MathDB

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

b - a = 3

. Anna wishes to maximize

N

. What is the maximum value of

N

that she can achieve regardless of how Bob plays?

Problem Statement