MathDB

This year, some contestants at the Memorial Contest ABC are friends with each other (friendship is always mutual). For each contestant

X

, let

t(X)

be the total score that this contestant achieved in previous years before this contest. It is known that the following statements are true:

1)

For any two friends

X'

and

X''

, we have

t(X') \neq t(X''),

2)

For every contestant

X

, the set

\{ t(Y) : Y \text{ is a friend of } X \}

consists of consecutive integers. The organizers want to distribute the contestants into contest halls in such a way that no two friends are in the same hall. What is the minimal number of halls they need?

Problem Statement