A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Alexander, Sofia, Samuel, David, Isabella, William, and Abigail. In a statement by Alexander: "Abigail is a knave". Sofia said that Isabella is not a knave. According to Samuel, "William is not a knave". David commented, "Isabella is not a knight". Isabella said that Sofia is a knight or William is a knight. William remarked, "Alexander is a knight or Abigail is a knave". Abigail said that William is a knave if and only if Isabella is a knave. So who is a knight and who is a knave?

Alexander Sofia Samuel David Isabella William Abigail

Alexander is a knave, Sofia is a knave, Samuel is a knave, David is a knight, Isabella is a knave, William is a knave, and Abigail is a knight.

(1) Alexander is a knave
(2) Sofia is a knave
(3) Samuel is a knave
(4) David is a knight
(5) Isabella is a knave
(6) William is a knave
(7) Abigail is a knight

Assume Alexander is a knight. No contradiction is found in their claim that Abigail is a knave.

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

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

Assume William is a knight. No contradiction is found in their claim that Alexander is a knight or Abigail is a knave.

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

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

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

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

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

Assume Alexander is a knave. No contradiction is found in their false claim that Abigail is a knave.

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

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

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

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

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

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

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

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

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

Assume David is a knight. No contradiction is found in their claim that Isabella 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 7 inhabitants: Riley, Henry, Elizabeth, Isabella, James, Benjamin, and Sophia. Riley stated, "Riley is a knight if and only if James is a knave". "Henry is a knight if and only if Benjamin is a knave," Henry declared. Elizabeth told you that If Benjamin is a knave then Riley is a knave. Isabella said, "Benjamin is a knave." James noted, "Riley is a knight and Sophia is a knight". In Benjamin's words: "Elizabeth is a knight". In a statement by Sophia: "Henry is a knave if and only if Elizabeth is a knight". So who is a knight and who is a knave?

Riley Henry Elizabeth Isabella James Benjamin Sophia

Riley is a knight, Henry is a knave, Elizabeth is a knave, Isabella is a knight, James is a knave, Benjamin is a knave, and Sophia is a knave.

(1) Riley is a knight
(2) Henry is a knave
(3) Elizabeth is a knave
(4) Isabella is a knight
(5) James is a knave
(6) Benjamin is a knave
(7) Sophia is a knave

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

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

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

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

Sophia cannot be a knight, because this would contradict the false claim of James that Riley is a knight and Sophia is a knight.

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

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

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

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

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

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

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

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

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

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

Assume Isabella is a knight. No contradiction is found in their claim that Benjamin 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 7 inhabitants: Zoey, Ava, Jacob, William, Henry, Isabella, and Aiden. Zoey remarked, "Aiden is a knight if and only if Jacob is a knight". Ava asserted: "Aiden is a knight or Zoey is a knave". According to Jacob, "Ava is a knight if and only if Aiden is a knight". William told you that William is a knight and Henry is a knight. "Jacob is a knave or Isabella is a knight," Henry claimed. Isabella asserted: "Ava is a knight if and only if Aiden is a knave". "Isabella is a knave or Jacob is a knave," Aiden declared. So who is a knight and who is a knave?

Zoey Ava Jacob William Henry Isabella Aiden

Zoey is a knight, Ava is a knight, Jacob is a knight, William is a knave, Henry is a knave, Isabella is a knave, and Aiden is a knight.

(1) Zoey is a knight
(2) Ava is a knight
(3) Jacob is a knight
(4) William is a knave
(5) Henry is a knave
(6) Isabella is a knave
(7) Aiden is a knight

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

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

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

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

Ava cannot be a knave, because this would contradict the false claim of their own that Aiden is a knight or Zoey is a knave.

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

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

Assume Ava is a knight. No contradiction is found in their claim that Aiden is a knight or Zoey is a knave.

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

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

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

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

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

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

Assume Henry is a knave. No contradiction is found in their false claim that Jacob is a knave or Isabella 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 7 inhabitants: Penelope, Oliver, Jacob, Mason, James, Emma, and Lucas. Penelope told you that Mason is a knave. Oliver was heard saying, "Lucas is a knave or Oliver is a knight". According to Jacob, "If Penelope is a knight then Emma is a knave". Mason expressed that Oliver is not a knave. "Mason is a knave if and only if Oliver is a knight," James mentioned. In a statement by Emma: "James is a knight if and only if Mason is a knave". Lucas asserted: "Emma is a knight or James is a knight". So who is a knight and who is a knave?

Penelope Oliver Jacob Mason James Emma Lucas

Penelope is a knave, Oliver is a knight, Jacob is a knight, Mason is a knight, James is a knave, Emma is a knight, and Lucas is a knight.

(1) Penelope is a knave
(2) Oliver is a knight
(3) Jacob is a knight
(4) Mason is a knight
(5) James is a knave
(6) Emma is a knight
(7) Lucas is a knight

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

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

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

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

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

Assume Lucas is a knight. No contradiction is found in their claim that Emma is a knight or James is a knight.

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Jacob is a knight. No contradiction is found in their claim that If Penelope is a knight then Emma 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 7 inhabitants: Avery, Ava, Mia, Penelope, Riley, Samuel, and Olivia. According to Avery, "Ava is a knight and Penelope is a knight". Ava said that Mia is a knight and Penelope is a knight. In a statement by Mia: "Penelope is a knave and Avery is a knight". Penelope noted, "Riley is a knight". "If Mia is a knave then Avery is a knight," Riley mentioned. "Penelope is a knave or Ava is a knave," Samuel claimed. "Samuel is a knight if and only if Avery is a knight," Olivia claimed. So who is a knight and who is a knave?

Avery Ava Mia Penelope Riley Samuel Olivia

Avery is a knave, Ava is a knave, Mia is a knave, Penelope is a knave, Riley is a knave, Samuel is a knight, and Olivia is a knave.

