Island- Who is Who

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?


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.

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