We find ourselves in the underground land of Subterranea inhabited by two types
ID: 3703360 • Letter: W
Question
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?
Explanation / Answer
1) During the day, everyone claims to be the day folk since day folk are saying the truth and night folk are lying.
At night, everyone claims to be night folk since night folk are saying the truth and day folk are lying.
Day folk can't claim that it is night as they will say no for it being night during the day and no even at night.
Vice versa for night folk and they can never claim it is day.
2) Is it day? Yes:- df and saying truth OR df and lying cause its night - So if yes then its day folk
No:- nf and saying truth cause its night OR nf and lying cause its day - So if no then its night folk
If answer to previous question is yes:
Are you df? Yes:- saying the truth and it is day as day folk says truth
No:- it is night and day folk are lying
else:
Are you df? Yes:- it is day and night folk are lying
No:- it is night and night folk are saying the truth
Hence 2 questions required
3) Is it day? Yes:- df and saying truth OR df and lying cause its night - So if yes then its day folk
No:- nf and saying truth cause its night OR nf and lying cause its day - So if no then its night folk
4) It is night time as nightfolk will lie in the daylight time
5) A night folk talking during day time. This is because he is lying about it being night when it is actually day. This makes him a night folk. He is lying right now about being day folk hence it is day time.
6) Both cannot be saying the truth because: if A is saying the truth then B is a day folk because B said A is night folk. They cannot say the truth together as one of them will lie whether it is day or night.
Assume A is saying the truth, B is lying. Then A is day folk and B is Day folk or night folk.
So here the answer will be A is day folk and B is night folk and it is day time since B is lying.
Assume A is lying and B is saying the truth. Then A is night folk and B is also night folk. This is ambiguous as either both of them should lie or both of them should tell the truth.
The answer is A is day folk and B is night folk and it is day time
Hope you find the question as entertaining as I did. Do leave an upvote to help other students with similar doubts.
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