You completely missed the point of my comment. The wording describes a specific instance. And additionally, the rhetorical convention implies that there is no instance of the problem for which the description doesn't hold. This part is unwritten; the reader is meant to apply it from context.
It seems like this is why there's a big disagreement about this particular write-up. Some people are applying this additional constraint, and others (yourself) aren't.
If you counter that this constraint isn't written, and therefore it shouldn't apply, I'm sorry but you're wrong. The author clearly intended it.
But the problem described a specific instance. You are reading it wrong. Right now you are just digging deeper into a hole.
If the problem actually was told as you describe then you would be right, but it isn't. It just describes a single instance, you are at the show, the host opens a door, what do you do?