Difference between number of red & blue integers ≤ 1000
Source: Itamo 2013, problem 3
May 17, 2013
absolute valuecombinatorics proposedcombinatorics
Problem Statement
Each integer is colored with one of two colors, red or blue. It is known that, for every finite set of consecutive integers, the absolute value of the difference between the number of red and blue integers in the set is at most . Prove that there exists a set of consecutive integers in which there are exactly red numbers and numbers blue.