MathDB

Initially, there are 2018 distinct boxes on a table. In the first stage, Yazan and Bozan, starting with Yazan, take turns make

2016

moves each, such that, in each move, the person whose turn selects a pair of boxes that is not written on the board, and writes the pair on the board.
In the second stage, Bozan enumerates the

4032

pairs with numbers from

1,2,\dots,4032

, in whichever order he wants, and puts

k

balls in each boxes written contained in the

k^{th}

pair. Is there a strategy for Bozan that guarantees that the number of balls in each box are distinct?

Problem Statement