MathDB

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

-n

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.

Problem Statement