Step 1: Preparing the relevant information: - Alan says: "Chris is a knave." - Bill says: "Alan is a knight." - Chris says: "I am the spy." Step 2: Plan: - Examine each person's statement to see if it is logically consistent. - Determine each person's role based on the statement's consistency. Step 3: Analyze the statements: - If Alan is a knight, he tells the truth, so Chris is a knave. Then Bill tells the truth, so Alan is a knight. But this would make both Alan and Bill knights, which is not possible since there is only one knight. - If Alan is a knave, he lies, which means Chris is not a knave. So, Chris must be a spy. Then Bill lies too, which means Alan isn't a knight. This is consistent with Alan being a knave. - If Alan is a spy, his statement can be true or false. If it's true, then Chris is a knave. If it's false, then Chris is a knight. However, Chris's statement contradicts both scenarios since he claims to be a spy. So, Alan can't be a spy. From this analysis, we can conclude that Alan is a knave, Bill is a knight, and Chris is a spy.