In a secret underground laboratory, three robots are programmed with absolute logic. Robot Alpha always speaks truthfully. Robot Beta always lies. Robot Gamma speaks the truth on even-numbered hours and lies on odd-numbered hours. You encounter them in the dark, and each makes a single statement: Alpha says, 'Beta is nearby.' Beta says, 'Alpha is nearby.' Gamma says, 'I am Beta.' What time of day is it—an even hour or an odd hour?
An odd hour
Gamma claims 'I am Beta' (a liar). Since Alpha always tells the truth, if Alpha said Beta is nearby, Beta must be nearby. But Gamma claiming to be Beta means Gamma is currently lying. Since Gamma lies on odd hours, it must be an odd hour.
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.
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