Knight and Knave Problems

Work on your own or with a partner to solve these knight and knave problems. Remember: Knaves always lie and knights always tell the truth. Show Your Work!

Once you are finished, choose one of your solutions and expand it to meet the criteria in the rubric. Showing all cases. (ie include and all relevant information and conclusions to the original problem)

1. You’re on the island of knights and knaves. You meet two inhabitants: Zoey and Mel. Zoey tells you that Mel is a knave. Mel says, `Neither Zoey nor I are knaves.'

So who is a knight and who is a knave?

Case 1: Zoey=Knave, Mel=Knight

Zoey says “Mel is Nave”, OK.

Mel says “Neither Zoey nor I are knaves” Which a false statement  MEL a Knight, spoke False CONTRADICTION

Case 2: Zoey=Knight, Mel=Knave

Zoey says “Mel is a Knave”, OK (Mel=knave)

Mel says “Neither Zoey nor I are knaves” which is a false statement. OK (Since Mel, a knave, always lies, so Zoey is a Knight)

Thus Zoey=Knight and Mel=Knave.

2. You’re on the island of knights and knaves. You meet two inhabitants: Peggy and Zippy. Peggy tells you that 'of Zippy and I, exactly one is a knight'. Zippy tells you that only a knave would say that Peggy is a knave.

3. You’re on the island of knights and knaves. You meet two inhabitants: Marge and Zoey. Marge says, `Zoey and I are both knights or both knaves.' Zoey claims, `Marge and I are the same.'

4. You’re on the island of knights and knaves. You meet two inhabitants: Zed and Alice. Zed tells you, `Alice could say that I am a knight.' Alice claims, `It's not the case that Zed is a knave.'

5. You meet three inhabitants: Zoey, Homer and Carl. Zoey says, `Carl could claim that I am a knight.' Homer says that only a knave would say that Zoey is a knave. Carl claims, `Zoey could say that I am a knave.'