(1) Avery is a knave
(2) Ava is a knave
(3) Mia is a knave
(4) Penelope is a knave
(5) Riley is a knave
(6) Samuel is a knight
(7) Olivia is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

(('and', ('telling-truth', 1), ('telling-truth', 3)), ('and', ('telling-truth', 2), ('telling-truth', 3)), ('and', ('lying', 3), ('telling-truth', 0)), ('telling-truth', 4), ('->', ('lying', 2), ('telling-truth', 0)), ('or', ('lying', 3), ('lying', 1)), ('<=>', ('telling-truth', 5), ('telling-truth', 0)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Penelope, Sofia, Lily, Aurora, Noah, Jackson, and Luke. Penelope expressed that Sofia is a knave. Sofia expressed that Luke is a knave. "Jackson is a knave and Aurora is a knight," Lily claimed. Aurora asserted: "Lily is not a knave". Noah was heard saying, "Jackson is not a knave". In Jackson's words: "Luke is not a knave". Luke commented, "Aurora is a knave if and only if Noah is a knave". So who is a knight and who is a knave?

Penelope Sofia Lily Aurora Noah Jackson Luke

Penelope is a knave, Sofia is a knight, Lily is a knight, Aurora is a knight, Noah is a knave, Jackson is a knave, and Luke is a knave.

(1) Penelope is a knave
(2) Sofia is a knight
(3) Lily is a knight
(4) Aurora is a knight
(5) Noah is a knave
(6) Jackson is a knave
(7) Luke is a knave

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

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

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

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

Assume Aurora 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 Jackson is a knave and Aurora is a knight.

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

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

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

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

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

Assume Aurora 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 claim of their own that Jackson is a knave and Aurora is a knight.

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

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

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

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

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

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

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

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

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

Assume Sofia 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 Sofia that Luke is a knave.

Assume Luke is a knave. No contradiction is found in their false claim that Aurora is a knave if and only if Noah is a knave.

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

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

Assume Noah is a knave. No contradiction is found in their false claim that Jackson 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 7 inhabitants: Matthew, Ella, Harper, Alexander, Penelope, Benjamin, and Ava. "Harper is a knight," Matthew declared. Ella was heard saying, "Ava is a knave or Matthew is a knave". Harper said, "Ava is not a knight." Alexander said, "Ella is a knight if and only if Ava is a knave." According to Penelope, "If Ava is a knight then Alexander is a knave". "Ava is a knight if and only if Harper is a knight," Benjamin declared. Ava stated, "If Matthew is a knave then Harper is a knave". So who is a knight and who is a knave?

Matthew Ella Harper Alexander Penelope Benjamin Ava

Matthew is a knave, Ella is a knight, Harper is a knave, Alexander is a knave, Penelope is a knight, Benjamin is a knave, and Ava is a knight.

(1) Matthew is a knave
(2) Ella is a knight
(3) Harper is a knave
(4) Alexander is a knave
(5) Penelope is a knight
(6) Benjamin is a knave
(7) Ava is a knight

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Benjamin is a knave. No contradiction is found in their false claim that Ava is a knight if and only if Harper 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 7 inhabitants: Matthew, Benjamin, Ethan, Mason, Victoria, Jacob, and Lucas. According to Matthew, "Victoria is not a knave". Benjamin commented, "If Mason is a knight then Matthew is a knave". Ethan was heard saying, "Matthew is a knight if and only if Lucas is a knight". Mason was heard saying, "Mason is a knight if and only if Victoria is a knight". Victoria was heard saying, "If Jacob is a knave then Benjamin is a knave". "Matthew is a knave" - Jacob. Lucas noted, "Benjamin is a knave if and only if Jacob is a knave". So who is a knight and who is a knave?

Matthew Benjamin Ethan Mason Victoria Jacob Lucas

Matthew is a knight, Benjamin is a knave, Ethan is a knight, Mason is a knight, Victoria is a knight, Jacob is a knave, and Lucas is a knight.

(1) Matthew is a knight
(2) Benjamin is a knave
(3) Ethan is a knight
(4) Mason is a knight
(5) Victoria is a knight
(6) Jacob is a knave
(7) Lucas is a knight

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

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

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

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

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

Assume Benjamin is a knave. No contradiction is found in their false claim that If Mason is a knight then Matthew is a knave.

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

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

Assume Lucas is a knight. No contradiction is found in their claim that Benjamin is a knave if and only if 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 7 inhabitants: William, Harper, Mason, James, Samuel, Amelia, and Matthew. William expressed that If Mason is a knight then Samuel is a knave. Harper stated, "Mason is a knight or James is a knight". Mason expressed that Samuel is a knave and Samuel is a knight. James told you that Amelia is not a knave. Samuel was heard saying, "William is not a knave". In a statement by Amelia: "Matthew is a knave if and only if James is a knave". According to Matthew, "If Harper is a knight then Amelia is a knave". So who is a knight and who is a knave?

William Harper Mason James Samuel Amelia Matthew

William is a knight, Harper is a knave, Mason is a knave, James is a knave, Samuel is a knight, Amelia is a knave, and Matthew is a knight.

(1) William is a knight
(2) Harper is a knave
(3) Mason is a knave
(4) James is a knave
(5) Samuel is a knight
(6) Amelia is a knave
(7) Matthew is a knight

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

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

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

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

Assume Harper is a knight. No contradiction is found in their claim that Mason is a knight or James is a knight.

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

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

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

Matthew cannot be a knave, because this would contradict the claim of Amelia that Matthew is a knave if and only if James is a knave.

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

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

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

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

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

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

James cannot be a knight, because this would contradict the false claim of Harper that Mason is a knight or James is a knight.

