Knights accuse each other in lying!
Source: Kyiv City MO 2024 Round 1, Problem 10.3
January 28, 2024
combinatoricslying
Problem Statement
There are people living on the island, each of whom is either a knight, i.e. always tells the truth, or a liar, which means they always lie. Some of the inhabitants of the island know each other, and everyone has at least one acquaintance, but no more than three. Each inhabitant of the island claims that there are exactly two liars among his acquaintances. a) What is the smallest possible number of knights among the inhabitants of the island?
b) What is the largest possible number of knights among the inhabitants of the island?Proposed by Oleksii Masalitin