contradict the claim of their own that Elizabeth is a knight.

Assume William is a knave. No contradiction is found in their false claim that Elizabeth is a knight.

Assume Harper is a knight. No contradiction is found in their claim that If Elizabeth is a knave then Sebastian is a knight.

Assume Sebastian is a knight. No contradiction is found in their claim that Emma is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Jackson, Amelia, Ava, William, and Jack. Jackson said, "If Ava is a knave then Jack is a knight." "Jack is not a knave," Amelia declared. Ava noted, "If Jack is a knight then Ava is a knight". William expressed that Jack is a knave or Jackson is a knight. In a statement by Jack: "If William is a knight then William is a knave". So who is a knight and who is a knave?

Jackson is a knight, Amelia is a knave, Ava is a knight, William is a knight, and Jack is a knave.

(1) Jackson is a knight
(2) Amelia is a knave
(3) Ava is a knight
(4) William is a knight
(5) Jack is a knave

Assume Jackson is a knight. No contradiction is found in their claim that If Ava is a knave then Jack is a knight.

Assume Ava is a knight. No contradiction is found in their claim that If Jack is a knight then Ava is a knight.

Assume Jack is a knight. No contradiction is found in their claim that If William is a knight then William is a knave.

William cannot be a knight, because this would contradict the claim of Jack that If William is a knight then William is a knave.

William cannot be a knave, because this would contradict the false claim of their own that Jack is a knave or Jackson is a knight.

We have exhausted all possibilities for William, so let us go back and reconsider Jack.

Assume Jack is a knave. No contradiction is found in their false claim that If William is a knight then William is a knave.

Assume William is a knight. No contradiction is found in their claim that Jack is a knave or Jackson is a knight.

Amelia cannot be a knight, because this would contradict the claim of their own that Jack is not a knave.

Assume Amelia is a knave. No contradiction is found in their false claim that Jack is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Ella, Aurora, Elizabeth, Evelyn, and Riley. "Elizabeth is not a knight," Ella declared. "Riley is a knave or Ella is a knave," Aurora declared. "Aurora is a knave and Riley is a knight" - Elizabeth. Evelyn noted, "Elizabeth is not a knave". Riley said that If Aurora is a knight then Ella is a knave. So who is a knight and who is a knave?

Ella is a knight, Aurora is a knight, Elizabeth is a knave, Evelyn is a knave, and Riley is a knave.

(1) Ella is a knight
(2) Aurora is a knight
(3) Elizabeth is a knave
(4) Evelyn is a knave
(5) Riley is a knave

Assume Ella is a knight. No contradiction is found in their claim that Elizabeth is not a knight.

Elizabeth cannot be a knight, because this would contradict the claim of Ella that Elizabeth is not a knight.

Assume Elizabeth is a knave. No contradiction is found in their false claim that Aurora is a knave and Riley is a knight.

Assume Aurora is a knight. No contradiction is found in their claim that Riley is a knave or Ella is a knave.

Riley cannot be a knight, because this would contradict the claim of Aurora that Riley is a knave or Ella is a knave.

Assume Riley is a knave. No contradiction is found in their false claim that If Aurora is a knight then Ella is a knave.

Evelyn cannot be a knight, because this would contradict the claim of their own that Elizabeth is not a knave.

Assume Evelyn is a knave. No contradiction is found in their false claim that Elizabeth is not a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Mason, Ava, William, Luke, and Jacob. Mason remarked, "William is not a knave". According to Ava, "Jacob is a knave". In a statement by William: "Jacob is a knight if and only if William is a knight". According to Luke, "William is a knight". "Mason is a knave," Jacob claimed. So who is a knight and who is a knave?

Mason is a knave, Ava is a knave, William is a knave, Luke is a knave, and Jacob is a knight.

(1) Mason is a knave
(2) Ava is a knave
(3) William is a knave
(4) Luke is a knave
(5) Jacob is a knight

Assume Mason is a knight. No contradiction is found in their claim that William is not a knave.

Assume William is a knight. No contradiction is found in their claim that Jacob is a knight if and only if William is a knight.