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

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

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

Assume Matthew is a knight. No contradiction is found in their claim that If Harper is a knight then Amelia 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 7 inhabitants: David, Aiden, Abigail, Alexander, Emma, Jackson, and Ava. David told you that Aiden is a knight if and only if Jackson is a knave. As Aiden put it, "Ava is a knave or Alexander is a knight". Abigail stated, "Alexander is a knave or Ava is a knight". According to Alexander, "Jackson is not a knight". Emma told you that If David is a knight then Abigail is a knight. Jackson said that David is a knight and Emma is a knave. Ava said, "If Emma is a knight then Alexander is a knight." So who is a knight and who is a knave?

David Aiden Abigail Alexander Emma Jackson Ava

David is a knight, Aiden is a knight, Abigail is a knight, Alexander is a knight, Emma is a knight, Jackson is a knave, and Ava is a knight.

(1) David is a knight
(2) Aiden is a knight
(3) Abigail is a knight
(4) Alexander is a knight
(5) Emma is a knight
(6) Jackson is a knave
(7) Ava is a knight

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

Assume Aiden is a knight. No contradiction is found in their claim that Ava is a knave or Alexander is a knight.

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

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

Assume Abigail is a knight. No contradiction is found in their claim that Alexander is a knave or Ava is a knight.

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

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

Assume Jackson is a knave. No contradiction is found in their false claim that David is a knight and Emma 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 7 inhabitants: Elizabeth, James, Aiden, Mia, Olivia, Zoey, and Aurora. Elizabeth stated, "If Mia is a knave then Zoey is a knave". James said, "Aiden is a knight." "Zoey is a knave or Elizabeth is a knave," Aiden declared. Mia was heard saying, "If James is a knave then Mia is a knight". Olivia commented, "If James is a knave then Aurora is a knave". "Mia is a knight or Aurora is a knight," Zoey declared. Aurora said, "Mia is not a knight." So who is a knight and who is a knave?

Elizabeth James Aiden Mia Olivia Zoey Aurora

Elizabeth is a knight, James is a knave, Aiden is a knave, Mia is a knight, Olivia is a knight, Zoey is a knight, and Aurora is a knave.

(1) Elizabeth is a knight
(2) James is a knave
(3) Aiden is a knave
(4) Mia is a knight
(5) Olivia is a knight
(6) Zoey is a knight
(7) Aurora is a knave

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

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

Assume James 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 Zoey is a knave or Elizabeth is a knave.

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

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

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

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

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

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

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

Assume Aiden is a knave. No contradiction is found in their false claim that Zoey is a knave or Elizabeth is a knave.

Assume Zoey is a knight. No contradiction is found in their claim that Mia is a knight or Aurora is a knight.

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

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

Assume Olivia is a knight. No contradiction is found in their claim that If James is a knave then 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 7 inhabitants: Grace, Scarlett, Amelia, Lily, Sebastian, Daniel, and Victoria. Grace was heard saying, "Daniel is a knight if and only if Daniel is a knave". Scarlett remarked, "Sebastian is a knave and Victoria is a knave". In a statement by Amelia: "Scarlett is a knave if and only if Victoria is a knight". "Daniel is not a knight," Lily mentioned. "If Amelia is a knave then Amelia is a knight," Sebastian mentioned. According to Daniel, "If Sebastian is a knight then Lily is a knave". Victoria expressed that Daniel is a knave if and only if Grace is a knave. So who is a knight and who is a knave?

Grace Scarlett Amelia Lily Sebastian Daniel Victoria

Grace is a knave, Scarlett is a knave, Amelia is a knight, Lily is a knight, Sebastian is a knight, Daniel is a knave, and Victoria is a knight.

(1) Grace is a knave
(2) Scarlett is a knave
(3) Amelia is a knight
(4) Lily is a knight
(5) Sebastian is a knight
(6) Daniel is a knave
(7) Victoria is a knight

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

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

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

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

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

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

Assume Scarlett is a knave. No contradiction is found in their false claim that Sebastian is a knave and Victoria is a knave.

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

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

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

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

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

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

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

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

Assume Scarlett is a knight. No contradiction is found in their claim that Sebastian is a knave and Victoria is a knave.

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

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

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

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

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

We have exhausted all possibilities for Victoria, Scarlett, Amelia, and Sebastian, so let us go back and reconsider Daniel.

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

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

Assume Lily is a knight. No contradiction is found in their claim that Daniel 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 7 inhabitants: Benjamin, Chloe, Emily, Riley, Mia, Isabella, and Penelope. "Emily is a knight and Isabella is a knave," Benjamin claimed. According to Chloe, "Penelope is a knight". Emily said, "Emily is a knight or Benjamin is a knave." Riley was heard saying, "Mia is a knave and Emily is a knave". According to Mia, "Isabella is a knight if and only if Emily is a knave". Isabella remarked, "Riley is not a knight". "Emily is a knight and Isabella is a knight," Penelope mentioned. So who is a knight and who is a knave?

Benjamin Chloe Emily Riley Mia Isabella Penelope

Benjamin is a knave, Chloe is a knight, Emily is a knight, Riley is a knave, Mia is a knave, Isabella is a knight, and Penelope is a knight.

(1) Benjamin is a knave
(2) Chloe is a knight
(3) Emily is a knight
(4) Riley is a knave
(5) Mia is a knave
(6) Isabella is a knight
(7) Penelope is a knight

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Penelope is a knight. No contradiction is found in their claim that Emily is a knight and Isabella 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 7 inhabitants: David, Benjamin, Michael, Evelyn, Charlotte, Amelia, and James. In David's words: "Michael is a knave". Benjamin stated, "Charlotte is not a knave". In Michael's words: "Charlotte is a knight if and only if David is a knight". In Evelyn's words: "James is a knight or Benjamin is a knave". "If Evelyn is a knight then Michael is a knave," Charlotte declared. Amelia told you that James is not a knave. In James's words: "David is a knight". So who is a knight and who is a knave?

