Question 22
Let $n$ be a positive integer. Some cells of an $n\times n$ grid contain a two-sided mirror along a diagonal. Outside each cell on the left and right sides is a laser pointing horizontally into the grid. The lasers on each side are numbered 1 to $n$, from top to bottom. A laser is red if it exits through the top edge and green if it exits through the bottom edge. Assuming every laser exits through the top or bottom, prove that the sum of the red laser numbers is at most the sum of the green laser numbers.