bw colorings of 1, 2, ... , 2021
Source: 2021 Grand Duchy of Lithuania, Mathematical Contest p2 (Baltic Way TST) https://artofproblemsolving.com/community/c1321893_grand
October 30, 2021
combinatoricsColoring
Problem Statement
Every number in the sequence is either white or black. At one step Alice can choose three numbers of the sequence and change the color of each of them (white to black and black to white) if one of those three numbers is the arithmetic mean of the other two. Alice wants to perform several steps so that at the end all the numbers in the
sequence are black. For which initial colorings of numbers can Alice achieve this?