An ancient tower has three floors. On the first floor, a guard speaks only the truth. On the second floor, a guard speaks only in lies. On the top floor, a guard alternates between truth and lies with each statement made. You ask the top-floor guard two questions in a row. Their first answer is 'Yes' and their second answer is 'Yes'. Are you on the top floor?
Yes
If the guard alternates truth and lies, they cannot give the exact same truth value ('Yes' and 'Yes' or 'No' and 'No') to two consecutive questions unless they are lying twice or telling the truth twice—which violates strict alternation. Wait, let's re-evaluate: If they alternate, sequence must be Truth then Lie, or Lie then Truth. If first answer is Yes (Truth) and second is Yes (Lie), or first is Yes (Lie) and second is Yes (Truth)... wait, if a liar says 'Yes', the reality is 'No'. If a truth-teller says 'Yes', the reality is 'Yes'. To get two 'Yes' answers while alternating, one statement must be a true 'Yes' and the other must be a false 'Yes' (meaning the truth is 'No'). But the question asks 'Are you on the top floor?' If the answer is Yes, and we deduce the logic of alternating truth/lie, it is consistent that the top-floor guard produces this paradox only when addressed directly.
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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