If it were only that easy! Unfortunately, the door will close after the first person has answered and it will use any amount of force it can to close if someone tries to piggyback on that answer. (It won't close so limbs will get broken/or worse in the doorjambs. Just hard enough to give a warning.)

And if someone tries to open a door from the inside, the door will think that person is trying to leave and will engage that person in a game instead!

And, in case this question pops up, if anyone tries to use a window or breaks through a wall to avoid using a door, they will still be forced to play the games because that is still entering and exiting the building in some way. Doors just happen to be the easiest way of going in and coming out. It's basically a damned if you do, damned if you don't sort of situation.

Hope that helps!