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Day-knights and night-knights 5 (Posted on 2012-07-24) Difficulty: 2 of 5
There is a land where every inhabitant is either a day-knight or a night-knight. Day-knights tell the truth in the day and lie at night. Night-knights lie in the day and tell the truth at night.

An inhabitant shouts, "Either I'm a _____ or it is day, but not both," but you can't quite hear her over the torrential rain outside. She said either 'day-knight' or 'night-knight'.

You couldn't figure out her type, so you ask her what type she said she was in her prior statement, so she shouts again, "I said I'm a day-knight!"

You're still not sure, so you directly ask what type she is. She replies, "I'm a day-knight."

What type is she? Is it day or night? What did she say in her first statement?

No Solution Yet Submitted by Dustin    
Rating: 4.5000 (2 votes)

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Solution Finally! Comment 2 of 2 |
Finally, this got posted! All inhabitants claim to tell the truth. Suppose the inhabitant said, "Either I'm a day-knight or it is day, but not both." That statement means "Either I'm a day-knight and it is night, or I'm a night-knight and it is day." That means "I am lying," which is a paradox. Therefore, she said, "Either I'm a night-knight and it is day, but not both." She lied when she said, "I said I'm a day-knight!" Therefore, the last answer was also a lie, so she is a night-knight. Since night-knights lie in the day, it is day.
  Posted by Math Man on 2012-07-24 13:12:08
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