Island of knights and liars
Source: 239 2019 J1
July 31, 2020
combinatorics
Problem Statement
On the island of knights and liars, a tennis tournament was held, in which people participated in. Each two of them played exactly time with the other one. After the tournament, each of the participants declared: “I have beaten as many knights as liars,” while all the knights told the truth, and all the liars lied. What is the largest number of knights that could participate in the tournament?