Jacob cannot be a knight, because this would contradict the claim of their own that Mason is a knave.

Jacob cannot be a knave, because this would contradict the claim of William that Jacob is a knight if and only if William is a knight.

We have exhausted all possibilities for Jacob, so let us go back and reconsider William.

William cannot be a knave, because this would contradict the claim of Mason that William is not a knave.

We have exhausted all possibilities for William, so let us go back and reconsider Mason.

Assume Mason is a knave. No contradiction is found in their false claim that William is not a knave.

William cannot be a knight, because this would contradict the false claim of Mason that William is not a knave.

Assume William is a knave. No contradiction is found in their false claim that Jacob is a knight if and only if William is a knight.

Assume Jacob is a knight. No contradiction is found in their claim that Mason is a knave.

Ava cannot be a knight, because this would contradict the claim of their own that Jacob is a knave.

Assume Ava is a knave. No contradiction is found in their false claim that Jacob is a knave.

Luke cannot be a knight, because this would contradict the claim of their own that William is a knight.

Assume Luke is a knave. No contradiction is found in their false claim that William is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Joseph, Jackson, Benjamin, Samuel, and Abigail. In Joseph's words: "Samuel is a knave and Jackson is a knight". According to Jackson, "Jackson is a knight if and only if Joseph is a knave". Benjamin noted, "If Samuel is a knight then Jackson is a knight". Samuel said, "Jackson is a knight and Benjamin is a knave." Abigail told you that Benjamin is not a knight. So who is a knight and who is a knave?

Joseph is a knave, Jackson is a knave, Benjamin is a knight, Samuel is a knave, and Abigail is a knave.

(1) Joseph is a knave
(2) Jackson is a knave
(3) Benjamin is a knight
(4) Samuel is a knave
(5) Abigail is a knave

Assume Joseph is a knight. No contradiction is found in their claim that Samuel is a knave and Jackson is a knight.

Samuel cannot be a knight, because this would contradict the claim of Joseph that Samuel is a knave and Jackson is a knight.

Assume Samuel is a knave. No contradiction is found in their false claim that Jackson is a knight and Benjamin is a knave.

Jackson cannot be a knight, because this would contradict the claim of their own that Jackson is a knight if and only if Joseph is a knave.

Jackson cannot be a knave, because this would contradict the claim of Joseph that Samuel is a knave and Jackson is a knight.

We have exhausted all possibilities for Jackson and Samuel, so let us go back and reconsider Joseph.

Assume Joseph is a knave. No contradiction is found in their false claim that Samuel is a knave and Jackson is a knight.

Assume Samuel is a knight. No contradiction is found in their claim that Jackson is a knight and Benjamin is a knave.

Assume Jackson is a knight. No contradiction is found in their claim that Jackson is a knight if and only if Joseph is a knave.

Benjamin cannot be a knight, because this would contradict the claim of Samuel that Jackson is a knight and Benjamin is a knave.

Benjamin cannot be a knave, because this would contradict the false claim of their own that If Samuel is a knight then Jackson is a knight.

We have exhausted all possibilities for Benjamin, so let us go back and reconsider Jackson.

Jackson cannot be a knave, because this would contradict the claim of Samuel that Jackson is a knight and Benjamin is a knave.

We have exhausted all possibilities for Jackson, so let us go back and reconsider Samuel.

Jackson cannot be a knight, because this would contradict the false claim of Joseph that Samuel is a knave and Jackson is a knight.

Assume Jackson is a knave. No contradiction is found in their false claim that Jackson is a knight if and only if Joseph is a knave.

Assume Benjamin is a knight. No contradiction is found in their claim that If Samuel is a knight then Jackson is a knight.

Abigail cannot be a knight, because this would contradict the claim of their own that Benjamin is not a knight.

Assume Abigail is a knave. No contradiction is found in their false claim that Benjamin is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: William, Ella, Jackson, Henry, and Aurora. "Jackson is a knave," William claimed. In a statement by Ella: "Henry is not a knight". Jackson remarked, "Aurora is a knight and Ella is a knight". Henry noted, "William is a knight if and only if Ella is a knight". Aurora commented, "Henry is a knave or Jackson is a knave". So who is a knight and who is a knave?