David Benjamin Michael Evelyn Charlotte Amelia James

David is a knave, Benjamin is a knave, Michael is a knight, Evelyn is a knight, Charlotte is a knave, Amelia is a knave, and James is a knave.

(1) David is a knave
(2) Benjamin is a knave
(3) Michael is a knight
(4) Evelyn is a knight
(5) Charlotte is a knave
(6) Amelia is a knave
(7) James is a knave

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Amelia is a knave. No contradiction is found in their false claim that James 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 7 inhabitants: Benjamin, Sofia, Mason, Ava, Aria, Abigail, and Liam. Benjamin expressed that Liam is a knave and Liam is a knight. Sofia stated, "Ava is a knight and Liam is a knight". According to Mason, "Ava is a knight or Abigail is a knave". "Liam is a knight or Abigail is a knave," Ava claimed. "Mason is a knight and Abigail is a knave," Aria claimed. In Abigail's words: "Ava is a knave and Benjamin is a knight". "Ava is a knave and Sofia is a knave" - Liam. So who is a knight and who is a knave?

Benjamin Sofia Mason Ava Aria Abigail Liam

Benjamin is a knave, Sofia is a knave, Mason is a knight, Ava is a knight, Aria is a knight, Abigail is a knave, and Liam is a knave.

(1) Benjamin is a knave
(2) Sofia is a knave
(3) Mason is a knight
(4) Ava is a knight
(5) Aria is a knight
(6) Abigail is a knave
(7) Liam is a knave

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

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

Assume Liam is a knight. No contradiction is found in their claim that Ava is a knave and Sofia is a knave.

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

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

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

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

Assume Ava is a knight. No contradiction is found in their claim that Liam is a knight or Abigail is a knave.

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

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

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

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

Assume Mason is a knight. No contradiction is found in their claim that Ava is a knight or Abigail is a knave.

Assume Aria is a knight. No contradiction is found in their claim that Mason is a knight and Abigail 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 7 inhabitants: Isabella, Lucas, Abigail, Ethan, Oliver, Zoey, and William. Isabella asserted: "If Oliver is a knight then William is a knight". Lucas said that Isabella is a knight. "Oliver is a knave and Abigail is a knight" - Abigail. Ethan told you that Zoey is a knave. Oliver noted, "Ethan is a knight if and only if Abigail is a knave". According to Zoey, "If Lucas is a knight then Isabella is a knight". "Zoey is a knave and Ethan is a knight," William claimed. So who is a knight and who is a knave?

Isabella Lucas Abigail Ethan Oliver Zoey William

Isabella is a knight, Lucas is a knight, Abigail is a knave, Ethan is a knave, Oliver is a knave, Zoey is a knight, and William is a knave.

(1) Isabella is a knight
(2) Lucas is a knight
(3) Abigail is a knave
(4) Ethan is a knave
(5) Oliver is a knave
(6) Zoey is a knight
(7) William is a knave

Assume Isabella is a knight. No contradiction is found in their claim that If Oliver is a knight then William is a knight.

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

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

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

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

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

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

Assume Zoey is a knight. No contradiction is found in their claim that If Lucas is a knight then Isabella is a knight.

Assume Lucas is a knight. No contradiction is found in their claim that Isabella is a knight.

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

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

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

Lucas cannot be a knave, because this would contradict the false claim of their own that Isabella is a knight.

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

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

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

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

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

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

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

Assume William is a knave. No contradiction is found in their false claim that Zoey is a knave 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 7 inhabitants: Logan, Emma, Grace, Alexander, Emily, Daniel, and Oliver. "Daniel is a knight" - Logan. Emma remarked, "Logan is not a knight". Grace was heard saying, "Daniel is a knight or Daniel is a knave". In Alexander's words: "If Daniel is a knave then Emily is a knight". Emily commented, "Oliver is a knight". Daniel remarked, "Grace is not a knave". Oliver said that Logan is a knave or Grace is a knight. So who is a knight and who is a knave?

Logan Emma Grace Alexander Emily Daniel Oliver

Logan is a knight, Emma is a knave, Grace is a knight, Alexander is a knight, Emily is a knight, Daniel is a knight, and Oliver is a knight.

(1) Logan is a knight
(2) Emma is a knave
(3) Grace is a knight
(4) Alexander is a knight
(5) Emily is a knight
(6) Daniel is a knight
(7) Oliver is a knight

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

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

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

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

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

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

Assume Emily 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 Logan is a knave or Grace 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 7 inhabitants: Ella, Victoria, Aurora, Noah, Lily, Henry, and Alexander. Ella stated, "Alexander is a knight or Aurora is a knight". "Lily is a knight and Lily is a knave," Victoria mentioned. "If Noah is a knight then Victoria is a knave" - Aurora. "Alexander is a knave or Henry is a knave," Noah claimed. Lily expressed that Victoria is a knave. As Henry put it, "Aurora is not a knight". In a statement by Alexander: "If Aurora is a knave then Alexander is a knight". So who is a knight and who is a knave?

Ella Victoria Aurora Noah Lily Henry Alexander

Ella is a knight, Victoria is a knave, Aurora is a knight, Noah is a knight, Lily is a knight, Henry is a knave, and Alexander is a knight.

(1) Ella is a knight
(2) Victoria is a knave
(3) Aurora is a knight
(4) Noah is a knight
(5) Lily is a knight
(6) Henry is a knave
(7) Alexander is a knight

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

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

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

Assume Noah is a knight. No contradiction is found in their claim that Alexander is a knave or Henry is a knave.

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

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

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

Assume Victoria is a knave. No contradiction is found in their false claim that Lily is a knight and Lily is a knave.

