Blue Face-Red Face
Imagine a world in which everyone has either a blue face or a red care. They can't tell which one they each have (and there are no mirrors or photo albums to give it away), and they don;t want to know, because they each believe that if they ever find out they have to kill themself that very same day at midnight. Everyone reasons perfectly and always tells the truth.
In this world, three roommates happen to live together, and they happen to each have a blue face. (we know this because we're listening to the story. None of these three knows this. They each only know that the other two have blue faces, and that the color of their face is unknown.) A pizza guy drops off a pizza on Monday at noon, doesn't like his tip, and tells the three roommates one thing : "At least one of you has a blue face." That's it. No one ever talks, and no face-reading of any kind needs to happen.
Question: In how many days are all three roommates dead?
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