William is a knave, Ella is a knight, Jackson is a knight, Henry is a knave, and Aurora is a knight.

(1) William is a knave
(2) Ella is a knight
(3) Jackson is a knight
(4) Henry is a knave
(5) Aurora is a knight

Assume William is a knight. No contradiction is found in their claim that Jackson is a knave.

Jackson cannot be a knight, because this would contradict the claim of William that Jackson is a knave.

Assume Jackson is a knave. No contradiction is found in their false claim that Aurora is a knight and Ella is a knight.

Assume Aurora is a knight. No contradiction is found in their claim that Henry is a knave or Jackson is a knave.

Assume Henry is a knight. No contradiction is found in their claim that William is a knight if and only if Ella is a knight.

Ella cannot be a knight, because this would contradict the claim of their own that Henry is not a knight.

Ella cannot be a knave, because this would contradict the claim of Henry that William is a knight if and only if Ella is a knight.

We have exhausted all possibilities for Ella, so let us go back and reconsider Henry.

Assume Henry is a knave. No contradiction is found in their false claim that William is a knight if and only if Ella is a knight.

Ella cannot be a knight, because this would contradict the false claim of Jackson that Aurora is a knight and Ella is a knight.

Ella cannot be a knave, because this would contradict the false claim of their own that Henry is not a knight.

We have exhausted all possibilities for Ella and Henry, so let us go back and reconsider Aurora.

Aurora cannot be a knave, because this would contradict the false claim of their own that Henry is a knave or Jackson is a knave.

We have exhausted all possibilities for Aurora and Jackson, so let us go back and reconsider William.

Assume William is a knave. No contradiction is found in their false claim that Jackson is a knave.

Assume Jackson is a knight. No contradiction is found in their claim that Aurora is a knight and Ella is a knight.

Henry cannot be a knight, because this would contradict the claim of Aurora that Henry is a knave or Jackson is a knave.

Assume Ella is a knight. No contradiction is found in their claim that Henry is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Henry, Jacob, Jackson, Charlotte, and Lily. Henry expressed that Jacob is a knight. In Jacob's words: "If Lily is a knight then Jackson is a knave". In Jackson's words: "Charlotte is a knave if and only if Jackson is a knight". According to Charlotte, "If Jackson is a knave then Jacob is a knave". Lily told you that Henry is a knave. So who is a knight and who is a knave?

Henry is a knight, Jacob is a knight, Jackson is a knave, Charlotte is a knave, and Lily is a knave.

(1) Henry is a knight
(2) Jacob is a knight
(3) Jackson is a knave
(4) Charlotte is a knave
(5) Lily is a knave

Assume Henry is a knight. No contradiction is found in their claim that Jacob is a knight.

Assume Jacob is a knight. No contradiction is found in their claim that If Lily is a knight then Jackson is a knave.

Lily cannot be a knight, because this would contradict the claim of their own that Henry is a knave.

Assume Lily is a knave. No contradiction is found in their false claim that Henry is a knave.

Assume Jackson is a knight. No contradiction is found in their claim that Charlotte is a knave if and only if Jackson is a knight.

Charlotte cannot be a knight, because this would contradict the claim of Jackson that Charlotte is a knave if and only if Jackson is a knight.

Charlotte cannot be a knave, because this would contradict the false claim of their own that If Jackson is a knave then Jacob is a knave.

We have exhausted all possibilities for Charlotte, so let us go back and reconsider Jackson.

Assume Jackson is a knave. No contradiction is found in their false claim that Charlotte is a knave if and only if Jackson is a knight.

Charlotte cannot be a knight, because this would contradict the false claim of Jackson that Charlotte is a knave if and only if Jackson is a knight.

Assume Charlotte is a knave. No contradiction is found in their false claim that If Jackson is a knave then Jacob is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Emma, Daniel, Ella, Joseph, and Logan. Emma noted, "If Ella is a knight then Ella is a knave". "Ella is a knight and Ella is a knave," Daniel claimed. "Emma is a knave and Emma is a knight," Ella declared. Joseph told you that If Emma is a knight then Logan is a knight. According to Logan, "Emma is not a knight". So who is a knight and who is a knave?