Assume Lily is a knight. No contradiction is found in their claim that Victoria 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 7 inhabitants: Olivia, David, Ava, Benjamin, Chloe, Amelia, and Daniel. In Olivia's words: "Benjamin is a knight if and only if David is a knave". David stated, "Amelia is a knave or Benjamin is a knight". According to Ava, "Chloe is a knight or Daniel is a knight". According to Benjamin, "David is a knave if and only if Benjamin is a knight". Chloe told you that If David is a knight then Daniel is a knight. Amelia remarked, "Amelia is a knight". "Ava is a knave," Daniel declared. So who is a knight and who is a knave?

Olivia David Ava Benjamin Chloe Amelia Daniel

Olivia is a knave, David is a knave, Ava is a knight, Benjamin is a knave, Chloe is a knight, Amelia is a knight, and Daniel is a knave.

(1) Olivia is a knave
(2) David is a knave
(3) Ava is a knight
(4) Benjamin is a knave
(5) Chloe is a knight
(6) Amelia is a knight
(7) Daniel is a knave

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

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

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

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

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

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

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

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

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

Assume Olivia is a knave. No contradiction is found in their false claim that Benjamin is a knight if and only if David is a knave.

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

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

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

Assume David is a knave. No contradiction is found in their false claim that Amelia is a knave or Benjamin is a knight.

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

Assume Ava is a knight. No contradiction is found in their claim that Chloe is a knight or Daniel is a knight.

Assume Chloe is a knight. No contradiction is found in their claim that If David is a knight then Daniel is a knight.

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

Assume Daniel is a knave. No contradiction is found in their false claim that Ava 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 7 inhabitants: Lily, James, Alexander, Owen, Scarlett, Sophia, and David. Lily expressed that Sophia is a knight. "Scarlett is a knave," James claimed. "James is a knight if and only if Lily is a knight," Alexander mentioned. "Owen is a knight or Scarlett is a knight" - Owen. In a statement by Scarlett: "If James is a knave then David is a knight". In Sophia's words: "David is a knight or Scarlett is a knight". In a statement by David: "Sophia is a knave or David is a knight". So who is a knight and who is a knave?

Lily James Alexander Owen Scarlett Sophia David

Lily is a knight, James is a knave, Alexander is a knave, Owen is a knight, Scarlett is a knight, Sophia is a knight, and David is a knight.

(1) Lily is a knight
(2) James is a knave
(3) Alexander is a knave
(4) Owen is a knight
(5) Scarlett is a knight
(6) Sophia is a knight
(7) David is a knight

Assume Lily is a knight. No contradiction is found in their claim that Sophia is a knight.

Assume Sophia is a knight. No contradiction is found in their claim that David is a knight or Scarlett is a knight.

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

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

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

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

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

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

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

(('telling-truth', 5), ('lying', 4), ('<=>', ('telling-truth', 1), ('telling-truth', 0)), ('or', ('telling-truth', 3), ('telling-truth', 4)), ('->', ('lying', 1), ('telling-truth', 6)), ('or', ('telling-truth', 6), ('telling-truth', 4)), ('or', ('lying', 5), ('telling-truth', 6)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Zoey, Evelyn, Sophia, Matthew, Jackson, Owen, and Benjamin. Zoey noted, "Zoey is a knight or Sophia is a knave". In a statement by Evelyn: "Zoey is a knight". Sophia asserted: "Jackson is a knave or Zoey is a knight". Matthew expressed that If Benjamin is a knave then Zoey is a knave. In a statement by Jackson: "Sophia is a knight". Owen noted, "Matthew is not a knight". "Zoey is a knight," Benjamin claimed. So who is a knight and who is a knave?

Zoey Evelyn Sophia Matthew Jackson Owen Benjamin

Zoey is a knight, Evelyn is a knight, Sophia is a knight, Matthew is a knight, Jackson is a knight, Owen is a knave, and Benjamin is a knight.

(1) Zoey is a knight
(2) Evelyn is a knight
(3) Sophia is a knight
(4) Matthew is a knight
(5) Jackson is a knight
(6) Owen is a knave
(7) Benjamin is a knight

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

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

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

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

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

Assume Benjamin is a knight. No contradiction is found in their claim that Zoey is a knight.

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

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

(('or', ('telling-truth', 0), ('lying', 2)), ('telling-truth', 0), ('or', ('lying', 4), ('telling-truth', 0)), ('->', ('lying', 6), ('lying', 0)), ('telling-truth', 2), ('not', ('telling-truth', 3)), ('telling-truth', 0))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Daniel, Alexander, Ava, Jacob, Benjamin, Matthew, and Abigail. As Daniel put it, "If Matthew is a knave then Abigail is a knight". "Matthew is a knave and Daniel is a knight" - Alexander. Ava commented, "Jacob is a knave". Jacob noted, "Daniel is a knight or Alexander is a knight". Benjamin expressed that Alexander is a knight and Alexander is a knave. In Matthew's words: "Benjamin is a knight and Ava is a knave". Abigail told you that Benjamin is not a knight. So who is a knight and who is a knave?

Daniel Alexander Ava Jacob Benjamin Matthew Abigail

Daniel is a knight, Alexander is a knight, Ava is a knave, Jacob is a knight, Benjamin is a knave, Matthew is a knave, and Abigail is a knight.

(1) Daniel is a knight
(2) Alexander is a knight
(3) Ava is a knave
(4) Jacob is a knight
(5) Benjamin is a knave
(6) Matthew is a knave
(7) Abigail is a knight

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

Assume Matthew is a knight. No contradiction is found in their claim that Benjamin is a knight and Ava is a knave.

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

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

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

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

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

Assume Alexander is a knight. No contradiction is found in their claim that Matthew is a knave and Daniel is a knight.

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

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

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

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 knave.

Assume Jacob is a knight. No contradiction is found in their claim that Daniel is a knight or Alexander is a knight.

