On the island of knights and knaves (where knights always tell the truth and knaves lie), you meet two islanders named Penny and Quinru.
Penny: Both Quinru and I are knaves!
What are Penny and Quinru?
Penny is a knave, Quinru is a knight.
If we assume that Penny is a knight, then it must be true that both Penny and Quinru are knaves. But this is a contradiction, so Penny can’t be a knight and must be a knave instead.
Since Penny is a knave, her statement “Both Quinru and I are knaves” must be a lie. If Quinru was a knave, this statement would not be a lie, so Quinru must be a knight instead.