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St. Petersburg MO 2017 Grade 10 P4

Source: St. Petersburg MO 2017 Grade 10 P4

May 3, 2018
number theorycombinatorics

Problem Statement

The numbers from 11 to 200022000^2 were written on a board. Vasya choose 20002000 of them whose sum of them equal to two thousandth of the sum of all numbers. Proof that his friend, Petya, will be able to color each of the remaining numbers by one of other 19991999 colors so that the sum of numbers with each of total 20002000 colors are the same.