Assume Abigail is a knight. No contradiction is found in their 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 7 inhabitants: Benjamin, Penelope, Victoria, Aiden, Michael, Isabella, and Jackson. "If Victoria is a knight then Michael is a knight," Benjamin declared. Penelope told you that Victoria is a knight or Aiden is a knave. Victoria commented, "Aiden is a knight". Aiden asserted: "Penelope is a knight or Victoria is a knave". Michael stated, "Benjamin is a knave or Michael is a knight". "Aiden is not a knave" - Isabella. Jackson asserted: "Benjamin is a knave". So who is a knight and who is a knave?

Benjamin Penelope Victoria Aiden Michael Isabella Jackson

Benjamin is a knight, Penelope is a knight, Victoria is a knight, Aiden is a knight, Michael is a knight, Isabella is a knight, and Jackson is a knave.

(1) Benjamin is a knight
(2) Penelope is a knight
(3) Victoria is a knight
(4) Aiden is a knight
(5) Michael is a knight
(6) Isabella is a knight
(7) Jackson is a knave

Assume Benjamin is a knight. No contradiction is found in their claim that If Victoria is a knight then Michael is a knight.

Assume Victoria 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 Penelope is a knight or Victoria is a knave.

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

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

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

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

Assume Jackson is a knave. No contradiction is found in their false claim that Benjamin 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 7 inhabitants: Isabella, Sophia, Matthew, Elizabeth, Lucas, Benjamin, and Owen. Isabella commented, "Owen is a knave and Sophia is a knave". Sophia said that Isabella is a knight if and only if Lucas is a knight. In Matthew's words: "Matthew is a knight if and only if Lucas is a knave". "Matthew is a knave and Sophia is a knave" - Elizabeth. According to Lucas, "Matthew is a knight if and only if Isabella is a knight". Benjamin noted, "Sophia is not a knave". According to Owen, "If Isabella is a knight then Sophia is a knave". So who is a knight and who is a knave?

Isabella Sophia Matthew Elizabeth Lucas Benjamin Owen

Isabella is a knave, Sophia is a knight, Matthew is a knight, Elizabeth is a knave, Lucas is a knave, Benjamin is a knight, and Owen is a knight.

(1) Isabella is a knave
(2) Sophia is a knight
(3) Matthew is a knight
(4) Elizabeth is a knave
(5) Lucas is a knave
(6) Benjamin is a knight
(7) Owen is a knight

Assume Isabella is a knight. No contradiction is found in their claim that Owen is a knave and Sophia is a knave.

Owen cannot be a knight, because this would contradict the claim of Isabella that Owen is a knave and Sophia is a knave.

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

Sophia cannot be a knight, because this would contradict the claim of Isabella that Owen is a knave and Sophia is a knave.

Sophia cannot be a knave, because this would contradict the false claim of Owen that If Isabella is a knight then Sophia is a knave.

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

Assume Isabella is a knave. No contradiction is found in their false claim that Owen is a knave and Sophia is a knave.

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

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

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

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

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

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

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

Assume Benjamin is a knight. No contradiction is found in their claim that Sophia 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 7 inhabitants: Benjamin, Ella, Ava, Abigail, Matthew, Charlotte, and Jack. "Jack is a knave if and only if Matthew is a knight" - Benjamin. According to Ella, "Jack is a knave or Ava is a knave". Ava was heard saying, "Matthew is not a knight". As Abigail put it, "Matthew is a knave if and only if Ava is a knight". "Jack is a knight and Benjamin is a knave" - Matthew. "Ella is a knight or Matthew is a knight" - Charlotte. "Ella is not a knave," Jack claimed. So who is a knight and who is a knave?

Benjamin Ella Ava Abigail Matthew Charlotte Jack

Benjamin is a knave, Ella is a knight, Ava is a knave, Abigail is a knight, Matthew is a knight, Charlotte is a knight, and Jack is a knight.

(1) Benjamin is a knave
(2) Ella is a knight
(3) Ava is a knave
(4) Abigail is a knight
(5) Matthew is a knight
(6) Charlotte is a knight
(7) Jack is a knight

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Assume Charlotte is a knight. No contradiction is found in their claim that Ella is a knight or Matthew 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 7 inhabitants: Jacob, Amelia, David, Evelyn, Mia, Sebastian, and Grace. Jacob said that Evelyn is not a knight. Amelia said, "If Grace is a knave then Evelyn is a knight." David remarked, "Jacob is a knight if and only if David is a knight". Evelyn said that Jacob is a knave or David is a knave. Mia noted, "Evelyn is a knave if and only if Grace is a knight". Sebastian noted, "Mia is a knight". Grace commented, "Jacob is a knave and Grace is a knight". So who is a knight and who is a knave?

Jacob Amelia David Evelyn Mia Sebastian Grace

Jacob is a knight, Amelia is a knave, David is a knight, Evelyn is a knave, Mia is a knave, Sebastian is a knave, and Grace is a knave.

(1) Jacob is a knight
(2) Amelia is a knave
(3) David is a knight
(4) Evelyn is a knave
(5) Mia is a knave
(6) Sebastian is a knave
(7) Grace is a knave

Assume Jacob is a knight. No contradiction is found in their claim that Evelyn is not a knight.

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

Assume Evelyn is a knave. No contradiction is found in their false claim that Jacob is a knave or David is a knave.

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

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

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

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

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

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

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

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

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

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

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

Assume Sebastian is a knave. No contradiction is found in their false claim that Mia 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 7 inhabitants: Sofia, Abigail, Ava, Ethan, Samuel, Michael, and Riley. Sofia said that Ava is a knave if and only if Ava is a knight. Abigail noted, "If Sofia is a knight then Riley is a knave". Ava asserted: "Abigail is not a knave". Ethan expressed that If Samuel is a knight then Michael is a knave. "Riley is a knight and Ava is a knave," Samuel claimed. "Riley is a knight and Ava is a knight" - Michael. Riley told you that Ethan is a knave or Sofia is a knight. So who is a knight and who is a knave?

