Question: The population of an island consists of two and only two types of people : the knights, who invariably tell the truth and the knaves who always lie. Three of the inhabitants called X, Y and Z were standing together. A newcomer to the island asked, "Are you a knight or a knave?" X mumbled his answer rather indistinctly, so the stranger could not quite make out what he had said. The stranger than asked Y, "What did X say?" Y replied, "X said that he was a knave." Whereupon Z said, "Don't believe Y, he's lying." What are Y and Z?
Answer:
The statement made by Y is false - "X said that he was a knave".
Case 1 Case 2 Case 3 Case 4
X Knight Knight Knave Knave
Y Knight Knave Knight Knave
Analyze the above 4 cases. In all the cases statement made by Y is contradictory and therefore false. Hence, Y is Knave and Z is Knight.