In each square of a garden shaped like a 2022×2022 board, there is initially a tree of height 0. A gardener and a lumberjack alternate turns playing the following game, with the gardener taking the first turn:[*] The gardener chooses a square in the garden. Each tree on that square and all the surrounding squares (of which there are at most eight) then becomes one unit taller.
[*] The lumberjack then chooses four different squares on the board. Each tree of positive height on those squares then becomes one unit shorter.We say that a tree is majestic if its height is at least 106. Determine the largest K such that the gardener can ensure there are eventually K majestic trees on the board, no matter how the lumberjack plays. combinatoricsIMO ShortlistAZE IMO TST