Consider a $3$ by $9$ board, where each cell is colored red or blue. First explain why there $8$ different options

for how the three cells of any column can be colored $($e$.$g$.$ the first column in the left$-$most board is

Red$/$Red$/$Blue$)$ and use this fact to prove that no matter how the colors are chosen, the board must contain

at least one rectangle or square whose four corner cells are all the same color.