Emma is a knight, Daniel is a knave, Ella is a knave, Joseph is a knave, and Logan is a knave.

(1) Emma is a knight
(2) Daniel is a knave
(3) Ella is a knave
(4) Joseph is a knave
(5) Logan is a knave

Assume Emma is a knight. No contradiction is found in their claim that If Ella is a knight then Ella is a knave.

Ella cannot be a knight, because this would contradict the claim of Emma that If Ella is a knight then Ella is a knave.

Assume Ella is a knave. No contradiction is found in their false claim that Emma is a knave and Emma is a knight.

Daniel cannot be a knight, because this would contradict the claim of their own that Ella is a knight and Ella is a knave.

Assume Daniel is a knave. No contradiction is found in their false claim that Ella is a knight and Ella is a knave.

Assume Joseph is a knight. No contradiction is found in their claim that If Emma is a knight then Logan is a knight.

Logan cannot be a knight, because this would contradict the claim of their own that Emma is not a knight.

Logan cannot be a knave, because this would contradict the claim of Joseph that If Emma is a knight then Logan is a knight.

We have exhausted all possibilities for Logan, so let us go back and reconsider Joseph.

Assume Joseph is a knave. No contradiction is found in their false claim that If Emma is a knight then Logan is a knight.

Logan cannot be a knight, because this would contradict the false claim of Joseph that If Emma is a knight then Logan is a knight.

Assume Logan is a knave. No contradiction is found in their false claim that Emma is not a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Sophia, Abigail, Samuel, Jacob, and Grace. In a statement by Sophia: "Abigail is a knave if and only if Abigail is a knight". As Abigail put it, "If Samuel is a knight then Grace is a knight". "Abigail is a knave and Sophia is a knight" - Samuel. Jacob remarked, "If Abigail is a knight then Sophia is a knight". As Grace put it, "Abigail is a knave if and only if Sophia is a knight". So who is a knight and who is a knave?

Sophia is a knave, Abigail is a knight, Samuel is a knave, Jacob is a knave, and Grace is a knight.

(1) Sophia is a knave
(2) Abigail is a knight
(3) Samuel is a knave
(4) Jacob is a knave
(5) Grace is a knight

Sophia cannot be a knight, because this would contradict the claim of their own that Abigail is a knave if and only if Abigail is a knight.

Assume Sophia is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Abigail is a knight.

Assume Abigail is a knight. No contradiction is found in their claim that If Samuel is a knight then Grace is a knight.

Samuel cannot be a knight, because this would contradict the claim of their own that Abigail is a knave and Sophia is a knight.

Assume Samuel is a knave. No contradiction is found in their false claim that Abigail is a knave and Sophia is a knight.

Assume Grace is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Sophia is a knight.

Jacob cannot be a knight, because this would contradict the claim of their own that If Abigail is a knight then Sophia is a knight.

Assume Jacob is a knave. No contradiction is found in their false claim that If Abigail is a knight then Sophia is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: James, Scarlett, Luke, Ella, and Jacob. James asserted: "Scarlett is a knave". "Luke is a knave," Scarlett mentioned. Luke said, "Ella is a knave and Scarlett is a knight." Ella noted, "If James is a knave then Jacob is a knight". Jacob remarked, "Luke is a knave if and only if James is a knave". So who is a knight and who is a knave?

James is a knave, Scarlett is a knight, Luke is a knave, Ella is a knight, and Jacob is a knight.

(1) James is a knave
(2) Scarlett is a knight
(3) Luke is a knave
(4) Ella is a knight
(5) Jacob is a knight

Assume James is a knight. No contradiction is found in their claim that Scarlett is a knave.

Scarlett cannot be a knight, because this would contradict the claim of James that Scarlett is a knave.

Assume Scarlett is a knave. No contradiction is found in their false claim that Luke is a knave.

Luke cannot be a knight, because this would contradict the claim of their own that Ella is a knave and Scarlett is a knight.

