Failed solution to extra credit.
Be a one-boxer. Open the second box first. Take the $100. Then open the first box and take the $100. You will not open the second box after opening the first box, so this is self-consistent. Net $200. Not $250.
Failed solution to extra credit.
Be a one-boxer. Open the second box first. Take the $100. Then open the first box and take the $100. You will not open the second box after opening the first box, so this is self-consistent. Net $200. Not $250.