Problem:
Each unit square of a square grid is colored either red, green, or blue. Over all possible colorings of the grid, what is the maximum possible number of L-trominos that contain exactly one square of each color? (L-trominos are made up of three unit squares sharing a corner, as shown below.)
Solution:
Notice that in each square contained in the grid, we can form 4 L-trominoes. By the pigeonhole principle, some color appears twice among the four squares, and there are two trominoes which contain both. Therefore each square contains at most 2 L-trominoes with distinct colors. Equality is achieved by coloring a square red if is even, green if is odd and is even, and blue if is even and is odd. Since there are nine squares in our grid, the answer is 。