There is a famous type of problem about an island inhabited by two types of people: knights and knaves. Knights always tell the truth and knaves always lie.
1. You meet a pair of islanders, Liam and Noel.
Liam says: “Both Noel and I are knaves.”
Is Liam a knight or a knave? What about Noel?
2. You meet a group of three islanders, Beyoncé, Kelly and Michelle.
Beyoncé says: “Kelly is the same type as me.”
Kelly says: “Michelle is a knave.”
Michelle says: “Beyoncé is a knave.”
What types of people are Beyoncé, Kelly and Michelle?
3. While out for a walk you get lost and come to a fork in the road. Two islanders, Sonny and Cher, are there. As islanders they know each other, and they also know which way leads back to your hotel.
Sonny says: “Cher is a knave.”
What question can you ask, and who do you ask it to, to find out whether to take the left fork or the right fork?