We find ourselves in the underground land of Subterranea inhabited by two types of people: Day folk and Night folk. They have never seen the light of day. Clocks, watches, and all time pieces are forbidden. But these people have a knack for knowing whether it is day or night. Day folk always tell the truth during the day and always lie at night. Night folk always tell the truth at night and lie during the day.

1. This place has a few interesting properties. During the day, everyone claims to be the same kind of folk. What kind? At night, everyone claims to be the same kind of folk. What kind? Can a Day folk ever claim that it is night? Can a Night folk ever claim that it is day? (These properties are useful in solving the problems that follow.)

2. Suppose you visit the city and lose track of time (your watch was confiscated when you arrived). You meet one of the inhabitants and can ask him as many questions as you'd like, but only ones with yes/no answers. What is the minimum number of questions you need to ask him to find out whether it is day or night? What are the questions?

3. Suppose instead that you simply want to know whether you're talking to a Day folk or a Night folk. How can you find out?

4. I met an inhabitant that told me ``During the daylight hours I claim that it is night.'' What time of day was it?

5. Another time I met someone who said ``During the day I claim that I am a Night folk. I am really a Day folk.'' What kind was he and what time of day was it?

6. I came across two inhabitants, A and B, and here is what they said: A: At least one of us is a Day folk. B: A is a Night folk. What kind of folk are they? Is it day or night?