In a meeting of 4042 people, there are 2021 couples, each consisting of two people. Suppose that A and B, in the meeting, are friends when they know each other. For a positive integer n, each people chooses an integer from ān to n so that the following conditions hold. (Two or more people may choose the same number). [*] Two or less people chose 0, and if exactly two people chose 0, they are coupled.
[*] Two people are either coupled or don't know each other if they chose the same number.
[*] Two people are either coupled or know each other if they chose two numbers that sum to 0. Determine the least possible value of n for which such number selecting is always possible. combinatoricsgraph theory