1. Logical Puzzles Truth and Lies

2. The Island of Rilas On the island of Rilas there are just two types of people: knights and knaves Knights always tell the truth Knaves always tell lies You cannot tell them apart just by their appearances.

3. Rilas 1 You meet two people, A and B, on Rilas, each of whom is either a knight or a knave. B says “At least one of us is a knave” What are A and B? Explain why.

4. Rilas 2 On another occasion you meet two more inhabitants, C and D, on Rilas. C says “I am a knave but D isn’t.” What are C and D? Explain why.

5. Rilas 3 This time you meet just one inhabitant of Rilas who is lazily lying in the sun. You can’t remember whether he is Mike or Mark, so you ask him his name. He answers “Mark.” Who is he?

6. Alice When Alice was in the Forest of Forgetfulness, she met the identical twins, Tweedledee and Tweedledum. One of these lies on Mondays, Tuesdays and Wednesdays and tells the truth the other four days. The other one lies on Thursdays, Fridays and Saturdays and tells the truth on the other four days. (Alice doesn’t know who does which.)

7. Tweedlewho? One day Alice met the brothers and they said; First one: “I’m Tweedledum.” Second One: “I’m Tweedledee.” Which one was really Tweedledee and which one was really Tweedledum? What day of the week was it?

8. Alice 2 On another occasion, Alice asked one of the brothers “Do you lie on Sundays?” He replied “Yes.” She then asked the other brother the same question. What did he answer?

9. The Truth Revealed You may be surprised to learn that in trying to solve the above puzzles, you were actually doing mathematics! The ability to analyse and solve such problems is developed (and taken much further) in courses on propositional logic and related topics.

10. Answers Rilas 1: B is a knight, A is a knave. Rilas 2: Both C and D are knaves. Rilas 3: He is Mike; after all, he was lazily lying in the sun. Tweedlewho: First is Tweedledum, second is Tweedledee. It is Sunday. Alice 2: He answered “No.”