When Brooks carves his "Brooks Was Here" in the halfway house, we see that he carves it on the left side of the beam. However, when we see Red leaving that *same* room, his "So Was Red" was right below that, on the *opposite side of the beam*!!
I don't agree. If you watch carefully you will see that Brooks carves his name on the same side of the beam as the door. The same side of the beam that is shown when we see that Red has written "So was Red".