Sofia Abigail Ava Ethan Samuel Michael Riley

Sofia is a knave, Abigail is a knight, Ava is a knight, Ethan is a knight, Samuel is a knave, Michael is a knave, and Riley is a knave.

(1) Sofia is a knave
(2) Abigail is a knight
(3) Ava is a knight
(4) Ethan is a knight
(5) Samuel is a knave
(6) Michael is a knave
(7) Riley is a knave

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

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

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

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

Assume Riley is a knight. No contradiction is found in their claim that Ethan is a knave or Sofia is a knight.

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

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

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

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

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

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

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

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

Michael cannot be a knight, because this would contradict the claim of their own that Riley is a knight and Ava is a knight.

Assume Michael is a knave. No contradiction is found in their false claim that Riley is a knight and Ava 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 7 inhabitants: James, Jackson, Emily, Liam, Jacob, Oliver, and Jack. James commented, "Jack is a knave if and only if James is a knight". "Jacob is not a knight," Jackson mentioned. In a statement by Emily: "Liam is a knave". In a statement by Liam: "James is a knight or Jackson is a knight". Jacob stated, "James is not a knave". According to Oliver, "Liam is not a knave". Jack remarked, "Jacob is not a knight". So who is a knight and who is a knave?

James Jackson Emily Liam Jacob Oliver Jack

James is a knight, Jackson is a knave, Emily is a knave, Liam is a knight, Jacob is a knight, Oliver is a knight, and Jack is a knave.

(1) James is a knight
(2) Jackson is a knave
(3) Emily is a knave
(4) Liam is a knight
(5) Jacob is a knight
(6) Oliver is a knight
(7) Jack is a knave

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

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

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

Assume Jacob is a knight. No contradiction is found in their claim that James is not a knave.

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

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

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

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

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

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

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

Assume Liam is a knight. No contradiction is found in their claim that James is a knight or Jackson is a knight.

Assume Oliver is a knight. No contradiction is found in their claim that Liam 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 7 inhabitants: William, Ella, Henry, Mason, James, Emma, and Harper. William asserted: "If William is a knight then Mason is a knave". Ella stated, "Mason is a knave". Henry commented, "Henry is a knight if and only if James is a knight". According to Mason, "Henry is a knave". "Henry is a knave or Henry is a knight," James claimed. "Henry is not a knave" - Emma. Harper expressed that William is a knight or Ella is a knave. So who is a knight and who is a knave?

William Ella Henry Mason James Emma Harper

William is a knight, Ella is a knight, Henry is a knight, Mason is a knave, James is a knight, Emma is a knight, and Harper is a knight.

(1) William is a knight
(2) Ella is a knight
(3) Henry is a knight
(4) Mason is a knave
(5) James is a knight
(6) Emma is a knight
(7) Harper is a knight

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

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

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

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

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

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

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

Assume Harper is a knight. No contradiction is found in their claim that William is a knight or Ella 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 7 inhabitants: Owen, Aria, Victoria, Penelope, Chloe, Jacob, and Olivia. Owen said, "Olivia is a knight if and only if Aria is a knight." Aria asserted: "Penelope is a knight or Olivia is a knave". As Victoria put it, "Penelope is a knight if and only if Jacob is a knave". Penelope asserted: "Jacob is a knave and Jacob is a knight". Chloe stated, "Olivia is not a knave". Jacob stated, "Victoria is a knave and Penelope is a knight". "If Victoria is a knight then Victoria is a knave," Olivia mentioned. So who is a knight and who is a knave?

Owen Aria Victoria Penelope Chloe Jacob Olivia

Owen is a knave, Aria is a knave, Victoria is a knave, Penelope is a knave, Chloe is a knight, Jacob is a knave, and Olivia is a knight.

(1) Owen is a knave
(2) Aria is a knave
(3) Victoria is a knave
(4) Penelope is a knave
(5) Chloe is a knight
(6) Jacob is a knave
(7) Olivia is a knight

Assume Owen is a knight. No contradiction is found in their claim that Olivia is a knight if and only if Aria is a knight.

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

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

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

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

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

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

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

Aria cannot be a knight, because this would contradict the claim of their own that Penelope is a knight or Olivia is a knave.

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

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

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

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

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

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

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

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

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

Assume Owen is a knave. No contradiction is found in their false claim that Olivia is a knight if and only if Aria is a knight.

Aria cannot be a knight, because this would contradict the false claim of Owen that Olivia is a knight if and only if Aria is a knight.

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

Assume Chloe is a knight. No contradiction is found in their claim that Olivia 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 7 inhabitants: Logan, Emma, Aurora, Liam, Jackson, Aria, and Aiden. "If Emma is a knight then Aurora is a knave," Logan claimed. Emma commented, "Liam is not a knave". Aurora said, "Jackson is not a knight." Liam stated, "Aria is a knight". "Logan is a knight," Jackson mentioned. According to Aria, "Aiden is a knave and Jackson is a knight". In Aiden's words: "If Jackson is a knight then Logan is a knave". So who is a knight and who is a knave?

Logan Emma Aurora Liam Jackson Aria Aiden

Logan is a knight, Emma is a knight, Aurora is a knave, Liam is a knight, Jackson is a knight, Aria is a knight, and Aiden is a knave.

(1) Logan is a knight
(2) Emma is a knight
(3) Aurora is a knave
(4) Liam is a knight
(5) Jackson is a knight
(6) Aria is a knight
(7) Aiden is a knave

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

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

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

Assume Aria is a knight. No contradiction is found in their claim that Aiden is a knave and Jackson is a knight.

