On a distant island, Knights always tell the truth and Knaves always lie. You meet three inhabitants: X, Y, and Z. X says, 'All three of us are Knaves.' Y says, 'Exactly one of us is a Knight.' What are X, Y, and Z?
X is a Knave, Y is a Knight, and Z is a Knave
X cannot be a Knight, because if X were a Knight, his statement would be true, meaning he is a Knave (a contradiction). Thus X is a Knave, making his statement false. Since X is a Knave, not all three are Knaves, so there is at least one Knight. If Y were a Knave, Y's statement would be false, leaving Z as the only possible Knight. But if Z is a Knight, then 'exactly one of us is a Knight' would be true, making Y's statement true (a contradiction). Therefore, Y must be a Knight, which makes Y's statement true: there is exactly one Knight (Y). Consequently, Z must be a Knave.
About this riddle
Logic riddles give you a few facts and ask what must be true. List what you know, cross out what cannot be, and see what is left.
Difficulty: Hard. More like this: Logic riddles with answers or try Einstein's Logic Grid for a different kind of puzzle.
More logic riddles
A line goes: swimmer, shell, swimmer, shell, swimmer. What comes next?
A master locksmith has three identical-looking brass keys that open three different doors: the Archive, the Vault, and the Study. Each key opens only one specific door. If the locksmith tests a key on the Archive door and it fails, what is the maximum number of additional trials needed to ensure every key is correctly matched to its door?
Two fathers and two sons go fishing together. They catch three fish total, and each person takes exactly one fish home. How is this possible without anyone sharing or stealing?
Four runners (Liam, Noah, Emma, and Olivia) finish a sprint. Liam did not come in first or last. Emma finished ahead of Noah. Olivia finished after Liam, but before Noah. Who won the race?
Four distinct positive integers—A, B, C, and D—add up to 20. A is twice as large as B. C is 1 greater than D. D is greater than A. What are the values of A, B, C, and D?
The ruler is smaller than the desk, and the desk is smaller than the student. Which one is the biggest?