Luke cannot be a knave, because this would contradict the false claim of Scarlett that Luke is a knave.

We have exhausted all possibilities for Luke and Scarlett, so let us go back and reconsider James.

Assume James is a knave. No contradiction is found in their false claim that Scarlett is a knave.

Assume Scarlett is a knight. No contradiction is found in their claim that Luke is a knave.

Luke cannot be a knight, because this would contradict the claim of Scarlett that Luke is a knave.

Assume Luke is a knave. No contradiction is found in their false claim that Ella is a knave and Scarlett is a knight.

Assume Ella is a knight. No contradiction is found in their claim that If James is a knave then Jacob is a knight.

Assume Jacob is a knight. No contradiction is found in their claim that Luke is a knave if and only if James is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Ethan, Lucas, Avery, Harper, and Mia. Ethan remarked, "Lucas is a knight and Harper is a knight". Lucas was heard saying, "Avery is a knave and Mia is a knight". Avery asserted: "Ethan is a knight if and only if Lucas is a knight". Harper remarked, "Mia is a knight or Avery is a knight". In a statement by Mia: "Ethan is a knave or Lucas is a knave". So who is a knight and who is a knave?

Ethan is a knave, Lucas is a knave, Avery is a knight, Harper is a knight, and Mia is a knight.

(1) Ethan is a knave
(2) Lucas is a knave
(3) Avery is a knight
(4) Harper is a knight
(5) Mia is a knight

Assume Ethan is a knight. No contradiction is found in their claim that Lucas is a knight and Harper is a knight.

Assume Lucas is a knight. No contradiction is found in their claim that Avery is a knave and Mia is a knight.

Avery cannot be a knight, because this would contradict the claim of Lucas that Avery is a knave and Mia is a knight.

Avery cannot be a knave, because this would contradict the false claim of their own that Ethan is a knight if and only if Lucas is a knight.

We have exhausted all possibilities for Avery, so let us go back and reconsider Lucas.

Lucas cannot be a knave, because this would contradict the claim of Ethan that Lucas is a knight and Harper is a knight.

We have exhausted all possibilities for Lucas, so let us go back and reconsider Ethan.

Assume Ethan is a knave. No contradiction is found in their false claim that Lucas is a knight and Harper is a knight.

Assume Avery is a knave. No contradiction is found in their false claim that Ethan is a knight if and only if Lucas is a knight.

Assume Mia is a knight. No contradiction is found in their claim that Ethan is a knave or Lucas is a knave.

Harper cannot be a knight, because this would contradict the false claim of Ethan that Lucas is a knight and Harper is a knight.

Harper cannot be a knave, because this would contradict the false claim of their own that Mia is a knight or Avery is a knight.

We have exhausted all possibilities for Harper, so let us go back and reconsider Mia.

Mia cannot be a knave, because this would contradict the claim of Lucas that Avery is a knave and Mia is a knight.

We have exhausted all possibilities for Mia and Avery, so let us go back and reconsider Lucas.

Assume Lucas is a knave. No contradiction is found in their false claim that Avery is a knave and Mia is a knight.

Assume Avery is a knight. No contradiction is found in their claim that Ethan is a knight if and only if Lucas is a knight.

Assume Harper is a knight. No contradiction is found in their claim that Mia is a knight or Avery is a knight.

(('and', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('lying', 2), ('telling-truth', 4)), ('<=>', ('telling-truth', 0), ('telling-truth', 1)), ('or', ('telling-truth', 4), ('telling-truth', 2)), ('or', ('lying', 0), ('lying', 1)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Matthew, Isabella, Emma, Abigail, and Henry. Matthew said that If Isabella is a knave then Emma is a knave. Isabella said, "Henry is a knight if and only if Abigail is a knave." Emma said that Abigail is a knave if and only if Isabella is a knave. Abigail asserted: "Matthew is not a knave". According to Henry, "If Henry is a knight then Abigail is a knight". So who is a knight and who is a knave?

Matthew is a knight, Isabella is a knave, Emma is a knave, Abigail is a knight, and Henry is a knight.

