×The key in this room is to put distance between you and the sword, which isn't too hard to do because the sword turns twice if it's perpendicular to you.

If you and the sword are both next to the exits, then when you go for the exit, the sword will too. (At the least this works if you're at the north exit and the sword is at the south; I'm not sure how the sword script works in regards to movement preferences, so it may not work the other way around.)