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Turkey EGMO TST 2017 P2

Source: Turkey EGMO TST 2017 P2

June 1, 2017
TurkeyEGMOTSTcombinatoricscontest problem

Problem Statement

At the beginning there are 20172017 marbles in each of 10001000 boxes. On each move Aybike chooses a box, grabs some of the marbles from that box and delivers them one for each to the boxes she wishes. At least how many moves does Aybike have to make to have different number of marbles in each box?