(1) Matthew is a knight
(2) Isabella is a knave
(3) Emma is a knave
(4) Abigail is a knight
(5) Henry is a knight

Assume Matthew is a knight. No contradiction is found in their claim that If Isabella is a knave then Emma is a knave.

Assume Isabella is a knight. No contradiction is found in their claim that Henry is a knight if and only if Abigail is a knave.

Assume Henry is a knight. No contradiction is found in their claim that If Henry is a knight then Abigail is a knight.

Abigail cannot be a knight, because this would contradict the claim of Isabella that Henry is a knight if and only if Abigail is a knave.

Abigail cannot be a knave, because this would contradict the false claim of their own that Matthew is not a knave.

We have exhausted all possibilities for Abigail, so let us go back and reconsider Henry.

Henry cannot be a knave, because this would contradict the false claim of their own that If Henry is a knight then Abigail is a knight.

We have exhausted all possibilities for Henry, so let us go back and reconsider Isabella.

Assume Isabella is a knave. No contradiction is found in their false claim that Henry is a knight if and only if Abigail is a knave.

Assume Abigail is a knight. No contradiction is found in their claim that Matthew is not a knave.

Emma cannot be a knight, because this would contradict the claim of Matthew that If Isabella is a knave then Emma is a knave.

Assume Emma is a knave. No contradiction is found in their false claim that Abigail is a knave if and only if Isabella is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Penelope, Ava, Grace, Olivia, and Amelia. "Ava is a knight if and only if Grace is a knight," Penelope declared. Ava said that Amelia is a knight if and only if Amelia is a knave. "If Olivia is a knight then Amelia is a knight," Grace mentioned. In Olivia's words: "Grace is a knight or Olivia is a knight". Amelia said, "Olivia is a knave if and only if Ava is a knave." So who is a knight and who is a knave?

Penelope is a knight, Ava is a knave, Grace is a knave, Olivia is a knight, and Amelia is a knave.

(1) Penelope is a knight
(2) Ava is a knave
(3) Grace is a knave
(4) Olivia is a knight
(5) Amelia is a knave

Assume Penelope is a knight. No contradiction is found in their claim that Ava is a knight if and only if Grace is a knight.

Ava cannot be a knight, because this would contradict the claim of their own that Amelia is a knight if and only if Amelia is a knave.

Assume Ava is a knave. No contradiction is found in their false claim that Amelia is a knight if and only if Amelia is a knave.

Assume Amelia is a knight. No contradiction is found in their claim that Olivia is a knave if and only if Ava is a knave.

Olivia cannot be a knight, because this would contradict the claim of Amelia that Olivia is a knave if and only if Ava is a knave.

Assume Olivia is a knave. No contradiction is found in their false claim that Grace is a knight or Olivia is a knight.

Grace cannot be a knight, because this would contradict the claim of Penelope that Ava is a knight if and only if Grace is a knight.

Grace cannot be a knave, because this would contradict the false claim of their own that If Olivia is a knight then Amelia is a knight.

We have exhausted all possibilities for Grace and Olivia, so let us go back and reconsider Amelia.

Assume Amelia is a knave. No contradiction is found in their false claim that Olivia is a knave if and only if Ava is a knave.

Assume Olivia is a knight. No contradiction is found in their claim that Grace is a knight or Olivia is a knight.

Assume Grace is a knave. No contradiction is found in their false claim that If Olivia is a knight then Amelia is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Ava, Harper, Emily, Abigail, and Sebastian. Ava was heard saying, "Harper is a knave and Abigail is a knight". As Harper put it, "Harper is a knight". Emily asserted: "Abigail is a knave if and only if Harper is a knight". "If Emily is a knave then Harper is a knave," Abigail declared. Sebastian said that Emily is a knight. So who is a knight and who is a knave?

Ava is a knight, Harper is a knave, Emily is a knight, Abigail is a knight, and Sebastian is a knight.

(1) Ava is a knight
(2) Harper is a knave
(3) Emily is a knight
(4) Abigail is a knight
(5) Sebastian is a knight

Assume Ava is a knight. No contradiction is found in their claim that Harper is a knave and Abigail is a knight.

