Question 2
A grid of cells is tiled with dominoes such that every cell is covered by exactly one domino. A subset $S$ of dominoes is chosen. Is it true that at least one of the following $2$ statements is false?
(1) There are $2022$ more horizontal dominoes than vertical dominoes in $S$.
(2) The cells covered by the dominoes in $S$ can be tiled completely and exactly by the tetrominoes shown below (including rotations & reflections):
(1) There are $2022$ more horizontal dominoes than vertical dominoes in $S$.
(2) The cells covered by the dominoes in $S$ can be tiled completely and exactly by the tetrominoes shown below (including rotations & reflections):