I agree that this additional information is necessary to understand the problem. I've seen that show maybe twice in my lifetime, both times when I was a little kid. I did not know that Monty never opens the door with the prize behind it. Not one time in the history of the show did he ever open the prize door. Knowing that is additional information, and can be used to figure out the problem. But you need to watch the show more than twice to know that.