Harper cannot be a knight, because this would contradict the claim of Ava that Harper is a knave and Abigail is a knight.

Assume Harper is a knave. No contradiction is found in their false claim that Harper is a knight.

Assume Abigail is a knight. No contradiction is found in their claim that If Emily is a knave then Harper is a knave.

Assume Emily is a knight. No contradiction is found in their claim that Abigail is a knave if and only if Harper is a knight.

Assume Sebastian is a knight. No contradiction is found in their claim that Emily is a knight.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Avery, Grace, Scarlett, Michael, and Elizabeth. In Avery's words: "Grace is a knight if and only if Elizabeth is a knave". As Grace put it, "Michael is a knave if and only if Scarlett is a knave". "Scarlett is a knight or Elizabeth is a knave" - Scarlett. Michael stated, "Grace is a knave and Scarlett is a knight". Elizabeth was heard saying, "Avery is a knave". So who is a knight and who is a knave?

Avery is a knave, Grace is a knight, Scarlett is a knave, Michael is a knave, and Elizabeth is a knight.

(1) Avery is a knave
(2) Grace is a knight
(3) Scarlett is a knave
(4) Michael is a knave
(5) Elizabeth is a knight

Assume Avery is a knight. No contradiction is found in their claim that Grace is a knight if and only if Elizabeth is a knave.

Assume Grace is a knight. No contradiction is found in their claim that Michael is a knave if and only if Scarlett is a knave.

Michael cannot be a knight, because this would contradict the claim of their own that Grace is a knave and Scarlett is a knight.

Assume Michael is a knave. No contradiction is found in their false claim that Grace is a knave and Scarlett is a knight.

Scarlett cannot be a knight, because this would contradict the claim of Grace that Michael is a knave if and only if Scarlett is a knave.

Assume Scarlett is a knave. No contradiction is found in their false claim that Scarlett is a knight or Elizabeth is a knave.

Elizabeth cannot be a knight, because this would contradict the claim of Avery that Grace is a knight if and only if Elizabeth is a knave.

Elizabeth cannot be a knave, because this would contradict the false claim of Scarlett that Scarlett is a knight or Elizabeth is a knave.

We have exhausted all possibilities for Elizabeth, Scarlett, and Michael, so let us go back and reconsider Grace.

Assume Grace is a knave. No contradiction is found in their false claim that Michael is a knave if and only if Scarlett is a knave.

Assume Michael is a knight. No contradiction is found in their claim that Grace is a knave and Scarlett is a knight.

Scarlett cannot be a knight, because this would contradict the false claim of Grace that Michael is a knave if and only if Scarlett is a knave.

Scarlett cannot be a knave, because this would contradict the claim of Michael that Grace is a knave and Scarlett is a knight.

We have exhausted all possibilities for Scarlett, so let us go back and reconsider Michael.

Scarlett cannot be a knight, because this would contradict the false claim of Michael that Grace is a knave and Scarlett is a knight.

Scarlett cannot be a knave, because this would contradict the false claim of Grace that Michael is a knave if and only if Scarlett is a knave.

We have exhausted all possibilities for Scarlett, Michael, and Grace, so let us go back and reconsider Avery.

Assume Avery is a knave. No contradiction is found in their false claim that Grace is a knight if and only if Elizabeth is a knave.

Assume Elizabeth is a knight. No contradiction is found in their claim that Avery is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Evelyn, Abigail, Ethan, Logan, and Sofia. Evelyn remarked, "Logan is a knight". Abigail remarked, "Sofia is a knight and Evelyn is a knave". "Logan is a knave or Evelyn is a knave," Ethan declared. Logan remarked, "Sofia is a knight if and only if Ethan is a knight". Sofia told you that Abigail is a knight or Logan is a knave. So who is a knight and who is a knave?

Evelyn is a knight, Abigail is a knave, Ethan is a knave, Logan is a knight, and Sofia is a knave.

(1) Evelyn is a knight
(2) Abigail is a knave
(3) Ethan is a knave
(4) Logan is a knight
(5) Sofia is a knave

Assume Evelyn is a knight. No contradiction is found in their claim that Logan is a knight.

