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 to were written on a board. Vasya choose 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 colors so that the sum of numbers with each of total colors are the same.