Problem

Source: Puerto Rico 2013 TST #6

Tags: combinatorics



A $9\times9$ checkerboard is colored with 2 colors. If we choose any $3\times1$ region on the checkerboard we can paint all of the squares in that region with the color that is in the majority in that region. Show that with a finite number of these operations, we can paint the checkerboard all in the same color.