Assume Logan is a knight. No contradiction is found in their claim that Sofia is a knight if and only if Ethan is a knight.

Assume Sofia is a knight. No contradiction is found in their claim that Abigail is a knight or Logan is a knave.

Abigail cannot be a knight, because this would contradict the claim of their own that Sofia is a knight and Evelyn is a knave.

Abigail cannot be a knave, because this would contradict the claim of Sofia that Abigail is a knight or Logan is a knave.

We have exhausted all possibilities for Abigail, so let us go back and reconsider Sofia.

Assume Sofia is a knave. No contradiction is found in their false claim that Abigail is a knight or Logan is a knave.

Assume Abigail is a knave. No contradiction is found in their false claim that Sofia is a knight and Evelyn is a knave.

Ethan cannot be a knight, because this would contradict the claim of their own that Logan is a knave or Evelyn is a knave.

Assume Ethan is a knave. No contradiction is found in their false claim that Logan is a knave or Evelyn is a knave.


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Jacob, Jack, Lucas, Avery, and Lily. Jacob told you that Lucas is a knight or Avery is a knight. Jack asserted: "Jack is a knight and Jacob is a knight". According to Lucas, "Jack is not a knight". Avery was heard saying, "Lucas is a knave if and only if Jacob is a knave". Lily said that Avery is a knight if and only if Lucas is a knight. So who is a knight and who is a knave?

Jacob is a knight, Jack is a knave, Lucas is a knight, Avery is a knight, and Lily is a knight.

(1) Jacob is a knight
(2) Jack is a knave
(3) Lucas is a knight
(4) Avery is a knight
(5) Lily is a knight

Assume Jacob is a knight. No contradiction is found in their claim that Lucas is a knight or Avery is a knight.

Assume Lucas is a knight. No contradiction is found in their claim that Jack is not a knight.

Jack cannot be a knight, because this would contradict the claim of Lucas that Jack is not a knight.

Assume Jack is a knave. No contradiction is found in their false claim that Jack is a knight and Jacob is a knight.

Assume Avery is a knight. No contradiction is found in their claim that Lucas is a knave if and only if Jacob is a knave.

Assume Lily is a knight. No contradiction is found in their claim that Avery is a knight if and only if Lucas is a knight.

(('or', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('telling-truth', 1), ('telling-truth', 0)), ('not', ('telling-truth', 1)), ('<=>', ('lying', 2), ('lying', 0)), ('<=>', ('telling-truth', 3), ('telling-truth', 2)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 5 inhabitants: Amelia, Avery, Sophia, Aurora, and Noah. Amelia told you that If Amelia is a knight then Aurora is a knave. Avery said that Noah is a knight or Aurora is a knight. Sophia was heard saying, "Sophia is a knight or Aurora is a knave". According to Aurora, "Avery is not a knave". In a statement by Noah: "Avery is a knight if and only if Amelia is a knight". So who is a knight and who is a knave?

Amelia is a knight, Avery is a knave, Sophia is a knight, Aurora is a knave, and Noah is a knave.

(1) Amelia is a knight
(2) Avery is a knave
(3) Sophia is a knight
(4) Aurora is a knave
(5) Noah is a knave

Assume Amelia is a knight. No contradiction is found in their claim that If Amelia is a knight then Aurora is a knave.

Aurora cannot be a knight, because this would contradict the claim of Amelia that If Amelia is a knight then Aurora is a knave.

Assume Aurora is a knave. No contradiction is found in their false claim that Avery is not a knave.

Avery cannot be a knight, because this would contradict the false claim of Aurora that Avery is not a knave.

Assume Avery is a knave. No contradiction is found in their false claim that Noah is a knight or Aurora is a knight.

Noah cannot be a knight, because this would contradict the false claim of Avery that Noah is a knight or Aurora is a knight.

Assume Noah is a knave. No contradiction is found in their false claim that Avery is a knight if and only if Amelia is a knight.

Assume Sophia is a knight. No contradiction is found in their claim that Sophia is a knight or Aurora is a knave.