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

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

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

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

Assume Aurora is a knave. No contradiction is found in their false claim that Jackson 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 7 inhabitants: Olivia, Aiden, Aurora, Michael, Lily, Amelia, and Noah. Olivia stated, "Amelia is a knight and Lily is a knave". Aiden noted, "Lily is a knave". Aurora stated, "Amelia is not a knight". Michael remarked, "Noah is a knight and Aurora is a knight". Lily remarked, "Aiden is a knight if and only if Amelia is a knave". Amelia expressed that If Michael is a knave then Lily is a knave. As Noah put it, "Lily is a knight and Amelia is a knave". So who is a knight and who is a knave?

Olivia Aiden Aurora Michael Lily Amelia Noah

Olivia is a knight, Aiden is a knight, Aurora is a knave, Michael is a knave, Lily is a knave, Amelia is a knight, and Noah is a knave.

(1) Olivia is a knight
(2) Aiden is a knight
(3) Aurora is a knave
(4) Michael is a knave
(5) Lily is a knave
(6) Amelia is a knight
(7) Noah is a knave

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

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

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

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

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

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

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

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

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

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

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

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

Assume Aurora is a knave. No contradiction is found in their false claim that Amelia 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 7 inhabitants: Mason, Michael, Benjamin, Jackson, Isabella, David, and Olivia. "Benjamin is not a knave," Mason mentioned. In a statement by Michael: "Michael is a knight and David is a knight". According to Benjamin, "Isabella is a knight". In a statement by Jackson: "Michael is a knight or Olivia is a knave". In Isabella's words: "Mason is a knave and David is a knight". David remarked, "Mason is a knight if and only if Isabella is a knave". Olivia remarked, "Benjamin is a knave and Michael is a knave". So who is a knight and who is a knave?

Mason Michael Benjamin Jackson Isabella David Olivia

Mason is a knave, Michael is a knave, Benjamin is a knave, Jackson is a knave, Isabella is a knave, David is a knave, and Olivia is a knight.

(1) Mason is a knave
(2) Michael is a knave
(3) Benjamin is a knave
(4) Jackson is a knave
(5) Isabella is a knave
(6) David is a knave
(7) Olivia is a knight

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

Assume Benjamin is a knight. No contradiction is found in their claim that Isabella is a knight.

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

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

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

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

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

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

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

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

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

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

David cannot be a knight, because this would contradict the false claim of Isabella that Mason is a knave and David is a knight.

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

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

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

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

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

Olivia cannot be a knave, because this would contradict the false claim of their own that Benjamin is a knave and Michael is a knave.

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

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

Assume Olivia is a knight. No contradiction is found in their claim that Benjamin is a knave and Michael 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 7 inhabitants: Luke, Michael, Grace, Ella, Avery, Sophia, and Ava. Luke was heard saying, "If Sophia is a knave then Ella is a knight". In a statement by Michael: "Luke is a knight or Sophia is a knight". Grace was heard saying, "Michael is a knight and Ella is a knight". Ella was heard saying, "Avery is not a knight". In a statement by Avery: "Ava is a knight". Sophia said that Avery is a knave. In Ava's words: "Avery is a knight if and only if Sophia is a knight". So who is a knight and who is a knave?

Luke Michael Grace Ella Avery Sophia Ava

Luke is a knight, Michael is a knight, Grace is a knight, Ella is a knight, Avery is a knave, Sophia is a knight, and Ava is a knave.

(1) Luke is a knight
(2) Michael is a knight
(3) Grace is a knight
(4) Ella is a knight
(5) Avery is a knave
(6) Sophia is a knight
(7) Ava is a knave

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

Assume Sophia 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 Sophia that Avery is a knave.

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

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

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

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

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

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

(('->', ('lying', 5), ('telling-truth', 3)), ('or', ('telling-truth', 0), ('telling-truth', 5)), ('and', ('telling-truth', 1), ('telling-truth', 3)), ('not', ('telling-truth', 4)), ('telling-truth', 6), ('lying', 4), ('<=>', ('telling-truth', 4), ('telling-truth', 5)))


A very special island is inhabited only by knights and knaves. Knights always tell the truth, and knaves always lie. You meet 7 inhabitants: Alexander, William, Liam, Henry, Olivia, Riley, and Sofia. "Henry is a knave or Liam is a knight" - Alexander. William stated, "Riley is a knight". Liam said that Olivia is a knave and Sofia is a knight. "If Olivia is a knave then Olivia is a knight," Henry declared. "Sofia is a knight," Olivia declared. "If William is a knight then Olivia is a knight," Riley claimed. In Sofia's words: "If Alexander is a knight then Olivia is a knight". So who is a knight and who is a knave?

Alexander William Liam Henry Olivia Riley Sofia

Alexander is a knave, William is a knight, Liam is a knave, Henry is a knight, Olivia is a knight, Riley is a knight, and Sofia is a knight.

(1) Alexander is a knave
(2) William is a knight
(3) Liam is a knave
(4) Henry is a knight
(5) Olivia is a knight
(6) Riley is a knight
(7) Sofia is a knight

Assume Alexander is a knight. No contradiction is found in their claim that Henry is a knave or Liam is a knight.

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

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

Assume Sofia is a knight. No contradiction is found in their claim that If Alexander is a knight then Olivia is a knight.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

We have exhausted all possibilities for Riley, William, Liam, Sofia, Olivia, and Henry, so let us go back and reconsider Alexander.

Assume Alexander is a knave. No contradiction is found in their false claim that Henry is a knave or Liam is a knight.

Liam cannot be a knight, because this would contradict the false claim of Alexander that Henry is a knave or Liam is a knight.

Assume Riley is a knight. No contradiction is found in their claim that If William is a knight then Olivia is a knight.

(('or', ('lying', 3), ('telling-truth', 2)), ('telling-truth', 5), ('and', ('lying', 4), ('telling-truth', 6)), ('->', ('lying', 4), ('telling-truth', 4)), ('telling-truth', 6), ('->', ('telling-truth', 1), ('telling-truth', 4)), ('->', ('telling-truth', 0), ('telling-truth', 4)))