Each integer is colored with one of two colors, red or blue. It is known that, for every finite set A of consecutive integers, the absolute value of the difference between the number of red and blue integers in the set A is at most 1000. Prove that there exists a set of 2000 consecutive integers in which there are exactly 1000 red numbers and 1000 numbers blue. absolute valuecombinatorics proposedcombinatorics