Anna and Bob, with Anna starting first, alternately color the integers of the set S={1,2,...,2022} red or blue. At their turn each one can color any uncolored number of S they wish with any color they wish. The game ends when all numbers of S get colored. Let N be the number of pairs (a,b), where a and b are elements of S, such that a, b have the same color, and bāa=3.
Anna wishes to maximize N. What is the maximum value of N that she can achieve regardless of how Bob plays? combinatoricsgameJuniorBalkanshortlist