Sean's math problems - #1 (The Village of Truths and Lies)

There were 2019 folks living in the Mathy village. Every one of them was either a noble, who always tells the truth, or a liar, who always lies. No exceptions.

AT LEAST 1,000 people in the village attended a party. They were asked to sit down in a huge circular table. Then, the manager asked every person to describe the two people beside them. Shockingly, all of the people spoke: "One of the people beside me is a noble, and the other is a liar". However, the manager, being clever, knew some people were lying.

Problems:
1) What is the MAXIMUM number of nobles there can be at the village (not the party!)
2) What is the MAXIMUM number of liars there can be at the village?
3) What is the MAXIMUM number of nobles there can be at the party (not the village!)
4) What is the MAXIMUM number of liars there can be at the party?

Difficult Questions:
5) Answer all the questions above, counting the number of people as 4019 instead of 2019 and the "party minimum" as 2000 instead of 1000.
6) Do the same as Question #5, but counting the number of people as 2x + 19 instead of 4019 and the "party minimum" as x (the variables are variables, do not substitute a random value).
7) Give the relationship between the number of nobles and liars at the party.

Life Challenges (choose 1):
8) Make a coding program for this problem. Let the user enter the number of people in the village and the "party minimum". You should answer Questions #1, #2, #3, #4.
9) Design another math problem similar to this one. It should include: Nobles and Liars
10) Design three math problems connecting to this one. Example: What is the probability that the manager will choose a noble when he is blindfolded and asked to choose anyone at the party?

Enjoy!

Sean's Problems
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