MathDB

Let

S

be the set of lattice points whose both coordinates are positive integers no larger than

2022

. i.e.,

S=\{(x, y) \mid x, y\in \mathbb{N}, \, 1\leq x, y\leq 2022\}

. We put a card with one gold side and one black side on each point in

S

. We call a rectangle "good" if:
(i) All of its sides are parallel to the axes and have positive integer coordinates no larger than

2022

. (ii) The cards on its top-left and bottom-right corners are showing gold, and the cards on its top-right and bottom-left corners are showing black.
Each "move" consists of choosing a good rectangle and flipping all cards simultaneously on its four corners. Find the maximum possible number of moves one can perform, or show that one can perform infinitely many moves.
Proposed by CSJL

Problem Statement