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?

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