Duke Leto Atreides knows for a fact that there are not one, but two traitors within his royal household. The suspects are Lady Jessica, Dr. Wellington Yueh, Gurney Halleck and Duncan Idaho. Leto’s advisor, Thufir Hawat, will assist him in questioning the four suspects. Anyone who is a traitor will tell a lie, while anyone who is not a traitor will tell the truth.
Upon interrogation, Jessica says that she is not the traitor, while Wellington similarly says that he is not the traitor. Gurney says that Jessica or Wellington is a traitor. Finally, Duncan says that Jessica or Gurney is a traitor. (Thufir, being the logician that he is, notes that when someone says thing A is true or thing B is true, both A and B can technically be true.)
After playing back the interrogations in his mind, Thufir is ready to report the name of one of the traitors to the duke. Whose name does he report?
Since Jessica's and Wellington's statements are independent of everyone's, a chart will be created of the four possibilities for them. Gurney's and Duncan's statements, being dependent, will be appropriately labeled.
| Scenario | Jessica | Wellington | Gurney | Duncan |
|---|---|---|---|---|
| 1 | Loyal | Loyal | Traitor | Loyal |
| 2 | Loyal | Traitor | Loyal | Traitor |
| 3 | Traitor | Loyal | Loyal | Loyal |
| 4 | Traitor | Traitor | Loyal | Loyal |
Scenarios 2 and 4 have exactly two traitors, and spoiler alert, Wellington is the common traitor to both.